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Math Mama Writes...
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Saturday, March 21, 2015
Sam Shah posted his list here. I loved his list, but wanted to rewrite it a bit for myself. (Also, Sam finds it more effective to review the algebra ahead of time, while I think it's more effective to review once we see the need in our exploration of calculus.) I am posting this now, so it's available as an answer to this question on math educators stack exchange.
I teach my calculus course in an order that I think will help students learn. I have four units:
Unit 1 includes history, graphing functions, slopes of tangent lines by approximation, algebraically finding the derivative using the limit (which we do not carefully define yet), seeing the similarities between velocity, rate of change, and slope, average versus instantaneous velocity, derivative from a graph, (estimated) derivative from a table of values.
Unit 4 includes integration (finding area under the curve), anti-derivatives, fundamental theorem of calculus, and substitution method. If there is time we include volumes of rotation (which I think is a perfect ending for the course).
Algebra Skills needed for Unit 1
Algebra
Determine the equation of a line given two points, or a point and a slope, or a graph of a line,
Find the average rate of change over an interval given a function or its graph,
Clearly express what is happening to an object given a position versus time graph,
Evaluate f(x+h) for any given function f(x),
Rationalize the numerator (to find the derivative of the square root function) ,
Friday, February 6, 2015
Before I share all the delicious goodies I've stumbled on, news of the book is in order:
Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers is just about done with page layout - and it's looking so beautiful! I am sending in the last proofreading corrections today, and will do the last fixes to page number mentions as soon as I've seen the final copy. Then it's off to the printers, then all the copies get shipped to the publisher, and finally get sent to the hundreds of people who ordered copies during the crowd-funding last summer. If you're eager for your own copy and weren't around for the crowd-funding, you can order now. (You know I'd be tickled if we sell out our first printing quickly!)
Christopher Danielson has made a shapes book, Which One Doesn't Belong?, that will tickle your logic funny bone. At first glance it's like the other books for very young kids, but this one will be fun for any age. This might be my new go-to present for 2-year-olds.
A video of Donald Knuth (author of the lovely little book, Surreal Numbers), talking about learning from his mistakes.
Kate Nowak pulls together what looks like a great (5-part) lesson on triangles - what you can figure out from what you are given (different combinations of sides and angles). I wonder if I can do anything with this in just one day with my pre-calc class... Shireen's lesson for inverse trig functions might be helpful too...
Numberplay appears in the New York Times (at least online) every Monday. Last month Daniel Finkel (of Math for Love) provided this new take on a favorite puzzle type:
There are two bags
of coins. One contains genuine silver dollars, and the other contains a
mix of two types of counterfeits, the first of which is too heavy by
0.01 ounce, and the second of which is too light by 0.01 ounce.
Using a balance,
you weigh the two bags and find that they both weigh exactly the same
amount. How many additional weighings will it take to determine which is
the bag of real silver dollars if there are 32 coins in each bag?
Two Truths and a Lie: Get calculus students to make up stories from their lives, using the idea of rate of change, and matching given graphs. Brilliant, Shireen!
I like this for a first day activity! (I just figured out how to link to this on my google calendar to remember to look at it in August!) Getting the students involved in discussing what education should be, and what productive failure might look like.
About half a year ago, I joined in the crowd-funding for the math game Prime Climb. It arrived in early December (or was it in Novemeber?) and we played it at my holiday party. People definitely enjoyed it. Now I've heard about another game being crowd-funded. Three Sticks is a geometric game, developed in India. It looks fun. For a $35 contribution, you get the full set (and escape the very high shipping charges).
The math in the solutions may be too hard to follow, but this problem is charmingly simple: Your hallway is one meter wide, and turns a corner. What is the greatest base area of an object that can be carried flat through the corner?
Every textbook I've seen that includes conic sections shows the conic, and then shows another definition, and never connects the two. This blog post makes some of the necessary connections. (Anything on Dandelin's spheres catches my eye.)
Tricky puzzle. (Do you like that sort of thing?) The 7 at the bottom is NOT a typo.
Estimation questions are a great way to build number sense. And Andrew Stadel has a twitter feed just for that. This week included a few questions about these Lego Lions: How many legos? How long to build? How many legos tall?
A Question
I'm teaching Linear Algebra, and I find it a bit odd that linear transformations by definition don't include lines like y = mx+b (with b not 0). A student asked the significance of the word linear (she thought it was a silly question, and I assured her it definitely was not silly), so I started searching online. I noticed this site, which defines a linear transformation for statistics - differently from the linear algebra definition. It looks like the two definitions contradict one another. Any ideas about how standard this statistics definition is, or pointers to discussions of this difference in definition?
[Oops! I lost a few weeks on the #YourEduStory challenge. Maybe I can get back to it. My pre-calc class is going better than usual. My calculus students loved having all those handouts in a coursepack. And I love thinking about all the connections in linear algebra. This week's topic: Define "learning" in 100 words or less.]
There were probably more on the list at the time. These are the ones I still remember. (And I'm losing the names. Yikes!) When I made the list, I noticed something interesting. There were about equal numbers of men and women on the list, but they were very different sorts of teachers. The men were good performers, and the women were good facilitators. A few did both well (the poetry guy and Gisela). I wanted to do both well. I thought about taking some drama courses to improve my performance skills. I did that while teaching in Muskegon, and realized I needed a different sort of course. Performing in a play is a lot different than performing as a teacher. Improv might be good for me. Hmm... I also learned a lot about facilitation over the years.
I know now that the best performers make students happy to come to class, but that's not enough. We need to get students actively engaging with the material for them to learn much. (Mr. West did that in lab, even though I remember his great lectures.) If you don't know the research done by Eric Mazur on this, check it out. (This video might include the best parts of the hour-long video I watched a few years ago.)
How is my approach different than theirs? I think it's only in the combination that I'm different. I try to pull in all my students (like my Shakespeare and history of feminism profs did). I ask them multiple times each class to show me with thumbs up, down, or sideways how well they understand what I've just explained. I call on students randomly. (Because teachers tend to call on male students more.) I come in as excited as my bouncy philosophy prof. I suggest my students try strange experiments, like my poetry prof did (he had us write at a cemetery and a mall). I try to be as accepting and as challenging as my best teachers were.
Nueva School, in Hillsborough, south of San Francisco, puts on a math night three times a year, with multiple math circles, along with a puzzle and game room. Nancy Blachman invited me to lead two math circles last night, one for 2nd and 3rd graders and another for 4th and 5th graders.
2nd and 3rd grade Circle
This circle met for just 30 minutes. I know that the Collatz conjecture is dependably fun for kids this age, so that was our main activity. I asked the kids what they thought mathematicians do, and got a reasonable answer, but saw that there wouldn't be time for useful discussion. So I said a bit about math being like a game for mathematicians, and how fun it was to come up with a new puzzle.
In 1937 (I just said it was about a hundred years ago), Lothar Collatz came up with this puzzle/game:
Pick a number.
If it's even, cut it in half. Write your new number.
If it's odd, triple it and add one. Write your new number.
(We drew an arrow from each number to the next.)
Repeat until you get back to a number you've already written.
Collatz conjectured (guessed) that the sequence would end up at 1, no mater what number you started with, but he couldn't prove his conjecture. Mathematicians have tried to prove this for over 75 years, and it is still an open question. (It is very likely to be true. Using computers, people have tested every number up to and past 5 quintillion.)
As I expected, the kids loved it. At the end, I showed them a "mind reading" trick.
Pick a number from 1 to 31. Don't say it, just keep it in your brain.
(I pretend I'm sucking their thoughts over to my own head.)
Now show me which of these five cards it's on.
(I barely glance at the cards.)
Your number is ___.
After we did it a few times, I had the parents cover their ears and told the kids how it worked. I had the five cards on the board, and half-size index cards for them to make their own cards. They loved it. 4th and 5th grade Circle
This circle met for an hour and a half. My plan was to analyze Spot It with them. (I've written at least 4 posts on using Spot It for math circles. Search on Spot It to find them.) We started out playing the game for about 15 minutes, which they all enjoyed.
The problem was, half of them had done this last year in their math class at Nueva! Luckily, one girl had come early and I had shown her the number trick. I asked her if she wanted to teach it to the others. She did.
I split the group in two, and she showed her group the number trick, while my group started thinking about the game. I had one boy who answered every question very quickly, and asking him to slow down didn't help. So, after we had figured out that there would be 57 different pictures, I got out the half-size index cards and suggested they make their own decks, with 4 pictures per card. Or, if they weren't into drawing pictures, 4 numbers per card. They worked hard at trying to make a deck where each card matched every other card on exactly one picture. Towards the end, they wanted to play with the number trick too.
About halfway through the girl who led the other group came over and said, "The number trick is done." So I joined their group for a bit, and asked, "Why does it work?" A few parents were there, thinking about it with their kids. I should have asked them to work with all the kids (about 6 of them), but didn't think to say it. A few kids wandered away, to the puzzle room, no doubt.
The kids who stayed worked hard on the problems and had fun. I had a great time.
Friday, January 16, 2015
8am
Calculus. Wednesday: Circle area. Archimedes. Zeno. Started Boelkins' Velocity of a Ball activity. On Thursday, we got through most of the Velocity of a Ball activity. The students did not recognize that (s(b) - s(a)) / (b-a) is a slope. So We are working through the parts they need to review. I am goign slower than in other semesters. I hope I'm not going too slowly.
10am
Linear Algebra. Wednesday: Discussed differences between Echelon Form and Reduced Echelon Form. I started with: a matrix in Echelon Form, and got them to tell me the values of the variables. I explained that this way is quicker for computers. We talked about number of possible solutions, and drew examples in 2D and 3D. Quiz tomorrow. (Quiz made and copied.)
Thursday: Most of them aced the quiz. The ones who didn't will be in my office to retake. We finished 1.2. (I hate referring to book sections, instead of math topics. Basically, we are working on row reducing matrices. We've started to think about parametric representation of solutions, where there are free variables.)
11am
Pre-Calc. Wednesday: We practiced an arithmetic sequence (find the nth term) and a geometric sequence. We looked at a problem that used a recursive definition for a n. I mentioned the Fibonacci sequence, but didn't do much with it. Quiz tomorrow.
Thursday: Only a few aced the quiz. It was harder than what we had done in class. I'll give a retake on Tuesday in class. We reviewed lines. I walked them through my proof that perpendicular lines have slopes that are negative reciprocals. (It's different from the text's proof.) In the process, I also walked them through the proof that the angles in a triangle add up to 180 degrees. I love how the result suddenly pops out of the picture. I asked them to show me with their thumbs (up, down, sideways) how cool it was. They all gave it a thumbs up and I said they were being too nice. The bigger proof (for perpendiculars) gets an 80% coolness rating from me.
1pm
Calc III. (I am sitting in on this class.) Wednesday: Ed showed us how to connect the tops first and use dotted lines for hidden lines. I noticed that it felt like we were seeing the xz-plane from the back. Thursday: Over an hour of lecture. Ed is a good lecturer, but that's too long for me. I fell asleep. I woke up for the quiz. It included drawing 3D surfaces. I understand all of this, but how well did I draw? I'm not satisfied yet.
Tuesday, January 13, 2015
8am
Calculus. I talked about what we had done yesterday with finding a line tangent to y=x2 at x=3. In algebra, we find the slope when we are given two points. We know one point, (3,9), and there is no other point that we know. [Last semester, at least one person used the y-intercept of the tangent line they had graphed as their second point. I liked that, but forgot to mention it today.]
I asked them to give their definitions of the word tangent.
First student definition of tangent: A line that touches the curve in one place only.
Sue's counter-example: I drew y=x3 and drew at tangent line at about x=1. They agreed that I had drawn a tangent. Then I extended the curve and the line. They cross at x = -2. I suggested that we could add the word nearby, and maybe this would work.
Second student definition of tangent: A line that touches the curve but doesn't cross it.
Sue's counter-example: I asked them what the tangent to y=x3 at x=0 would look like. They told me it would be horizontal. I drew it in. Hmm. (I told them that later we'll talk about concavity, and showed it with my hand curved. I said that I think the only time the tangent line crosses the curve is when it's tangent at an inflection point. Is that true? I should try to prove it.)
Third student definition of tangent: A line that determines the direction of the curve.
I think this one is about as good as we can get at this point, although it's hard to turn it into something precise. I talked about thinking of the curve as a road, and your point being a car driving along the curve. Its headlights make half the tangent line, and its taillights make the other half.
Talked just a bit about history of calculus, and gravity. Got some volunteers who will drop a heavy and a light object, and see what happens.
Then we started our circle activity. I had a picture of a circle of radius 10cm on the back of the handout. I asked for the radius, a rough estimate of the area, and a more careful estimate of the area. (I asked them to pretend they knew no formulas. Next I had them fold a round coffee filters in half through the middle over and over, then cut it into wedges, and play with them. Tomorrow we'll do the area formula from that. Today I gave the definition of pi (C/D), and talked about how C=2*pi*r comes easily from this definition. I got a few volunteers who will measure around a circle and across it, using string, and will bring in their string tomorrow. Area is different...
10am
Linear Algebra. I used a desk corner as the origin, drew the x and y axes with my finger along its edges, and the z axis coming up from the corner. I asked them to figure out (in groups of four) what the equation x+y+z=1 would look like. I heard someone say circle. It is not at all obvious to most of them yet that it will be a plane. But we got there.
Was that before or after we worked on the definition of a linear equation? Yesterday I had asked for their definitions from their heads. I got four volunteers today (yay!) to give me their definitions to put on the board. They were all different, and none matched the official definition. So, after I went over the official definition from our textbook, I asked them to use that to prove or disprove each of the statements given by students. I think this will help them with proofs and with what a linear equation is.
Next I continued with the problem we had done, algebra style (no matrix), yesterday. I talked about computers, and representing it with just the coefficients, and wrote the matrix. I showed them the matrix that would represent the solution, and said our steps will be similar to those we used yesterday, but our order will be different. We did our same problem matrix-style, and I identified the three elementary row operations as we used them. (We never used the swap rows operation, but I talked about when it would be needed, and how you'd never do that with the algebra-style method.)
I finished up with one book problem.
11am
Pre-Calc. Stamped their homework. Had them share with their group the list of 5 problems they couldn't do. Had them each pick a problem from their partner's list, that they would later explain to their partner. Some people working hard; others feeling unsure what to do. (Everyone willing to participate.)
Showed them y=mx+b on desmos, but got caught up in another problem. We'll come back to this tomorrow.
They worked on finding an, with the hint that it might be good to find a100 first, for the sequence 12, 17, 22, 27. (I got starting value and jump size from students. Good it was five - some people struggle with arithmetic.) We worked on that a while, and then did a problem from 12.1 (Stewart) that turned out to be geometric. It was good to see the similarities.
Monday, January 12, 2015
So I have this health problem. It's seems to be a GI problem, but no one has managed to diagnose it. It used to happen about once a year, for a week. Now it happens more often. Always before my tummy hurts, I notice that my back is tight. I've had lots of ultrasound scans - no gall stones. And a GI scope - no ulcer. It is not clear what's happening. The chiropractor seems to help, but it still lasts a week or so, just milder. The first few times, I was in the emergency room, in agony. This time, I made it through my first day of classes, able to ignore it, and am distracting myself by writing a blog post. Digestive enzymes may be helping. Stress is a factor: the last time it happened was the beginning of fall semester. The time before was when we were interviewing candidates for a position in our department. I think it's time to figure out how to notice stress, and not internalize it this way. Meditation? Yoga? Definitely, I need to get more active.
I was very pleased that I was well enough to ignore my body while I was teaching. I hate not being chipper on the first day. I was probably less prepared, and less organized in some ways. But that meant that I did new things that I liked.
8am
Calc I. I had 42 students. I talked about math not being as much about memorizing as many students think. We listed some of the things that do need to be memorized, and then I talked about which things might not belong on the list. Then we did the tangent line activity I always start with. Time was a little tight, and I didn't finish attendance. (I'll have to attend to that tomorrow.) ;^) Tomorrow we'll look at area of a circle, think a little more about today's activity, and start on the first activity from the Boelkins text. I've put together a coursepack with all the handouts for this first unit, so students won't feel so scattered. (We do very little from our Anton textbook in this first unit, and then use the textbook much more for the rest of the course.)
Even though the way I started wasn't anything exciting, I feel excited just because I did something new with the students. It feels like today was a good start.
10am
Linear Algebra. I used the same warmup activity from the last time I taught the course. I don't need to do anything new to be excited about this course. What's new it that I'll be grading their homework (with help from an assistant), instead of just stamping it.
In one of my classes, I talked about neuron development during learning. But I don't remember which class. I am nervous about having two classes in a row with no break between. I hope I can keep track of what I've done and want to do next.
11am
Pre-Calc. I only had 15 students. There is some chance the college will cancel the course. I think I have a great bunch of students, so I am already feeling very invested in doing this course. I have no control over whether it gets canceled, though...
This is the class I wanted to change up some. Our first day hadn't been very memorable in the past few semesters. I couldn't think of anything better than asking them to add up the numbers 1 to 100 (without adding one by one). They worked in groups of four. They looked very stuck for a long time, but seemed willing to keep at it. One student knew a formula, and had the answer written. I asked her to hide that, and try to figure it out without the formula. In another group, I heard something about adding up pairs. When I finally called them all together, I asked for volunteers and got none, and then asked M to explain. They had started out by adding up the numbers one to ten. (I had suggested that might give them some ideas.) They did the sum one by one at first, so they knew what number it would be. When they noticed 1+10 = 11, and the total was 55, they looked for a reason to multiply by 5. Their reason didn't make much sense to me. (There are five ways to add two numbers to get 10, one of which is 5+5.) So I agreed that multiplying by 5 made sense, and asked if we could think again about that 1+10 pairing. I had to nudge more than I would have with a math circle, but they still did most of the work. They found the sum of one to a hundred in their groups. And then we came up with a 'formula' for summing the numbers one to n. I liked how it went.
I think this class may take off this semester...
1pm
I'm sitting in on Calc III. I loved Ed Cruz's talk, about how bad a student he was at first, and how he evolved to become a better student, and then a teacher. No math yet.
Tomorrow my 8am and 11am classes meet for an hour and a half. From 8am to 12:30pm, I'll only have half an hour outside the classroom. Yikes! But being done so close to noon sounded too great to pass up, so I didn't try to change this strange schedule. I see my chiropractor tomorrow afternoon.
Sunday, January 11, 2015
I decided to join the Share #YourEduStory Blogging Challenge 2015 this morning. Last month was the first month I ever skipped completely on this blog, since I started in 2009, and last year I posted less than any other. So this is a good time to push myself a little.
One Word
The group that set this up (folks from edcamps) has created a list of topics for those who need them. The first week's topic (last week) was:
What is your "one word" that will inspire you in your classroom or school in 2015?
I'll choose 'Connect'. I want to connect with my students in the classroom and out. I want to connect with my colleagues as I work on creating a new course. I want to connect with friends more - I need more of that in my life.
I'd like to get photos of my classroom up, and videos of lessons. But I won't make a commitment to that. Just one new thing at a time...
A Better World
Week Two's topic question:
Inspired by MLK: How will you make the world a better place?
I hope my book, Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, will help people to enjoy math, fear it less, and overcome the hurdles math requirements place in their way. It's coming out within the next month or two.
Join Us
I've been following hundreds of math teacher blogs, and, though I haven't pared down my list, I'm seeing very little writing from math teachers these days. Will you join the Share #YourEduStory Blogging Challenge 2015? Each week you write a post and tweet it, and read a post and comment. That's it.
Tuesday, January 6, 2015
Linda taught me this game when I was visiting her in Muskegon. She just called it "the five-letter word game." I thought it needed a name, and Think is as good as any.
Preparation
Each person thinks of a five-letter word with all five letters different, and writes it down in a hidden spot.
Goal
Guess your opponent's word.
Play
The players take turns offering a five-letter word (all letters different), as guesses, and as clue-gathering. If the guess is not the right word, then the opponent tells how many letters are right.
The game is similar to mastermind, but there's no information about where the letters go. (So you could get all five letters right, and still have the wrong word!) It's not a math game, but it is a logic game, and I think logic and math are twins
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Calculus is the basis of all advanced science and math. But it can be very intimidating, especially if you're learning it for the first time! If finding derivatives or understanding integrals has you stumped, this book can guide you through it. This indispensable resource offers hundreds of practice exercises and covers all the key concepts of calculus,... more...
While Volume I (by W.A.J. Luxemburg and A.C. Zaanen, NHML Volume 1, 1971) is devoted to the algebraic aspects of the theory, this volume emphasizes the analytical theory of Riesz spaces and operators between these spaces. Though the numbering of chapters continues on from the first volume, this does not imply that everything covered in Volume I is
Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this... more...
This book contains survey papers based on the lectures presented at the 3rd International Winter School "Modern Problems of Mathematics and Mechanics" held in January 2010 at the Belarusian State University, Minsk. These lectures are devoted to different problems of modern analysis and its applications. An extended presentation of modern... more...
The Manga Guide to Calculus teaches calculus in an original and refreshing way, by combining Japanese-style Manga cartoons with serious content. This is real calculus combined with real Manga. The book's story revolves around heroine, Noriko. Noriko takes a job with a local newspaper and quickly befriends the geeky Kakeru, a math whiz who wants... more...
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Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
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I read this book for the first time when I was in college. It addresses many fundamental and practical questions with tremendous clarity. It particularly stands out in my mind because of its simple and compelling answers to three questions: Why do we need models of reality? What are the constraints on rigorous modelling (trade-offs between precision vs. generality vs.simplicity)? How to evaluate a mathematical model?
If you are curious about mathematical modelling and do not know where to start this book is surely for you. This little, old and inexpensive volume will effectively introduce you to the basics of mathematical modelling. It is true that is dated now, as it was first published in 1978, but I will always prefer and recommend it over other extremely expensive books out in the market.
There are so many expensive books on this subject, this gives you a concise introduction to the field of mathematical modeling that is informative and interesting. The author doesn't tackle the mathematical models of any one field. Instead he tries to illustrate the process of designing and analyzing mathematical models by showing examples from a variety of disciplines. There are plenty of examples in this book, but don't expect recipes, because there really is no such thing as a mathematical modeling recipe. There are multiple approaches and thus multiple answers to just about every modeling problem. What the author does is make you comfortable with these facts and give you some questions to ask when approaching any modeling problem. Anybody with an understanding of calculus and ordinary differential equations and maybe a dash of probability theory should feel at home with this book. Highly recommended, especially before tackling some of the more expensive and specialized books on this subject.
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Subject: Mathematics Title: Using a Calculator for Finding the Equation of a FunctionAdd Bookmark Description: To determine the function of best fit for a set of data, students should recognize which category of function bests fit the data and know how to use technology to obtain a function. Students will use linear regression to find the best function. This lesson teaches these skills and prepares students for the subsequent lesson(s), in which they will collect their own data. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.
Mathematics of the 19th century : geometry, analytic function theory
Presents a study of the history of mathematics in the nineteenth century. This book describes the development of geometry. It discusses analytic function theory, and shows how the work of mathematicians like Cauchy, Riemann and Weierstrass led to fresh ways of understanding functions.Read more...
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All About Circuits is a website that ?provides a series of online textbooks covering electricity and electronics.? Written by Tony R. Kuphaldt, the textbooks available here are wonderful resources for students, tea...
This site includes an encyclopedic collection of descriptions of electronics circuitry and principles to introduce or reacquaint readers with a wide variety of concepts. In addition to passive and active components,...
In this lesson from Math Machines, students will learn how automated systems transform input data into output actions. The class will program a graphing calculator, collect input data and observe output actions....
Although it is labeled as an introduction to PC game programming, the tutorials given on Atrevida additionally cover many aspects of mathematics and general computer science. A modest background in the C language is...
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Goldsteins BriefCalculus and Its Applications, Twelfth Edition is a comprehensive print and online program for readers interested in business, economics, life science, or social sciences. Without sacrificing mathematical integrity, the book clearly presents the concepts with a large quantity of exceptional, in-depth exercises. The authors' proven formulapairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of exerciseshas proven to be tremendously successful with both students and instructors. The textbook is supported by a wide array of supplements as well as MyMathLab® and MathXL®, the most widely adopted and acclaimed online homework and assessment system on the market.
Functions; The Derivative; Applications of the Derivative; Techniques of Differentiation; Logarithm Functions; Applications of the Exponential and Natural Logarithm Functions; The Definite Integral; Functions of Several Variables; The Trigonometric Functions; Techniques of Integration
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible.
Student Study Guide for Linear Algebra and Its Applications An integral part of this text, the Study Guide incorporates detailed solutions to every third odd-numbered exercise, as well as solutions to every odd-numbered writing exercise for which the main text only provides a hint. Full description
More editions of Student Study Guide for Linear Algebra and Its Applications:
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Algebra and Trigonometry-Stud. Solution Manual - 2nd edition a
lso included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry. also included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry. ...show less
0470433760
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Any way you slice it, fractions are foundational
Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler describes powerful diagnostic methods for error analysis that pinpoint specific student misconceptions and supplies specific intervention strategies and activities... more...
Based in Melbourne, Bill Handly is recognized as an authority of mathematics and study methods in Australia and overseas. His methods of teaching maths, learning and thinking strategies have achieved astonishing results in schools worldwide. more...
This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equationsaredeveloped in this text.A synopsis of the geometry of Banach spaces, aspects... more...
In North America, the most prestigious competition in mathematics at the undergraduate level is the William Lowell Putnam Mathematical Competition. This volume is a handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the Putnam and other undergraduate mathematical competitions. Indeed, it will... more...
Any child can overcome the disadvantages of mediocre math teaching in school and parental math anxiety at home. Math Power offers easy-to-follow and concrete strategies for teaching math concepts. These lively techniques ? including games, questions, conversations, and specific math activities ? are suitable for children from preschool to age 10....
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A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg. Exercises are included at the end of each chapter. "The topics are so well motivated, the exposition so lucid and delightful, that the book's appeal should be virtually universal . . . Every library should have several copies" — Choice. 1976 edition.
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Mr. Trudeau has done a fabulous job of introducing graph theory in a way which is understandable and intellectually provocative. He mentions that some of the problems are easy, and that some have been unsolved. In both cases, they both are fully illustrative of the subject matter. If you want to begin exploring graph theory, this book is for you!
This book make you want to know more about graph theory. The concepts are first intuitively explained and then formally stated. The numerous examples are completely treated and then easy to follow. R. Trudeau devoted a large part of the book to the puzzling problems of planar graphs and coloring and explains them in a very pleasant manner. As a result, these problems almost appear as trivial (which of course is not the case). The main criticism I would make is the following. This book is a corrected and enlarged version of another book. Unfortunately, the updating is not very convincing when the "four color problem" is a conjecture in the body of the book and a theorem in footnotes and afterwords.
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Hi,
In general, I think the methods used by Mathematica are vastly different
from those used in hand calculations. For example, a lot of integration
is done using very complicated objects known as HypergeometricPFQ and
MeierG functions. These are translated back to something simpler (where
possible) before the result is presented.
The problem with your idea is that unless you actually do a fair amount
of math by hand, you don't get the feel for what it really means and how
things work. It may seem a waste of time, but I would encourage you to
bear with it! Perhaps the lecturers should discuss this issue a bit.
Mathematica can be a great help in learning math provided that you don't
just use it to cheat. You can use it to generate examples of similar
problems to the one you are looking at, or to explore more difficult
problems.
David Bailey
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Mathematics - General (484 results)
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as well-informed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large "safety factor of dead wood" in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing.<br><br>The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:<br><br>1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
eBook
Discoveries in MathematicsIntroducing New Principles, Formulæ,& Double Equations, Which Abridge All the Operations of Algebra & Arithmetic
by Heyer M. Nexsen
Discoveries in Mathematics by Heyer M. Nexsen is a handbook that would help every student of mathematics in deconstructing complex formulae, equations and principles underlying algebra and arithmetic. Nexsen understands the general impediments to students of the subject in terms of memorising theorems, special cases as well as hypotheses and therefore provides a pointed discussion on abridging them for quick recall and application. Nexsen opens with an introductory note on algebraic formulae including logs, differentiation, powers and roots among various other concepts. He provides an innovative method for calculating the root of numbers which is much faster and simpler than the existing methodology. He then discusses specific operations like multiplication in double equations, squaring and square roots, cubes as well as formulae for many coefficients. Discoveries in Mathematics is brief which makes it even more appealing for students as referencing is quick and easy and Nexsen makes sure that concepts are explained in the most simplistic manner possible with multiple examples and sample equations. Of the various topics covered, the notes on algebra are perhaps explained the best. In the end, the use of this book would ensure that students of mathematics will be able to reduce calculation times substantially as it holds within its pages some excellent tips and tricks for various mathematical principles.
eBook
Rapid ArithmeticQuick and Special Methods in Arithmetical Calculation Together With a Collections of Puzzles and Curiosities of Numbers
by T. O'Conor Sloane
Rapid Arithmetic: Quick and Special Methods in Arithmetical Calculation, authored by doctor and lawyer T. O'Conor Sloane, is a guidebook to improving your mental math skills. The book is a mixture of valuable and applicable strategies for solving problems of arithmetic, and simple and amusing mental diversions. It is a work that treats the subject of mathematics as something that can be enjoyed. Rapid Arithmetic opens with a brief section on notation and signs before delving more fully into the subject matter. Separate chapters are presented covering addition, subtraction, multiplication and division, as well as fractions, the decimal point, exponents, and several other topics. Each chapter consists of an overview of the topic, as well as a variety of different strategies for tackling different mathematical problems. The author presents short practice activities throughout the work, intended to both reinforce the lesson and serve as fun diversion for the reader. T. O'Conor Sloane has a gift for making a challenging subject entertaining. Rapid Arithmetic is not a book only for the math enthusiast, but for anybody that sees the value in honing their arithmetical skills. It is a well-written and clearly presented treatise on the topic. Rapid Arithmetic: Quick and Special Methods in Arithmetical Calculation is the rare text about mathematics that can appeal even to one not interested in the subject. Sloane's methods can actually improve the daily life of the reader by allowing one to more quickly work out common math problems, and for this reason his work is highly recommended.
Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it.
The orientalists who exploited Indian history and literature about a century ago were not always perfect in their methods of investigation and consequently promulgated many errors. Gradually, however, sounder methods have obtained and we are now able to see the facts in more correct perspective. In particular the early chronology has been largely revised and the revision in some instances has important bearings on the history of mathematics and allied subjects. According to orthodox Hindu tradition the Surya Siddhanta, the most important Indian astronomical work, was composed over two million years ago! Bailly, towards the end of the eighteenth century, considered that Indian astronomy had been founded on accurate observations made thousands of years before the Christian era. Laplace, basing his arguments on figures given by Bailly considered that some 3,000 years B. C. the Indian astronomers had recorded actual observations of the planets correct to one second; Playfair eloquently supported Bailly's views; Sir William Jones argued that correct observations must have been made at least as early as 1181 B. C.; and so on; but with the researches of Colebrooke, Whitney, Weber, Thibaut, and others more correct views were introduced and it was proved that the records used by Bailly were quite modern and that the actual period of the composition of the original Surya Siddhanta was not earliar than A. D. 400.<br><br>It may, indeed, be generally stated that the tendency of the early orientalists was towards antedating and this tendency is exhibited in discussions connected with two notable works, the Sulvasutras and the Bakhshali arithmetic, the dates of which are not even yet definitely fixed present collection of Exercises, gathered from many sources, is one which has accumulated through several years, and consists of papers set weekly or bi-weekly to boys of all ages during that time. They serve to recall back work, and keep boys always ready for the examination. The First Series contains 261 papers, about half the total number, and commences with exercises in Arithmetic suitable to boys who have gone through the First Four Rules, Simple and Compound, and are beginning Fractions; and Algebraical Exercises consisting chiefly of Numerical Values, Addition, and Subtraction. From these onward, the exercises rise in difficulty by careful gradations, reaching Cube Root and Compound Interest in Arithmetic, and Quadratic Equations in Algebra, at the end of the First Series.<br><br>The Second Series is a continuation of the First, and includes problems in Higher Algebra, Logarithms, Trigonometry, and easy Mechanics, and Analytical Geometry.
The old order in mathematics teaching is rapidly giving way to a newer one more interesting, more vital, and more effective. Formerly, all phases of arithmetic were taught in the seventh and eighth grades. In the ninth grade, the foundations of algebra were laid. The latter had practically no connection with the arithmetic that came before nor with the geometry that came after. It was mostly the juggling of symbols that symbolized nothing. This algebra took on some meaning later for the few who continued the study of mathematics in higher schools. But for the many, it never functioned.<br><br>With the organization of the junior high schools has come a reorganization of mathematics. It is now taught in cycles, each complete in itself and adapted to the needs and abilities of the pupil, regardless of whether he continues the study of mathematics in school or applies it in the office, store, or shop. The purpose of the junior cycle is to give the pupil a broad knowledge and usable power and skill in the field of elementary mathematics. This cannot be done by the old tandem courses of arithmetic, algebra, geometry, and trigonometry. Nor will alternate bits of formal algebra, geometry, and trigonometry solve the problem. The result is a mastery of none and a confusion of all.<br><br>In this series the elements of arithmetic, geometry, algebra, and trigonometry are taught as one subject. Book One is largely arithmetical, but it uses the graph and the formula.
In issuing this new volume of my Mathematical Puzzles, of which some have appeared in the periodical press and others are given here for the first time, I must acknowledge the encouragement that I have received from many unknown correspondents, at home and abroad, who have expressed a desire to have the problems in a collected form, with some of the solutions given at greater length than is possible in magazines and newspapers. Though I have included a few old puzzles that have interested the world for generations, where I felt that there was something new to be said about them, the problems are in the main original. It is true that some of these have become widely known through the press, and it is possible that the reader may be glad to know their source.<br><br>On the question of Mathematical Puzzles in general there is, perhaps, little more to be said than I have written elsewhere. The history of the subject entails nothing short of the actual story of the beginnings and development of exact thinking in man. The historian must start from the time when man first succeeded in counting his ten fingers and in dividing an apple into two approximately equal parts. Every puzzle that is worthy of consideration can be referred to mathematics and logic. Every man, woman, and child who tries to "reason out" the answer to the simplest puzzle is working, though not of necessity consciously, on mathematical lines. Even those puzzles that we have no way of attacking except by haphazard attempts can be brought under a method of what has been called "glorified trial" - a system of shortening our labours by avoiding or eliminating what our reason tells us is useless. It is, in fact, not easy to say sometimes where the "empirical" begins and where it ends.<br><br>When a man says, "I have never solved a puzzle in my life," it is difficult to know exactly what he means, for every intelligent individual is doing it every day. The unfortunate inmates of our lunatic asylums are sent there expressly because they cannot solve puzzles - because they have lost their powers of reason. If there were no puzzles to solve, there would be no questions to ask; and if there were no questions to be asked, what a world it would be! We should all be equally omniscient, and conversation would be useless and idle.<br><br>It is possible that some few exceedingly sober-minded mathematicians, who are impatient of any terminology in their favourite science but the academic, and who object to the elusive x and y appearing under any other names, will have wished that various problems had been presented in a less popular dress and introduced with a less flippant phraseology.
The purpose o Fthis monograph is to present in a consecutive form the principal features of abstract and substitution group theory. The development of this branch of mathematics has been very rapid, especially in the last few years, and consequently there is much of great value to be found in a more or less fragmentary form throughout the various mathematical journals that has yet to be collected and discussed. It has been my purpose to examine in detail all memoirs dealing directly with such group theory (excluding, in particular, that of linear groups) and to construct from this material a continuous treatise on the subject. In order to secure uniformity of terminology and method I may seem to have taken liberties with the work of others, I trust that such will not be found unwarranted. The amount of space at my disposal has compelled me to omit all proofs; instead I have given with each theorem or definition a reference to nearly every source, original or secondary. Corrections or additions will be most gratefully appreciated. It is proper to add that as I was granted a Harrison Senior Fellowship to obtain opportunity for revising this work, its present form differs materially from that presented in May of 1901 to the Faculty of Philosophy of the University of Pennsylvania as a dissertation in partial fulfilment of the requirements for the degree of Doctor of Philosophy. The original draft was devoted to substitution theory alone and contained full proofs, with references to only the principal treatises.
Until recently upper elementary and high school work in mathematics was planned for the pupil who was expected to continue it in the university. Although logical, its arrangement was neither psychological nor pedagogical, but some progress has been made recently in adapting the study to the needs and abilities of pupils.<br><br>In the junior high or intermediate school, work in mathematics in the seventh, eighth, and ninth grades should be complete in itself and at the same time preparatory to senior high school work. No effort should be made to "finish" of all.<br><br>Experience has proved that the necessary elements of arithmetic can be taught and certain definite skill developed in the first six grades. In the seventh grade business applications of arithmetic with the simplest elements of bookkeeping should be given.
Until recently upper elementary and high school work in mathematics was planned for the pupil who was expected to continue it in the university. Although logical, its arrangement was neither psychological nor pedagogical. Some progress, however, has been made recently in adapting the study to the needs and abilities of pupils. In the junior high and intermediate school, work in mathematics in the seventh, eighth, and ninth grad should be complete in itself and at the same time preparatory to senior high school work. No effort should be made to finish in all. Experience has proved that the necessary elements of arithmetic can be taught and certain definite skill developed in the first six grades. In the seventh grade business applications of arithmetic with the simplest elements of bookkeeping should be given.
Higher Arithmetic, Designed for the Use of High Schools, Academies, and Colleges is a great math resource for students and teachers written by George Roberts Perkins, principal and professor of mathematics at Utica Academy. Perkins begins this book by arguing the merits and importance of arithmetic declaring it the "branch of mathematics upon which all other are based…" While Perkins acknowledges that there exists a wealth of math text books from which the teacher and student can select, he insists that his book is different because of its highly approachable nature and the ease with which it engages students with any level of mathematical skill. The book is broken down into chapters which group a variety of mathematical concepts into sections that are easily identifiable, and progress from easiest (in the first chapters) to hardest (in the final chapters). The first chapter discusses essential content such as mathematical definitions, symbols, integers, and prime numbers. Further chapters discuss the addition, subtraction, division and multiplication of fractions and decimals; repetends; arithmetical progression; and geometrical progression. The final chapters discuss complex mathematical ideas and practices such as involution defined, evolution defined, square roots, tables, interest, and permutations. Higher Arithmetic, Designed for the Use of High Schools, Academies, and Colleges provides a vast amount of mathematical information for the student and instructor of mathematics. This is a tremendous resource for anyone who needs to know basics, but also excellent for someone looking to explore more highly complex ideas and concepts. This incredibly approachable book also stands out as a go-to addition to any library for individuals who need to remember or re-learn the mathematics they learned as children.
This book has been written to meet the demand for a practical course in applied mathematics which shall coordinate the schoolroom lesson and the actual problem of the industrial and commercial world. It presents the body of mathematical information which is likely to be of daily service, no matter what ones occupation may be. Applied Mathemdties is the outgrowth of twelve years of experimentation in a high school of over two thousand students, and the exercises in the book have stood the test of classroom trial. The examples and problems have been selected from many fields industrial, commercial, mechanical, agricultural and, as far as possible, are such as occur in the household, on the farm, in the factory, and at the office. The book gives in teachable form:(1) An adequate treatment of the fundamental operations of arithmetic, with proper attention to modern methods of performing these operations.(2) A consideration of ordinary business transactions.(8) A sufficient acquaintance with the symbols of algebra and of algebraic operations to enable the student to interpret and apply simple formulas.(4) Enough geometry to enable him to compute the areas and volumes of the common geometric figures.(5) A study of graphic charts and their use.(6) Training in the use of mathematical tables.(7) Practice in the power to judge a computed result with reference to its reasonableness.
In this book, all the principles of Arithmetic are fully developed, and sufficient examples are given to fix them on the mind.<br><br>When a student is very apt and thoroughly understands the Primary Lessons, he may omit the Elementary, and immediately take up this book, which is complete in itself.<br><br>I have discarded puzzles of every kind, which only perplex the student without advancing him a step in science.<br><br>A few simple principles of algebra are introduced, in order to elucidate more clearly, the different functions of interest, the series of equal ratios, and the square and cube root.<br><br>Problems in mensuration are also given, the principles of which are derived from Geometry.<br><br>Arithmetic is a pure mathematical science, and if its principles are systematically developed, the student will progress with easy and rapid steps, and when he has finished this book, he will discover that he has already so far ascended the hill of science that a retrospect will present to him many beauties which are greatly enhanced when seen in their harmonious relation to each other.
The most any author can do to aid him is to present, in more or less detail, an outline of a practical scheme of instruction based upon the latest and best thought in number teaching; and even this is a task that none but the superficial would undertake without fear and trembling. Neither theory nor practice alone is a sufficient endowment for the work. Every theory, every method, every device must be weighed in the class-room balance. That which is to be taught is the child not arithmetic. Holding these views, the writers of this book have spared no effort in its preparation. With a wholesome respect for the injunction, Prove all things; hold fast that which is good, they have endeavored to steer carefully between the Scylla of modern fad and the Charybdis of mechanical drudgery and stupefying monotony. Their aim has been to furnish for the teacher a sound and practical work presenting the matter in an approved order and suggesting rational methods of obtaining the most desirable results. As to how well they have succeeded the teacher must decide. Arrangement. Before entering school the child learns a little of a great many things, not a great deal about one thing. There is no topical arrangement in nature. And Nature, the dear old nurse, permits the order of the childs mental development to determine the arrangement of the material, which is always a progressive one. The child learns a little about many things to-day, a little more to-morrow, adds an increment to his knowledge and widens his range of subjects day by day. This arrangement keeps interest alive, without which there is no substantial progress.
For the slightly more advanced student of mathematics Ray's New Higher Arithmetic: A Revised Edition of the Higher Arithmetic is one in a series of mathematics textbooks authored by Joseph Ray presenting a more advanced math curriculum than Ray's New Practical Arithmetic. Ray's New Higher Arithmetic is an all-encompassing treatise on the subject of arithmetic, geared slightly towards the more advanced learner. The book still begins with the basics however, and early chapters focus on numeration and notation, as well as addition, subtraction, multiplication, and division. From there, the author introduces more advanced topics, including decimal fractions, compound denominate numbers, proportion, evolution, and mensuration. Throughout the work Ray introduces and explains the laws of mathematics and presents example problems illustrating the theory. The book concludes with a section of miscellaneous review questions, presented alongside the correct answer. Ray's New Higher Arithmetic is certainly successful in presenting its subject matter in an effective manner. The book would be appropriate for both the independent learner as well as math teachers. While the content is aimed at the more advanced student, the material is presented in such a way that this volume could be used as an introductory text by a willing and hard worker.
William Timothy Call was a mathematician and an individual interested in using mathematics to improve daily life. In A New Method in Multiplication and Division, Call presents a method he personally devised to solve multiplication and division problems. In his introduction the author acknowledges that the method presented in this book is of no great significance, rather it is a curious way of attacking a problem that likely differs from what the reader has been taught. It is clear from the beginning that this is a book aimed at those with a keen interest in math. The book opens with Call's method for solving simple multiplication problems, before progressing to his method for problems of division. A New Method in Multiplication and Division is a brief work and one that will appeal to those for whom mathematics is a hobby. The subject matter is largely trivial, and while the methods detailed are effective, they are presented largely as a novelty. Those who are passionate about mathematics will likely enjoy the casual approach of the author and the general tone of the book. For readers passionate about mathematics and problem solving, William Timothy Call's A New Method in Multiplication and Division is recommended. This is not a textbook or a resource guide, but rather a lighthearted presentation of a simple but alternative mathematical approach, intended to entertain and inform the reader.
Bfe aaass EkuUm District afPermsyhsan Utotoii: Be It Remembered, That on the fifleentb lis I yof January, in the forty-ninth year of the Inf Jdependence of the United States of America, A.D. 1825, John Grigg, of the said district, hath deposited in this office, the title of a book, the right whereoi he claims as proprietor, in the words floiring, to wit: The New Federal Calculator, or Scholars Assistant: Containiag the most concise and accurate rules for performing the operations in common Arithmetic; together with numerous examples under each of the rules, varied so as to make them conformable to almost every kind of business. For the use of Schools and Counting Houses. Bj Thomas T.Smilet, Teacher. Author of an Easy Introduction to the Study of Geography. Also, of Saa GeograIy for the use of Schools. In conformity to the act of the Congress of the United States, entitled, An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprie.ors of sucii copies, during the times therein mentioned. And alsor to the Act, entitled, An Act supplementary to an Act, entitled, An Act ror the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned, and extending the benefits thereof to the arts of designing, engraying, and etching historical and other prints. D.Caldwell, Clerk of the Ecutem DistHci Pennaylwaiku Stereotyped by J.Howe.
Increasing demands for instruction in practical or trade subjects have made it necessary to develop courses of study having special application to particular trades. In the past much of this instruction has been done without textbooks, or if textbooks have been used, they have not been satisfactory. Since, in many cases, it has been necessary to supplement the class-room instruction with lesson material prepared by some method of duplication other than printing, it has been brought to the attention of publishers that here is an undeveloped field, particularly for books in mathematics. Old-fashioned academic books are not at all satisfactory, for example, in the teaching of Practical Mathematics to classes of electricians and machinists. These trades have many problems, more or less related, which are concrete examples of the days work and can be effectively used for study material. These chapters have been prepared with the object, first, of establishing and holding the interest of adult students; and second, of presenting for study only those parts of the common mathematical subjects which a quaUfied electrician or machinist will be likely to use either in his present employment or in the future work he will do as a result of study and advancement. Throughout this book, as much as possible, the language used by practical men has been followed, and the presentation has been made direct, intimate, and personal. Whenever possible, unusual mathematical terms, symbols, and names have been avoided. For example, in nearly all parts of this book names Uke digit, factor, multiplicand, etc.
The Normal Mental Arithmetic: A Thorough and Complete Course by Analysis and Induction is a textbook written by Edward Brooks. This work provides readers with the opportunity to access a textbook that was used in Pennsylvania public schools in the mid-nineteenth century. The focus of Edward Brooks' textbook is to impart the mental skills required for success at arithmetic on public school students. In the introduction, the author criticizes the state of arithmetic teaching, stating that the methods current as of this text's publication were focused too much on formulas and not enough on developing mental skills. Thus, the focus of The Normal Mental Arithmetic is to teach students to use their ingenuity to solve mathematical problems. The book is structured as most textbooks are, with the text divided into lessons, each of which either presents a new topic or builds on a previously discussed topic. The majority of the work is a series of sample questions to be posed to students, with little in the way of explanation. Unlike many textbooks, the correct responses are not included anywhere in the book. The Normal Mental Arithmetic is not a candidate to be used in the classroom today. Modern teaching methods and textbooks have evolved far beyond those of the nineteenth century, and this book is good evidence of that development. The book is thus valuable to those interested in examining the history of educational methods and practices, and anybody else keenly interested in nineteenth century textbooks. The Normal Mental Arithmetic poses arithmetic problems that can still serve as good practice for the mathematic learner, however other facets of this text make it less suited for use in today's classroom. If you are a reader seeking to examine a nineteenth century textbook, Edward Brooks' work is a good example of one that was used in public schools throughout Pennsylvania.
Mental Arithmetic is not intended to supersede written arithmetic, but should rather be its constant auxiliary. Without proper mental training, the pupil becomes accustomed to depend almost entirely on rules and formuUe not capable of interpreting the latter, and entirely in the dark as to the reasons of the former. The long and barren reign of rule and routine is due to the fact that I ational methods in teaching the Logic of the Public School have been too generally ignored that Mental Arithmetic, which, by easy steps, leads the pupil into an intelligent possession of principles, and renders him expert and logical in their application, has hitherto held an utterly insignificant place in school-room work. Given a slate, a pencil, a rule, and a salutary dread of coming trouble and a pupil was supposed to be seized of all the elements necessary to make him a first-rate arithmetician. But better methods have begun to prevail; and the improvement in teaching written arithmetic which has taken place during the past few years has only to be supplemented by systematic mental training, in order to reach the highest results of the study of the same. This is recognizedly the various educational authorities throughout the Dominion. Most of them iiave, it is believed, made it imperative that their teachers shall have a thorough training in Mental Arithmetic, and prove by actual examination, their knowledge of rational metboda as well as their ability to teach them.
Notwithstanding the perfection to which the majority of th arts and sciences have been carried yet it is acknowledged by all considerate persons, that British handicrafts are by no means so well informed, as to the principles of their respective operations, as the excellent workmanship they produce would lead us to suppose! The fact is, that the mechanic is a mere automaton, under the guidance of a skilful director, in whose absence, therefore, either the work must stop, or there must be a perpetual risk of error, and of consequent loss. If we except such as have served regular apprenticeships under men of superior abihty, and those who have laboured in great cities, or at extensive manufactories, where knowledge will flow in upon the mind, few, indeed are the artizans that can account for any one proportion, or form, they habitually construct: the smallest deviation occasions hesitation at least, if it does not completely derange the operator; and such is the obstinacy of ignorant men, that, even when they do follow the directions they receive from their employers, it is, usually, with a bad grace, if not with a bad will; such as rarely fails to injure, and perhaps to frustrate the good effects of the proposed improvement.
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Once this is mastered, we begin exploring how mathematics and the natural sciences "reason logically" and how our basic understandings of natural laws develop from basic relationships between words and objects. Social studies explores the relationship between individuals and their government at ...
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G22.3033-002
Applied Math for Algorithms
Siegel
Mondays 5-6:50, room 102
Office hours: M 7:00-8:00
Graduate Division
Computer Science
Although many mathematics courses have content that is
useful in the design and analysis of algorithms, the more applicable material often
comprises no more than 10% of the curriculum.
This course will endeavor to present that critical 10% as culled from a handful
of math courses and other sources. We will also endeavor to show how this
material is applied in the design and analysis of algorithms.
Some of the subjects that will be covered are:
Performance-related equations and their
direct solution. Recurrence equations: first order
difference equations and beyond. Eigenfunction methods, multiplicity
of eigenvalues, etc.
ODEs and their use in performance analyses. A limited
presentation of limit theorems.
PDEs and their use in performance analyses. Limited
implications of limit theorems.
Probability, and what properly
educated theoreticians might wish to know.
Conditional expectations are a powerful, highly expressive tool with a
foundation that is based on measure theory.Yet the concept is very pragmatic, and allows us to present proofs and to acquire
understandings about probabilistic processes that would otherwise be difficult
to formalize.
It is also worth understanding what the central limit theorem says, what it
means, what it implies, and what it does not imply.
Likewise, it is useful to understand the more basic probability distributions
and the physical processes that they model.
Statistics is a little different from
probability.
One of the areas of statistical analysis that has had significant impact in TCS
is the theory of Hoeffding-Chernoff bounds. It is
probably a good idea to know how this material applies to more than Bernoulli Trials, and to stopping times in particular.
We might also cover some issues in the computation of random variables, and at
least comment on the importance of extreme points in the space of probability
distributions (which is to say that we will survey majorization
results).
Complex variables gives valuable insights about the solution to many
algorithms-based difference equations, and provides the
theory necessary for computing saddle point estimates and understanding some of
the limit results for ODEsPDEs.
Combinatorics is
less systematic than analysis, but gives a rich set of techniques that are as
varied as tableau methods (used to count seemingly complicated outcomes) and
the probabilistic method (which is arguably more combinatorial that
probabilistic).
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Intermediate Algebra 11th edition
0321613368
9780321613363
Details about Intermediate Algebra:
The Bittinger Worktext Series changed the face of developmental education with the introduction of objective-based worktexts that presented math one concept at a time. This approach allowed readers to understand the rationale behind each concept before practicing the associated skills and then moving on to the next topic. With this revision, Marv Bittinger continues to focus on building success through conceptual understanding, while also supporting readers with quality applications, exercises, and new review and study materials to help them apply and retain their knowledge.
Back to top
Rent Intermediate Algebra 11th edition today, or search our site for Marvin L. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson.
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MATHEMATICS
MATH-154
Great Ideas in Mathematics (4)
Course Level: Undergraduate
This course explores a sample of beautiful branches of modern mathematics, concentrating on conceptual underpinnings rather than technical aspects. Includes study of infinity, number theory, fractals, and modern geometry, among other mathematical ideas. The course focuses on verbal and written communication skills and problem solving. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.
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Cynwyd, PA PrecalculusIt is important for students first to understand the concepts (tools), then learn how to use them in specific contexts, and finally to generalize. Solving the problem is usually easy, but understanding WHY we solve it that way is often more challenging. One question students will frequently hea...
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TEKS Math Grade 8
Mathematics, Grade 8.
(a) Introduction.
(1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 8 are using basic principles of algebra to analyze and represent both proportional and non-proportional linear relationships and using probability to describe data and make predictions.
(2) Throughout mathematics in Grades 6-8, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use concepts, algorithms, and properties of rational numbers to explore mathematical relationships and to describe increasingly complex situations. Students use algebraic thinking to describe how a change in one quantity in a relationship results in a change in the other; and they connect verbal, numeric, graphic, and symbolic representations of relationships. Students use geometric properties and relationships, as well as spatial reasoning, to model and analyze situations and solve problems. Students communicate information about geometric figures or situations by quantifying attributes, generalize procedures from measurement experiences, and use the procedures to solve problems. Students use appropriate statistics, representations of data, reasoning, and concepts of probability to draw conclusions, evaluate arguments, and make recommendations.
(3) Problem solving in meaningful contexts, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics. Throughout mathematics in Grades 6-8, students use these processes together with graphing technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve problems as they do mathematics.
(b) Knowledge and skills.
(8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems.
The student is expected to:
(A) compare and contrast proportional and non-proportional linear relationships; and
(B) estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
(8.4) Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship.
The student is expected to generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description).
(8.5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems.
The student is expected to:
(A) predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and
(B) find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change).
(8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense.
The student is expected to:
(A) generate similar figures using dilations including enlargements and reductions; and
(B) graph dilations, reflections, and translations on a coordinate plane.
(8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world.
The student is expected to:
(A) draw three-dimensional figures from different perspectives;
(B) use geometric concepts and properties to solve problems in fields such as art and architecture;
(C) use pictures or models to demonstrate the Pythagorean Theorem; and
(D) locate and name points on a coordinate plane using ordered pairs of rational numbers.
(8.8) Measurement. The student uses procedures to determine measures of three-dimensional figures.
The student is expected to:
(A) find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models);
(B) connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects; and
(C) estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.
(8.9) Measurement. The student uses indirect measurement to solve problems.
The student is expected to:
(A) use the Pythagorean Theorem to solve real-life problems; and
(B) use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.
(8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures.
The student is expected to:
(A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and
(B) describe the resulting effect on volume when dimensions of a solid are changed proportionally.
(8.11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions.
The student is expected to:
(A) find the probabilities of dependent and independent events;
(B) use theoretical probabilities and experimental results to make predictions and decisions; and
(C) select and use different models to simulate an event.
(8.12) Probability and statistics. The student uses statistical procedures to describe data.
The student is expected to:
(A) select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation;
(B) draw conclusions and make predictions by analyzing trends in scatterplots; and
(C) select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.
(8.13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data.
The student is expected to:
(A) evaluate methods of sampling to determine validity of an inference made from a set of data; and
(B) recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.
(8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.
The student is expected to:
(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;
(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;
(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and
(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.
The student is expected to:
(A) make conjectures from patterns or sets of examples and nonexamples; and
(B) validate his/her conclusions using mathematical properties and relationships.
Source: The provisions of 111.24 adopted to be effective September 1, 1998, 22 TexReg 7623; amended to be effective August 1, 2006, 30 TexReg 1930.
_______________________________________
The TAKS Solution is a registered trademark of Mathematical Solutions Publishing Company and is not affiliated in any way with the TAKS testing program or the Texas Education Agency.
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Blackline master book designed
to complement a remedial Math program for small groups of students.
Explains
the basic concepts of number, exploring in detail the processes of addition,
subtraction, multiplication and division.
Decimals are investigated in detail as
well as their relationship with percentages. The activities are sequenced in
line... more...
This book is a collection of selected papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sinaia, Romania, in 2006. The series of SCEE conferences aims at addressing mathematical problems which have a relevance to industry, with an emphasis on modeling and numerical simulation of electronic circuits,... more...
Presents computational issues arising in financial mathematics. This guide to the financial engineering features revisions that concern topics like calibration, Monte Carlo Methods, American options, exotic options and Algorithms for Bermuda Options. It includes various figures, exercises, background material of financial engineering. more...
Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites,... more...
Accessible Mathematics is Steven Leinwand?s latest important book for math teachers. He focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts... more...
This book is a collection of 65 selected papers presented at the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in Espoo, Finland, in 2008. The aim of the SCEE 2008 conference was to bring together scientists from academia and industry, e.g. mathematicians, electrical engineers, computer scientists, and... more...
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree... more...
This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. All the most used formulations are taken into account, placing the problem in a rigorous functional framework. Nodal or edge finite elements are used for approximation. A detailed analysis of each formulation is presented,... more...
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Welcome!
Welcome to the Department of Mathematics and Statistics. We offer a wide variety of undergraduate and graduate degree programs designed for students with diverse career or higher educational goals. Our faculty members maintain active research programs in the fields of combinatorics, algebra, analysis, applied mathematics and applied statistics. In a nod toward the unity of mathematics, we offer the following question—whose answer requires several of the above fields, as well as geometry:
A collection of small waves are travelling through shallow water and happen to collide. What happens next?
The first half of the above sentence is governed by the famous KdV equations. (Jerry Bona, UIC, spoke at our colloquium about these waves not long ago.)
The second half of the above sentence is governed by cells in the totally positive part of the Grassmannian and plabic graphs. (Dr. Lauve can tell you more about this aspect of the theory of totally positive matrices.)
See our Faculty Research page for a list of local people to ask for more details, or consult the original sources:
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Contents
The series was originally developed in the 1930s by Daniel Schaum, son of eastern European immigrants, and has continued as an aid to students to this day. Titles are continually revised to reflect current educational standards in their fields, including updates with new information, additional samples, the use of calculators and computers, etc. New titles are introduced in emerging fields.
Despite being marketed as a supplement, several Schaum's Outlines have become widely used as primary textbooks[citation needed] (the Discrete Math and Statistics titles are examples) for courses. This is particularly true in settings where an important factor in the selection of a text is the price, such as in community colleges.
Schaum's Outlines are a staple[citation needed] in the educational sections of retail bookstores, where books on topics such as chemistry and calculus may be found. Many titles on advanced topics are also available, such as complex variables and topology, but these are typically not found in retail stores.
The titles feature noted authors in their respective fields, such as Murray R. Spiegel and Seymour Lipschutz. Originally, the series was designed for college-level students as a supplement to a course textbook. As a supplement, each title typically has introductory explanations of topics, plus many fully worked examples, and further exercises for the student.
Condensed versions of the full Schaum's Outlines called "Easy Outlines" have appeared in recent years, aimed at high-school students and AP courses. These feature the same material in their full-size counterparts, but edited for length and suitability. They also cost about half the price of the full outline. The smaller size of the Easy Outlines makes them more portable.
Schaum's Outlines are part of the educational supplements niche. They are frequently seen alongside the Barron's "Easy Way" series and McGraw-Hill's own "Demystified" series. The "Demystified" series is introductory in nature, for middle and high school students, favoring more in-depth coverage of introductory material at the expense of fewer topics. The "Easy Way" series is a middle ground: more rigorous and detailed than the "Demystified" books, but not as rigorous and terse as the Schaum's series. Schaum's originally occupied the niche of college supplements, and the titles tend to be more advanced and rigorous. With the expansion of AP classes in high schools, Schaum's Outlines are positioned as AP supplements. The outline format makes explanations more terse than any other supplement. Schaum's has a much wider range of titles than any other series, even for some graduate level courses, but these are typically not found at retail outlets.
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At NOVA's Origins website, users can "journey back to the beginning of everything: the universe, Earth, and life itself." The web site offers a series of interactive modules where visitors can decide if life exists on...
In general, a triangle is defined by its three elements. SAS, ASA, and SSS provide three well-known examples but there are many more. Bogomolny provides a table of constructions (linked to constructions) and invites...
Algebra.help is an online resource designed to help people learn algebra. It offers lessons to teach or refresh old skills, calculators that show how to solve problems step-by-step, and interactive worksheets for...
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More About
This Textbook
Overview
This extremely readable, highly regarded, and widely adopted text presents innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formula – pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises – has proven to be tremendously successful with both students and instructors.
Functions; The Derivative; Applications of the Derivative; Techniques of Differentiation; Logarithm Functions; Applications of the Exponential and Natural Logarithm Functions; The Definite Integral; Functions of Several Variables; The Trigonometric Functions; Techniques of Integration; Differential Equations; Taylor Polynomials and Infinite Series; Probability and Calculus
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9780130652430Excerpts
This text discusses partial differential equations in the engineering and physical sciences. It is suited for courses whose titles include Fourier series, orthogonal functions, or boundary value problems. It may also be used in courses on Green''s functions, transform methods, or portions on advanced engineering mathematics and mathematical methods in the physical sciences. It is appropriate as an introduction to applied mathematics. Simple models (heat flow, vibrating strings, and membranes) are emphasized. Equations are formulated carefully from physical principles, motivating most mathematical topics. Solution techniques are developed patiently. Mathematical results frequently are given physical interpretations. Proofs of theorems (if given at all) are presented after explanations based on illustrative examples. Over 1000 exercises of varying difficulty form an essential part of this text. Answers are provided for those exercises marked with a star (*). Further details concerning the solution for most of the starred exercises are available in an instructor''s manual. Standard topics such as the method of separation of variables, Fourier series, orthogonal functions, and Fourier transforms are developed with considerable detail. Finite difference numerical methods for partial differential equations are clearly presented with considerable depth. A briefer presentation is made of the finite element method. This text also has an extensive presentation of the method of characteristics for linear and nonlinear wave equations, including discussion of the dynamics of shock waves for traffic flow. Nonhomogeneous problems are carefully introduced, including Green''s functions for Laplace''s, heat, and wave equations. Numerous topics are included such as differentiation and integration of Fourier series, Sturm-Liouville and multidimensional eigenfunctions, Rayleigh quotient, Bessel functions for a vibrating circular membrane, and Legendre polynomials for spherical problems. Some optional advanced material is included (for example, asymptotic expansion of large eigenvalues, calculation of perturbed frequencies using the Fredholm alternative, stability conditions for finite difference methods, and direct and inverse scattering). Applications briefly discussed include the lift and drag associated with fluid flow past a circular cylinder, Snell''s law of refraction for light and sound waves, the derivation of the Eikonal equation from the wave equation, dispersion relations for water waves, wave guides, and fiber optics. The text has evolved from the author''s experiences teaching this material to different types of students at various institutions (MIT, UCSD, Rutgers, Ohio State, and Southern Methodist University). Prerequisites for the reader are calculus and elementary ordinary differential equations. (These are occasionally reviewed in the text, where necessary.) For the beginning student, the core material for a typical course consists of most of Chapters 1-5 and 7. This will usually be supplemented by a few other topics. The text is somewhat flexible for an instructor, since most of Chapters 6-13 depend only on Chapters 1-5. Chapter 11 on Green''s functions for the heat and wave equation is an exception, since it requires Chapters 9 and 10. Chapter 14 is more advanced, discussing linear and nonlinear dispersive waves, stability, and perturbation methods. It is self-contained and accessible to strong undergraduates. Group velocity and envelope equations for linear dispersive waves are analyzed, whose applications include the rainbow caustic of optics. Nonlinear dispersive waves are discussed, including an introductory presentation of solitons for the weakly nonlinear long wave equation (Korteweg-de Vries) and the weakly nonlinear wave envelope equation (Nonlinear Schrodinger). In addition, instability and bifurcation phenomena for partial differential equations are discussed as well as perturbation methods (multiple scale and boundary layer problems). In Chapter 14, I have attempted to show the vitality of the contemporary study of partial differential equations in the context of physical problems. I have made an effort to preserve the third edition so that previous users will find little disruption. Nearly all exercises from the previous edition have been retained with no change in the order to facilitate a transition for previous users. Only a few new exercises were created (especially for Chapter 1). The fourth edition contains many improvements in presentation and the following new material: diffusion of a chemical pollutant, Galerkin numerical approximation for the frequencies, similarity solution for the heat equation, two-dimensional Green''s function for the wave equation, nonuniqueness of shock velocity and its resolution, spatial structure of traveling shock wave, stability and bifurcation theory for systems of ordinary differential equations, two spatial dimensional wave envelope equations, analysis of modulational instability, long wave instabilities, pattern formation for reaction diffusion equations, and the Turing instability. There are over 200 figures to illustrate various concepts, which were prepared by the author using MATLAB. The MATLAB m-files for most of the mathematical figures may be obtained from my Web page: Modern technology is especially important in its graphical ability, and I have tried to indicate throughout the text places where three-dimensional visualization is helpful. Overall, my object has been to explain clearly many fundamental aspects of partial differential equations as an introduction to this vast and important field. After achieving a certain degree of competence and understanding, the student can use this text as a reference, but for additional information the reader should be prepared to refer to other books such as the ones cited in the Bibliography. Finally, it is hoped that this text enables the reader to find enjoyment in the study of the relationships between mathematics and the physical sciences. The author gratefully acknowledges the contributions of the following reviewers of the manuscript: Andrew Belmonte, Penn State University, Julie Levandosky, Stanford University, and Isom Herron, Rensselaer Polytechnic Institute. I wish to thank past, present, and future readers of the book (students and faculty). Shari Webster was of great help in preparing the LATEX for the previous edition. Richard Haberman
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Provide through examples with sidebar hints and notes; and Lesson Practice questions with lesson reference numbers underneath the question number. Online connections are given throughout for additional help. Real-world applications and continual practice & review provide the time needed to master each concept, helping students to...
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Provide students with a college-prep math course that will give them the foundation they need to successfully move into higher levels of math. Saxon Algebra 1, 4th Edition covers all of the traditional first-year algebra topics while helping students build higher-order thinking skills, real-world application skills, reasoning, and an understanding of interconnecting math strands. Saxon Algebra 1 focuses on algebraic thinking through multiple representations, including verbal, numeric, symbolic, and graphical, while graphing calculator labs model mathematical situations. Incremental lessons include a Warm Up activity; New Concepts section that introduces new concepts through examples with sidebar hints and notes; and Lesson Practice questions with lesson reference numbers underneath the...
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Repetition, drills, and application exercises ensure mastery of computational skills with Lifepac Math: Pre-Algebra and Pre-Geometry 2. Students will progress to higher-level cognitive reasoning and analysis as their problem solving ability increases. Lifepac math programs use mastery-based learning along with spiraling review to encourage long-term student success 8. 2014 Edition. Subjects covered include: The Real Number System Modeling Problems in Integers Modeling Problems with Rational Numbers Proportional reasoning More with Functions Measurement...
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Product Description Provide thro skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations. Explanations and practical examples that mirror today's teaching methodsRelevant cultural vernacular and referencesStandar d For Dummies materials that match the current standard and design Basic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra
The main portion of Algebra is comprised of problems, to which students are recommended to: Solve the problem individually, compare your solution with the solution in the book (if it exists) and go to the next problem. However, if students have difficulties solving a problem, they may read the hint or start to read the solution. There is no teacher's guide, workbook or answer keys for this book. Solutions are provided for some of the problems. For Mathematics teachers and serious Mathematics students, Algebra does not cover all topics in Algebra 1 or 2, and concentrates on theory rather than application. 149 pages, softcover.
Pre Algebra Math 7 Box Set - - Prepare your middle school student for higher level math courses with the Horizons Pre-Algebra Set from Alpha Omega Publications! This year-long course takes students from basic operations in whole numbers decimals fractions percents roots and exponents and introduces them to math-building concepts in algebra trigonometry geometry and exciting real-life applications. Divided into 160 lessons this course comes complete with one consumable student book a student tests and resources book and an easy-to-use teacher's guide. Every block of ten lessons begins with a challenging set of problems that prepares students for standardized math testing and features personal interviews showing how individuals make use of math in their everyday lives. - Introduce your...
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Repetition, drills, and application exercises ensure mastery of computational skills with Lifepac Math. Students will progress to higher-level cognitive reasoning and analysis as their problem solving ability increases 7. 2014 Edition. Subjects covered include: Integers Fractions Decimals Patterns and equations Ratios and proportions Probability and graphing Data Analysis Measurement and Area Surface Area and Volume
Product Description Boost your students understanding of Saxon Math with DIVE's easy-to-understand lectures! Each lesson in Saxon Math's textbook is taught step-by-step on a digital whiteboard, averaging about 10-15 minutes in length; and because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. After the lesson, students complete the 30-question Problem Set in the Saxon text; a few problems in the set come f
Buy Basic Math and Pre-Algebra For Dummies by Mark Zegarelli and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
Make math matter to students in all grades using Math Tutor: Pre-Algebra Skills! This 80-page book provides step-by-step instructions of the most common math concepts and includes practice exercises, reviews, and vocabulary definitions. The book covers factoring, positive and negative numbers, order of operations, variables, exponents, and formulas such as perimeter, area, and volume. It aligns with state, national, and Canadian provincial standards.
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Kobo eBooksAlgebra Readiness Made Easy: Grade 2: An Essential Part of Every Math Curriculum eBook
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the definition of a polynomial, polynomial multiplication and degree of polynomial products are introduced. Special products and factoring cubics are presented before modeling with polynomials is discussed.
Beginning with the definition of a polynomial, polynomial multiplication and degree of polynomial products are introduced. Special products and factoring cubics are presented before modeling with polynomials is discussed.
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Product Description
This 4-DVD set accompanies the Introductory Logic, 4th Edition curriculum by Douglas Wilson and James Nance. Revised and expanded, this course will walk students through each lesson in the text. Designed for 8th-grade and up, the lessons captured in this DVD set cover definitions, logical statements, fallacies, syllogisms, and many other elements of logical thinking. Three discs cover lessons 1-36, with the fourth DVD providing detailed explanations of answers for the tests and a comprehensive exam. DVDs must be used with sold-separately text materials. Four DVDs.
DVD Playable in Bermuda, Canada, United States and U.S. territories. Please check if your equipment can play DVDs coded for this region. Learn more about DVDs and Videos
Couldn't imagine teaching/learning logic without these DVDs. Most helpful for myself as well as my daughters to understand/learn logic. And his white board (TV screen) with charts and points already written is most helpful. Excellent DVDs!
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More About
This Textbook
Overview
Larson IS student success. INTERMEDIATE ALGEBRA: ALGEBRA WITHIN REACH owes its success to the hallmark features for which the Larson team is known: learning by example, a straightforward and accessible writing style, emphasis on visualization through the use of graphs to reinforce algebraic and numeric solutions and to interpret data, and comprehensive exercise sets. These pedagogical features are carefully coordinated to ensure that students are better able to make connections between mathematical concepts and understand the content. With a bright, appealing design, the new Sixth Edition builds on the Larson tradition of guided learning by incorporating a comprehensive range of student success materials to help develop students' proficiency and conceptual understanding of algebra. The text also continues coverage and integration of geometry in examples and exercises.
Meet the Author
Dr 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE,
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books.google.co.uk - Al... in the History of Modern Algebra (1800-1950)
Al call modern algebra is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a rising sea in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries.Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century.The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.
About the author (2007)
Jeremy Gray is Professor of the History of Mathematics and Director of the Centre for the History of the Mathematical Sciences at the Open University in England, and is an Honorary Professor in the Mathematics Department at the University of Warwick. He is the author, co-author, or editor of 14 books on the history of mathematics in the 19th and 20th Centuries and is internationally recognised as an authority on the subject. His book, Ideas of Space, is a standard text on the history of geometry (see competitive literature).
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Mathematical modeling is concerned with translating a natural phenomenon into a mathematical form. In this abstract form the underlying principles of the phenomenon can be carefully examined and real-world behavior can be interpreted in terms of mathematical shapes. The models we investigate include feedback phenomena, phase locked oscillators, multiple population dynamics, reaction-diffusion equations, shock waves, and the spread of pollution, forest fires, and diseases. We will employ tools from the fields of differential equations and dynamical systems. The course is intended for students in the mathematical, physical, and chemical sciences, as well as for students who are seriously interested in the mathematical aspects of physiology, economics, geology, biology, and environmental studies.
Class Format: lecture
Requirements/Evaluation: evaluation will be based primarily on performance of problem sets and exams
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Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference... more...
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing... more...
In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems.... more...
This book is Volume II of the series DSP for MATLAB? and LabVIEW?. This volume provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z -Transform (including definition and... more...
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how... more...
Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."— Zentralblatt MATH ". . . carefully structured with many detailed worked examples."— The Mathematical Gazette The Second Edition of the highly regarded... more...
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book presents 49 space-related math problems published weekly on the SpaceMath@NASA site during the 2011-2012 academic year. The problems utilize information, imagery, and data from various NASA spacecraft missions that span a variety of math...(View More) skills in pre-algebra and algebra
This book offers an introduction to the electromagnetic spectrum using examples of data from a variety of NASA missions and satellite technologies. The 84 problem sets included allow students to explore the concepts of waves, wavelength, frequency,...(View More) and speed; the Doppler Shift; light; and the energy carried by photons in various bands of the spectrum. Extensive background information is provided which describes the nature of electromagnetic radiation.(View Less)
This is a booklet containing 87 problem sets that involve a variety of math skills, including scale, geometry, graph analysis, fractions, unit conversions, scientific notation, simple algebra, and calculus. Each set of problems is contained on one...(View More) page. Learners will use mathematics to explore varied space science topics in the areas of Earth science, planetary science, and astrophysics, among many others. This booklet can be found on the Space Math@NASA website.(View Less)
This is a booklet containing 36 problem sets that involve a variety of math skills, including scientific notation, algebra, geometry, and calculus. Each set of problems is contained on one page. Learners will use mathematics to explore varied space...(View More) science topics including radiation effects on humans and technology, solar science, and other mathematics topics.(View Less)
This is a booklet containing 96 mathematics problems involving skills relating to algebra, fractions, graph analysis, geometry, measurement, scale, calculus, and other topics. Learners will use mathematics to explore NASA science and space...(View More) exploration content relating to space weather, the study of the Sun and its interactions with Earth. Each problem or problem set is introduced with a brief paragraph about the underlying science, written in a simplified, non-technical jargon where possible. Problems are often presented as a multi-step or multi-part activities, and there are problem sets for learners in grades 3-5, 6-8 and 9-12. This booklet can be found on the Space Math@NASA website.(View Less)
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Linear Programming is a revolutionary development that permits us, for the first
time in our long evolutionary history, to make decisions about the complex world
in which we live that can approximate, in some sense, the optimal or best
decision.
George B. Dantzig [80]
A short survey about the fields of linear optimization1 and interior-point
methods is presented in this chapter. Based on the simple model of standard
linear optimization problems, some basic concepts of interior-point methods
and various strategies used in the algorithm are introduced. The purpose of
this work, as well as some intuitive observations that sparked the authors'
research, are described. Several preliminary technical results are presented
as a preparation for later analysis, and the contents of the book are also
outlined.
For some historical reason, the name "linear programming" was coined in the early
stages of the field of linear optimization. In this monograph we choose its more
natural name "linear optimization". This also distinguishes the field from general
programming works related to computers.
Print this page
While we understand printed pages are helpful to our users, this limitation is necessary
to help protect our publishers' copyrighted material and prevent its unlawful distribution.
We are sorry for any inconvenience.
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The easy way to brush up on the math skills you need in real life Not everyone retains the math they learned in school. Like any skill, your ability to speak "math" can deteriorate if left unused. From adding and subtracting money in a bank account to figuring out the number of shingles to put on a roof, math in all of its forms factors into daily... more...
Technical Math For Dummies is your one-stop, hands-on guideto acing the math courses you'll encounter as you work towardgetting your degree, certification, or license in the skilledtrades. You'll get easy-to-follow, plain-English guidance onmathematical formulas and methods that professionals use every dayin the automotive, health,... more...
The easy way to score high on the PANCE and PANRE Physician Assistant Exam For Dummies, Premier Edition offers test-taking strategies for passing both the Physician Assistant National Certifying Exam (PANCE) and the Physician Assistant National Recertifying Exam (PANRE). It also offers information on becoming a certified Physician Assistant (PA)... more...
Dr. Richard W. Snyder , DO is an osteopathic physician, board certified in both internal medicine and nephrology. He has authored and coauthored several articles in peer-reviewed journals. Barry Schoenborn is a longtime technical writer and is the coauthor of Technical Math For Dummies . more...
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The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation.
The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels.
Grigor'yan has written this book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.
Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
Readership
Graduate students and research mathematicians interested in geometric analysis; heat kernel methods in geometry and analysis.
Reviews
"And the book under review is indeed a wonderful source for this material. The author's approach is both broad and deep, and extremely thorough and rigorous. ... poised to be an important book in the field and a valuable pedagogical contribution. It is bound to be an important player on the scene for years to come."
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Combinatorics of Finite Geometries is an introductory text on the combinatorial theory of finite geometry. Assuming only a basic knowledge of set theory and analysis, it provides a thorough review of the topic and leads the student to results at the frontiers of research. This book begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes. Later, it addresses polar spaces, partial geometries, and generalized quadranglesEditorial Reviews
Review
"The whole book is warmly recommended to undergraduate students." Tamás Szõnyi, Mathematical Reviews
Book Description
This book is an introductory text on the combinatorial theory of finite geometry. It assumes only a basic knowledge of set theory and analysis, but soon leads the student to results at the frontiers of researchMost Helpful Customer Reviews
This is my favorite finite geometry text. The treatment is a mixture of basic and complex and is hence suitable for a wise variety of readers, probably best for undergraduate/beginning graduate courses, but works well for self-study. I am excited about the generalized quadrangles sections.
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A qualified bestseller since 1973, this third edition refines the information and improves features of the book to provide greater clarity and motivation to learn. It includes useful theorems to make the formulas more transparent and easier to understand. It offers a simplified proof of the fundamentals of algebra requiring only basic real analysis....ocusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the... more...
The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world. In the first four chapters the authors cover material for competitions at high school level. The level advances with... more...
The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry.
Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language... more...
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism. more...
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The book provides a clear understanding of the issues that students face in assimilating this highly mathematical subject. It is a comprehensive analytical treatment of signals and systems with a strong emphasis on solving problems.
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This is a short eBook that describes how to get free high school Algebra 1 help online without having to spend any money, buy anything, join any free trials, or anything like that. Free High School Algebra 1 Help Online | Algebra 1 Help.org.
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra. How to Subtract Integers Without Getting Confused | Algebra 1 Help.org
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More About
This Textbook
Overview
Students of mathematics, engineering, and science can learn how to apply classroom techniques to workplace problems with this concise single-volume text. It employs MATLAB and other strategies to resolve issues related to statistical reasoning, data acquisition, cost-benefit analysis, and other common workplace procedures.
Each chapter begins with a brief review of relevant mathematics, followed by an examination of the material's typical industrial applications. The author demonstrates the problem-solving power of interweaving analytic and computing methods and integrates MATLAB code into the narrative flow. Topics include the Monte Carlo method, the discrete Fourier transform, linear programming, regression, microeconomics, ordinary and partial differential equations, and frequency domain methods. A concluding chapter on technical writing explains how to present mathematical data in a variety of situations and offers helpful suggestions for assembling formal technical reports, progress reports, executive summaries, and other statements
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Suggestions for a comprehensive discrete math textbook
Hey again,
I'm having some trouble finding a suitable book for discrete math.
In my current class the teacher makes and prints his own textbook. It's not bad it's just not working out for me. I checked my local book store and they don't even have anything. Shopped around online and didn't find anything suitable. If anyone has or knows of a fairly comprehensive book I would love to hear suggestions.
Thanks in advance!
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* Numbers and algebra Solve equations, calculating with fractions or divider, once put together or move on. See also the rules of brackets, powers, roots and order of rain species.
* Statistics and Probability Learn about diagrams, set theory, observations, combinatorics and probability.
* Features Learn about the different types of functions and calculate or draw them into our drawing machine.
* Play Train the small table or rain species order.
* Tables See the "small" or "large" table.
Mathinary app is made by Site Project ApS, which is also behind the website regneregler.dkNaN Geometry Solver is the most advanced application for solving geometry problems.
NaN Geometry Solver will calculate all the parameters of the figure, if you enter the necessary data. The order of data entry depends on you!
- Do you want to calculate a side of the square? No problem. Nan Geometry Solver will do it for you. - Do you have an angle and a side of the right triangle? Perfect. Other values can be calculated.
None of your geometry tasks will be a problem now with NaN Geometry Solver. This application has very advanced, powerful and easy - to - use interface.
Additionally, it contains all the useful formulas which you will need to solve geometry tasks. But thats not enough! You do not have to figure it out how did you get a result. This application not only gives you the solution, it also shows you all the formulas which had been used. Pythagorean Theorem, sines and cosines are no longer a problemiMathematics is the best app on Android Market for the study of mathematics! With more than 120 topics, over 1000 formulas, attractive interface and with 7 solvers and calculators! Try it for free, if you like it you can buy iMathematics Pro!
================================ FEATURES ================================
✔ A complete porting of the famous iPhone version! ✔ 8 apps in 1: 7 calculators and 1 form! ✔ Over 1000 formulas, definitions and theorems! The more complete form on Android Market.. constantly updated! ✔ 7 magnificent Utilities to help you in the exercises: Quadratic Equations Solver, Fraction Approximator, Graphic Calculator, Advanced Calculator, Systems Solver, Matrices Solver, and math Glossary! ✔ Beautiful graphical user interface, simple and intuitive! ✔ Support for new High Resolution devices! ✔ Very complete form, divided into sections for an easy consultation! ✔ More than 50 Quizzes on the topics to test your knowledge! ✔ Links to Wikipedia for every topic! ✔ Possibility to try iMathematics for free or unlock it completely buying iMathematics Pro!"OMS Fractions Calculator" is handy tool for addition, subtraction , multiplication and division of fractions and mixed numbers (fractions with integer part). Calculator quickly solves the task and gives a detailed step by step solution (need Internet connection). Application gives you all calculations in detail and shows how to: - convert improper fractions to mixed numbers; - convert fractions to a common denominator; - simplify fractions; - convert mixed numbers to improper fractions. Calculator with detailed solutions helps you better understand how to solve task with fractions. And always will help parents check homework of their children. You can always use this and many other mathematical online calculators by visiting my website OnlineMSchool.com.
This calculator performs the following operations with fractions : multiplication, division , addition, subtraction , and reduces the fractions and converts the answer as a decimal . They are very easy to use: click on an empty entry field and use the keypad to type in the desired value at the bottom . If you want to enter a negative fraction, click on the small square in front of the input field and shot it appears the sign "-" (if you click this button again the "- " disappears) . Then select the desired operation by pressing the appropriate button on the left of the keyboard ( if you do not select the operation calculator will simply reduce fractions with output greatest common divisor - GCD ) . By clicking on the most right button, your answer becomes a value in the first input field , and you can continue a series of calculations.
AutoMath Smart Text Calculator supports: (photo calculator not yet available for most of the below) Any other math problems such as calculus, equation systems, complex math, graphing, table of values, and more"OMS Quadratic Equation Solver " is handy tool for solving quadratic equations. Quadratic equations calculator not only calculates the answer (discriminant and the roots of the quadratic equation), but also shows a detailed step by step solution (need Internet connection). Application gives you all calculations in detail and shows how to: - find discriminant; - find roots of quadratic equation. The advantage of this calculator is the fact that as the coefficients of the quadratic equation, you can input integer numbers, decimals and fractions. Calculator with detailed solutions helps you better understand how to solve task with quadratic equations. And always will help parents check homework of their children. You can always use this and many other mathematical online calculators by visiting my website OnlineMSchool.com.Math topics carefully written to make it easy to understand math, calculators that give explanations and intermediate results, and a collection of formulas. Does not require network access.
Mathinary is a powerful educational math tool for students and parents who help their children with math.
Mathinary contains formulas, explanations and calculators. The calculators give explanations, intermediate results and final results. The calculators are simulating how a person would calculate the result, by showing every step of the calculation including descriptions.
The topics in Mathinary are described with text, which has been carefully written to avoid difficult words, and making it simple for students and their parents to understand math. Mathinary is an invaluable app for children in school, their parents and others who needs help with math or those who just wants to freshen up their knowledge.
Mathinary is concentrated on math in school from the 5th to the tenth grade, but is also covering topics used in higher educations.
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This is the first sequel course to MAT 114. The content goals of the course are: to understand the definition of definite and indefinite integrals and the fundamental theorems of Calculus; to learn techniques for computing integrals in terms of elementary functions; and to learn how to apply these ideas to problems in geometry, physics, engineering, and beyond. In addition, the supplemental goals are: to adopt the language of Calculus; work towards proficiency in technical written/oral/visual communication; and learn mathematical problem solving strategies.
Syllabus, assignments, exam information, and ancillary materials for the course are available through Cal Poly's Blackboard system.
Integral Calculus finds great application in the computation volumes of irregular three dimensional shapes, such as the bucket of a front end loader. Image credit: LeTourneau Technologies, Inc..
Fall 2011, MAT 321, Introduction to Topology
The content goals of the course are: to understand the abstract definitions of topological spaces and continuous maps between them and their origins; learn the properties which distinguish types of topological spaces such as connectedness and compactness and the interplay of these notions with continuous maps; be exposed to a wide array of examples of topological spaces from mathematics and beyond. In addition, the supplemental goals are: to gain comfort with abstraction; learn the technical skills of proof writing and rigorous argument; and learn to communicate mathematics to other mathematicians.
Syllabus, assignments, exam information, and ancillary materials for the course are available to registered students through Cal Poly's Blackboard system.
A bio-molecular network as an example of a topological space. Researchers seek topological observables which can distinguish such networks from simple random graphs to explain animal diversity and adaptability. Image credit: Michael Laessig, University of Cologne.
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More About
This Textbook
Overview
Designed to demonstrate the essential mathematical concepts—comprehensively and economically—without re-teaching basic material or laboring over superfluous ideas, this text locates the necessary information in a practical economics context. Utilizing clear exposition and dynamic pedagogical features, Mathematical Tools for Economics provides students with the analytical skills they need to better grasp their field of study.
A short introduction to mathematics for students of economics
Demonstrates essential mathematical concepts necessary for economic analysis, such as matrix algebra and calculus, simultaneous linear equations, and concrete and discrete time
Incorporates applications to econometrics and statistics, and includes computational exercises illustrating the methods and concepts discussed in the text
Clear explanations and dynamic pedagogical features provide students with the analytical skills they need to better grasp their field of study.
Mathematical Tools for Economics is supported by an instructor's manual featuring solutions, available at
Product Details
ISBN-13: 9781405133807
Publisher: Wiley
Publication date: 11/28/2006
Edition description: Revised
Edition number: 1
Pages: 380
Product dimensions: 0.88 (w) x 9.21 (h) x 6.14 (d)
Meet the Author
Darrell A. Turkington is Professor of Economics at the University of Western Australia. He has a Ph.D in theoretical econometrics from the University of California, Berkeley and has held visiting appointments at Berkeley, the University of Warwick, the University of British Columbia, and Nuffield College, Oxford. He is co-author of the Econometric Society monograph, Instrumental Variables (1985), as well as author of Matrix Calculus and Zero-One Matrices (2002
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Text
Essential Calculus, by James Stewart. Cengage
Learning, 2007. There is a new edition available now for a lot
more money but any edition will do so I'd recommend the cheapest
one you can find. The same text is used in Calculus I and Calculus
III (MAT 191 and 211). In Calculus II we'll cover chapters
6,7,8,9.
The text is available in our campus bookstore. As with any
purchase you should shop around to get the best price. Used books
may be available.
Please do not imagine that you can pass this course without a
textbook. Students who try that always fail. The course is too
hard to learn without careful study. You'll need your textbook
starting on the first day of class.
Websites
Calendar of assignments
and tests
( This
will be updated frequently, so check back often.
Grading Policy, Make-up Work
Students' grades are based on homework, tests, and a final
exam.
Homework
=20% of grade
3 chapter tests
= 45% of grade (15% each)
Final exam
= 35% of grade
Homework is the most important thing on this list because
practice is the key to learning. People who do well on homework
usually do well on tests, but people who don't do the homework
always fail the tests.
I normally do not accept make-up work or give make-up tests.
Please arrange your schedule so you can finish the work on time
and take the tests when scheduled.
Minimum grades. Of course if you get 90% of all possible points you are
guaranteed to get an A, if you get 80% you will get at least a B, and so on.
These are minimum grades -- this is a very hard class
so your grade may be higher than that.
Exam Dates and Assignment schedule
Exam dates and paper-based assignments are listed on the
course calendar
Attendance Requirements
I normally do not require attendance except on exam days, but
long experience shows that students who miss a significant number
of classes always flunk, or have to drop out, and lose their
registration fees. If you are serious you will come to class,
work hard, and learn a lot of mathematics, but if you are not
serious please don't register for this class.
Academic Integrity
The mathematics department does not tolerate cheating.
Students who have questions or concerns about academic integrity
should ask their professors or the counselors in the Student
Development Office, or refer to the University Catalog for more
information. (
to providing reasonable accommodations for students with
temporary and permanent disabilities. If you have a disability
that may adversely affect your work in this class, I encourage
you to register with Disabled Student Services (DSS) and to talk
with me about how I can best help you. All disclosures of
disabilities will be kept strictly confidential. Please note: no
accommodation may be made until you register with the DSS in WH
D180. For information call (310) 243-3660 or to use
telecommunications Device for the Deaf, call (310) 243-2028.
Computer and Information Literacy
Computers can't do calculus for you, what you need are your brain cells.
However computers can generate nice diagrams and do tedious arithmetical calculations
that would take you a lot of time to do by hand, so we'll use them sometimes
in class. Most computer computer programs are designed to be pretty easy
to use, all you really need to be able to do is turn the machine on,
type in your name and password so you can log in, and read and follow
instructions. If you use a calculator read your manual!! If you
have lost the manual you can probably find one online -- just use a search
engine like Google or Microsoft Bing to search for one. You'll need to
use WeBWorK to do the homework problems, which means you'll need to have
access to the internet, use a web browser, and type in answers to math
problems. Don't worry about this -- just follow the instructions. If
you have trouble just ask me or somebody else to help.
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Eric Weisstein's World of Science supplies great, online encyclopedias in astronomy, physics, chemistry, and mathematics, as well as a biography of renowned scientists. Users can find excellent, concise explanations of...
Mathworld, hosted and sponsored by Wolfram Research, Inc., is an online mathematics encyclopedia intended for students, educators, math enthusiasts, and researchers. This amazing resource was compiled over 12 years by...
This website was initiated by Cory Futrell, a self-acknowledged math addict, who is currently a sophomore math and physics dual major at the University of Oklahoma. A key feature of the website is an encyclopedia with...
It's hard to believe it's all free! This trove of information from thefreedictionary.com offers all sorts of information on math. From algebra and integers to derivatives and polynomials, it's all here. By scrolling...
HyperMath is "a growing collection of examples of applied mathematics with links to their applications to problems in physics and astronomy." The author, Carl R. (Rod) Nave of the Department of Physics and Astronomy at...
| 677.169 | 1 |
More About
This Textbook
Overview
This workbook offers a variety of exercises, worksheets, and visualization that will help you prepare for success in math. Detailed explanations of methods and examples from actual case histories help make concepts understandable
| 677.169 | 1 |
This best-selling, classic textbook continues to provide a complete one-semester introduction to mathematical logic. The sixth edition incorporates recent work on Gödel?s second incompleteness theorem as well as an appendix on consistency proofs for first-order arithmetic. It also offers historical perspectives and many new exercises of varying difficulty,... more...
Schaum's Outline of Beginning Calculus, 3ed
1. Coordinate Systems on a Line
2. Coordinate Systems in a Plane
3. Graphs of Equations
4. Straight Lines
5. Intersections of Graphs
6. Symmetry
7. Functions and Their Graphs
8. Limits
9. Special Limits
10. Continuity
11. The Slope of a Tangent Line
12. The Derivative
13. More on the Derivative... more...
Transitions: Legal Change, Legal Meanings illustrates the various intersections, crises, and shifts that continually occur within the law, and how these moments of change interact with and comment on contemporary society.
Together the essays in this volume investigate the transformation of US law during moments of political change and explore... more...
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This website is a lesson plan to help teachers make computer science and engineering fun for students. By stating the...
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Computer Science and Engineering to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Making Computer Science and Engineering
Select this link to open drop down to add material Making Computer Science and EngineeringA common problem when students learn about the slope-intercept equation y = mx + b is that they mechanically substitute for m...
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A common problem when students learn about the slope-intercept equation y = mx + b is that they mechanically substitute for m and b without understanding their meaning. This lesson is intended to provide students with a method for understanding that m is a rate of change and b is the value when x = 0. This kinesthetic activity allows students to form a physical interpretation of slope and y-intercept by running across a football field. Students will be able to verbalize the meaning of the equation to reinforce understanding and discover that slope (or rate of movement) is the same for all sets of points given a set of data with a linear relationship 2 to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Movement with Functions: Lesson 2
Select this link to open drop down to add material Movement with Functions: Lesson 2 to your Bookmark Collection or Course ePortfolio
In this lesson, students use remote-controlled cars to create a system of equations. The solution of the system corresponds...
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In this lesson, students use remote-controlled cars to create a system of equations. The solution of the system corresponds to the cars crashing. Multiple representations are woven together throughout the lesson, using graphs, scatter plots, equations, tables, and technological tools. Students calculate the time and place of the crash mathematically, and then test the results by crashing the cars into 3 to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Movement with Functions: Lesson 3
Select this link to open drop down to add material Movement with Functions: Lesson Graphing Calculator App for iOS to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Online Graphing Calculator App for iOS
Select this link to open drop down to add material Online Graphing Calculator App for iOS to your Bookmark Collection or Course ePortfolio
This is a StAIR presentation that is meant to help teach sixth grade students how to solve basic one and two step equations....
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This is a StAIR presentation that is meant to help teach sixth grade students how to solve basic one and two step equations. As long as they have internet access, students will be able to work through this presentation and gain the necessary skills needed to solve one and two step equations. They will be assessed three different times through Equations StAIR Presentation to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material Solving Equations StAIR Presentation
Select this link to open drop down to add material Solving Equations StAIR PresentationThis resource has multiple concepts for geometry and trigonometry. The concepts are divided among chapters with links on...
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This resource has multiple concepts for geometry and trigonometry. The concepts are divided among chapters with links on common unknown concepts to help students understand the text. This resource also provides exercises that can be done by the students (answers are provided Math Page: Trigonometry to your Bookmark Collection or Course ePortfolio
Select this link to close drop down of your Bookmark Collection or Course ePortfolio for material The Math Page: Trigonometry
Select this link to open drop down to add material The Math Page:
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Schaum's has Satisfied Students for 50 Years.
Now Schaum's Biggest Sellers are in New Editions!
For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates its 50th birthday with a brand-new look, a new format with hundreds of practice problems,... more...
Trigonometry has always been the black sheep of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their... more...
Trigonometry focuses on the principles, operations, formulas, and functions involved in trigonometry. The publication first takes a look at the six trigonometric functions, right triangle trigonometry, and radian measure. Discussions focus on radiance and degrees, unit circle and even and odd functions, length of arc and area of a sector, trigonometric... more...
CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. CliffsQuickReview Trigonometry provides you with all you need to know to understand the basic concepts of trigonometry — whether you need a supplement to your... more...
Trigonometry: A Complete Introduction is the most comprehensive yet easy-to-use introduction to Trigonometry. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of trigonometry including the theory and equations of tangent,... more...
Stan Gibilisco is one of McGraw-Hill?s most diverse and best-selling authors. His clear, friendly, easy-to-read writing style makes his electronics titles accessible to a wide audience and his background in mathematics and research make him an ideal handbook editor. He is the author of The TAB Encyclopedia of Electronics for Technicians and Hobbyists
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Bob Miller's Basic Math and Pre-Algebra for the Clueless [NOOK Book]...
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This Book Pre-Algebra for the Clueless enhances students' facility in these techniques and in understanding the basics.
This valuable new addition to Bob Miller's Clueless series provides students with the reassuring help they need to master these fundamental techniques, gives them a solid understanding of how basic mathematics works, and prepares them to perform well in any further mathematics courses they 15, 2014
I'm a math teacher today because of being in Miller's math class
I'm a math teacher today because of being in Miller's math class......ccny 1980
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Anonymous
Posted April 6, 2006
Math Made Easy!
Bob Miller takes very difficult concepts and makes them extremely easy to grasp. It is the one math book that will not make you tear your hair out of your head! The author uses a bit of humor and emotion to make math understandable to the average layman. The books are meant to be a supplement to whatever math text you are using. After Bob explains the concepts you will breeze through your textbook's examples. A great book at a great price!
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Anonymous
Posted May 29, 2005
A Good Review of High School Mathematics
This text is easy to understand and gives a good review for those who need to brush up on basic mathematics. It is intended for use in conjunction with and supplementary to a course, but is also accessable to those of us who just need to dust off principles already learned. There are not many exercises, but those included all have step-by-step solutions. I would recomend this text as a springboard into further study.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
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Document Actions
About the Mary P. Dolciani Mathematics Learning Center
The Mary P. Dolciani Mathematics Learning Center (formerly called the Math Learning Resource Center) opened in 1971 through a grant secured by Professor Mary P. Dolciani, a faculty member in the Mathematics Department. The first of its kind in CUNY and one of the first in the country, it was an audio-visual Center with the main thrust being to aid underprepared students in the learning of calculus and finite mathematics. Students progressed through courses using in-house prepared slides and tapes that covered all the topics in the course. Tutors were available to answer students' questions. The Center was upgraded through a generous grant from the Dolciani-Halloran Foundation in 1986, after the death of Professor Dolciani.
Location
The Center was originally located on the 12th floor of the North Building. Upon its move to 51st Street in 1973, the Center was able to house three sections of MATH 100 simultaneously. In 1979, the Center moved to the second floor of Thomas Hunter where the Access Center is now located. Today the Center is located in Rooms 300 through 306A HN.
Upgrades and Expansions
Timeline of Location of Dolciani Mathematics Learning Center
1986:
The Center was upgraded to a computer facility and had as its primary role, the delivery of remedial mathematics instruction.
1990:
The Center expanded to provide support services to students in all math/stat courses.
1995:
The Center expanded to provide classroom instruction in calculus and statistics.
2000:
The Center expanded physically to incorporate the delivery of computer-based pre-calculus, and statistics instruction.
Today's Center
As part of the Department of Mathematics and Statistics' Strategic Plan, the Center has identified broad goals for the next seven years. In addition to our current responsibilities we hope to:
• Continue to encourage other departments using math/stat in their courses to send their students to our Center for multi-media support. • Explore the feasibility of offering on-line tutorial assistance during the hours in which the Center is closed. • Continue to support curriculum implementation and enhance the learning experience. Explore the feasibility of offering on-line tutorial assistance during the hours in which the Center is closed. • Create new support materials for upper-level courses. • Expand our on-line materials. • Work more closely with the Welcome Center and Advising Services to expand our visibility during their orientation programs. • Conduct focus groups at satellite campuses to explore what is needed to better serve this population. • Sponsor Open Houses/luncheons for faculty and staff to update them on new offerings and equipment. • Re-institute our monthly Round-Table Discussions on new technology and topics of interest to students, faculty and staff. • Formalize our outreach to staff members at the college so that those who are preparing to come back to school, take math/stat courses or sit for professional exams can receive academic support. • Expand our staff development programs. • Re-institute our linkages with high schools in the area to identify strong high school seniors to train as tutors. • Explore the possibility of re-instituting internal internships or field placements with Teacher Education/McNair programs and other scholar programs. • Continue to work towards NLCA accreditation.
What You Can Do to Help
- Encourage students to come to the Center. - Volunteer to write a lesson on selected topics needed. - Identify students (or adjuncts) who can tutor or assist in other DMLC related work.
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Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration and Martingales; measure and topology and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying... more...
This major textbook on real analysis is now available in a corrected and slightly amended reprint. It covers the basic theory of integration in a clear, well-organized manner using an imaginative and highly practical synthesis of the 'Daniell method' and the measure-theoretic approach. It is the ideal text for senior undergraduate and first-year graduate... more...
Your light-hearted, practical approach to conquering calculus Does the thought of calculus give you a coronary? You aren't alone. Thankfully, this new edition of Calculus Workbook For Dummies makes it infinitely easier. Focusing "beyond the classroom," it contains calculus exercises you can work on that will help to increase your confidence and... more...
Fundamentals of Calculus encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills. In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets. Specifically, finite calculus... more...
First course calculus texts have traditionally been either "engineering/science-oriented" with too little rigor, or have thrown students in the deep end with a rigorous analysis text. The How and Why of One Variable Calculus closes this gap in providing a rigorous treatment that takes an original and valuable approach between calculus
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Fall 2012 Elementary Algebra (5 units)
Section 2123 Class Begins 8/20/2012
Course Description
This course will cover the topics of operations with real numbers, solution techniques of single-variable linear equations and inequalities, graphing linear equations in two variables, solving systems of linear equations, simplifying and combining polynomials, calculating roots and radicals, and solving quadratic equations. Students will: learn to solve applied problems using linear equations, use slope to graph two-variable linear equations, solve applied problems using two variables, and solve quadratic equations by factoring and using the Quadratic Formula.
Instructor: M Snider
Email: msnider@mendocino.edu
After the class has started, please use MyMathLab Private Messages for communication.
Estimated Time per Week: Students can expect to spend approximately 15 hours per week reading, working on research assignments, taking quizzes and participating in online class discussions. This class is not self-paced. Specific assignments and discussions are meant to be completed for the whole class at the same time.
Special Requirements: Log into ETUDES by the first day of class and begin follow the instructions. Be sure to go through the orientation and follow directions to MyMathLab.
Assignments & Tests: Assignments and tests are outlined on MyMathLab.
Additional Comments: The entire course will be conducted online through the MyMathLab course management system. Students are required to have Internet access, an active email account, the ability to use word processing, conduct Internet searches, attach files, send emails and private messages, and work independently.
New to Etudes: Here is an Online Orientation (Flash presentation opens in a new window) that will show you the basics of how to use Etudes. Here is a flash tutorial (Flash presentation opens in a new window) that demonstrates the log in protocol. Be sure to check System Requirements before getting started with Etudes. You need to do this on each computer you use while taking a class through Etudes.
Etudes Course: You will log into the Etudes classroom with the log-in information provided below.
Login ID
Password
First 2 letters of first name +
First 2 letters of last name +
Last 5 digits of Student COLLEAGUE ID
(Type using all lower case letters)
Example: Jose A. Garcia
Student ID: 1021945
Username = joga21945
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Learning outcome
This course will greatly enhance your skills in many areas of mathematics, giving you a greater understanding of core mathematics components such as geometry, trigonometry, calculus and more as well as expanding your knowledge base in areas such as chance, data distributions, statistics, probability, correlations and regression.
You will learn about using binomial expansions for problem solving and will understand the relationship between the graphs of functions and their antiderivatives.
You will be able to confidently create graphs and make advanced calculations such as straight-line calculations, kinematics, motion, vectors, algebra, binomial expressions, and quadratic functions.
The free online Diploma in Mathematics course from ALISON gives you a comprehensive knowledge and understanding of key subjects in mathematics. This course covers calculus, geometry, algebra, trigonometry, functions, vectors, data distributions, probability and probability and statistics. Math qualifications are in great demand from employers and this Diploma will greatly enhance your career prospects.
License
Release Date
07 May 2013
Content
Course Duration (Avg Learner)
15-20 Hours
Video/Audio
None
Audio Only
None
Animation
LowClaire GrossmanUnited Kingdom
it was great and at last I've passed with 84% i'm so chuffed I will get the Diploma framed and put it on the wall'
Not bad for somebody whose had 2 strokes 2015-02-17 12:02:55
Cain A MupasiUnited Kingdom
Very well put together. Just needs more examples to try out and then the right answers to check that I have done them right. 2015-02-05 00:02:43
Glen MashalaSouth Africa
This is very good, a very good way to improve my understanding mathematics as an engineering student. 2014-12-01 17:12:52
Michael O MahonyIreland
I thought the course was very good and comprehensive. Some of it I was very familiar width but other parts of the course were well explained and good examples provided. 2014-07-16 19:07:05
Savitri KawallTrinidad and Tobago
really easy to understand new and old math topics
2014-06-17 16:06:39
MOHAMED SIYATH NASEERSri Lanka
It is successful course, It is giving us more knowledge about Mathematics. 2014-06-07 05:06:11
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Contains nine new introductory chapters, in addition to updated chapters from the previous edition
Contains over 1000 individual exercises and selected solutions
Companion website contains hints and solutions to all exercises
Biggs' Discrete Mathematics has been a best-selling textbook since the first and revised editions were published in 1986 and 1990, respectively. This second edition has been developed in response to undergraduate course changes and changes in students' needs. New to this edition are chapters on statements and proof, logical framework, and natural numbers and the integers, in addition to updated chapters from the previous edition. The new chapters are presented at a level suitable for mathematics and computer
science students seeking a first approach to this broad and highly relevant topic. Each chapter contains newly developed tailored exercises, and miscellaneous exercises are presented throughout, providing the student with over 1000 individual tailored exercises. This edition is accompanied by a website containing hints and solutions to all exercises presented in the text, providing an invaluable resource for students and lecturers alike. The book is carefully structured, coherent and comprehensive, and is the ideal text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory, coding theory
and abstract algebra.
Readership: Students and lecturers in mathematics and computer science
Norman L. Biggs, Professor of Mathematics, London School of Economics, University of London
"This is a new edition of a successful textbook ... this revision is particularly welcome ... The text is written in a fluent but rigorous style and should appeal to sixthformers and undergraduates who are alienated by more formal presentations. There are plenty of approachable exercises, ranging from easy riders to establish technique to more challenging problems which introduce new ideas, and a bonus is that all the answers are available on a companion web-site. I can thoroughly recommend this text." - The Mathematical Gazette
"A well known definition says that a textbook is a book such that everybody thinks he can write a
better one. Biggs' Discrete Mathematics is an exception - not only for its wide range of topics and its clear organization but notably for its excellent style of explanation." - EMS
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Developed as an open source project, SAGE is a comprehensive mathematics software that uses other open source apps and the Python programming language to help you study elementary, advanced, pure, or applied mathematics. Considering the complexity of the tools included in the app, SAGE can be successfully used both for study and research projects.
Open the SAGE notebook in your web browser or in the command line
The SAGE installation creates a local server that enables you to access the app functionalities via a web console, or by using the command line. Take into account that the server must be started each time you are using SAGE, and you must stop it when you are done.
The SAGE user interface, regardless if you open it in a browser or in the Terminal, is considered to be a notebook, where you get to input mathematical expressions, embed graphics, plot 2D or 3D graphs, and so on.
Perform mathematical calculations by using basic and complex functions
SAGE provides support for basic algebra and calculus, plotting, unvariate and multivariate polynomials, linear algebra, or finite groups. At the same time, the app includes support for algebraic geometry, creating elliptic curves, Dirichlet characters, or modular forms.
Since SAGE integrates a large collection of algorithms, you can use the app as a calculator for complex functions. All in all, SAGE puts together more that 100 different open source packages that deal with different mathematical problems.
Comprehensive software suite that can help you study various math problems
SAGE is a reliable, open source mathematical software that can be successfully employed when studying various branches of mathematics. SAGE can deal with algebra, geometry, calculus, graph theory, cryptography, and much more. Thanks to all the built in capabilities, SAGE can also be used as a complex calculator.
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Pre-algebra
The ACT covers a wide range of topics in pre-algebra, such as prime
numbers, factors, fractions, percentages, exponents, means, medians and
probability. Our ACT Companion
tutorial reviews the basic properties of numbers that are important
for the ACT.
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Descriptions and Ratings (2)
This is a set of notebooks (created by Martin Brown) which allow students to visualize and experiment with math concepts typical of the Calculus I and II courses. There are a lot of interactive examples that allow students to visualize and reflect on the the answer, rather than the detail of the derivations.
Symbolic Math Toolbox™ extends MATLAB by providing functions for solving and manipulating symbolic expressions. In R2007b, we introduced a notebook interface called the MuPAD Notebook App. It provides an interactive environment for performing symbolic calculations and creating a dynamic document.
The concepts that are covered are:
Vectors
Complex Numbers
Differentiation
Integration
Taylor Series
Multivariable Calculus
Ordinary Differential Equations
Laplace Transform
Vector Calculus
Linear Algebra
A set of hyperlinked maths notebooks which allow Y1 and Y2 engineering students to visualize and experiment with difficult maths concepts. The aim is to allow students to do lots of examples, in an interactive fashion, without focussing on the derivation. The notebooks encourage the students to visualize and reflect on the the answer, rather than the detail of the derivations. As such it can also be used in lectures.
To run the notebooks, simply unzip mathexplorer.zip in a folder, start Matlab and double click on the MathExplorer.mn file. This has all the other files linked in.
The green variables at the top are for students to alter and re-evaluate the notebook. A set of exercises are at the end of each file.
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About the Apps
Calculus is math in motion, and in many ways awakens the curious mind. When points, lines, and curves start to move, it makes math more applicable to the world around us. If taught correctly, calculus could be the springboard to a wide variety of careers in physics, astronomy, aerospace engineering, and several others.
In this section, we cite apps that serve as intros to calculus and pre-calculus, which is often taken in the junior or senior years of high school. Graphing polynomials, sin, cos, tangent, square root, absolute, and other functions becomes essential in order to visualize movement of points on the coordinate plane.
The toolbox of calculus apps consists of calculator apps, reference apps, and teaching apps. Reading about concepts and definitions is important, but acquiring a true understanding of these basic concepts and definitions is critical. That is why we recommend these apps among many serviceable options.
Calca is a new entry to the App Store that provides a fresh take on calculations and math problems. It helps students develop problem solving skills by requiring them to think about domain (inputs, variables) and ranges (outputs). Using written English to represent problems, students will learn how to relate real world situations to mathematics.
Wolfram Calculus Course Assistant is an app that will support new calculus students and perform any calculation they are likely to encounter. The calculation engine by Wolfram Alpha is excellent, but this app's interface is specifically tailored to high school calculus so it's easy for students to quickly access the help they need.
After becoming familiar with the basics, one may want to check-out Pre-Calculus to test definitions and conceptual understanding, just as you would refer to a text book. You will quickly be directed to the desired category, a series of well-documented procedures and examples that will assist the student navigate through these important topics.
Of course, any calculator used for calculus requires more than add, subtract, multiply and divide buttons. The best and most comprehensive calculator for this topic is Solve - A calculator like no other.
The final app is Math Pro, which boasts an extremely professional approach to solving the problems recently learned and practiced. By filling in the missing data for given inputs to a function, the calculator reveals the solution along with an explanation, if necessary.
Using these recommended calculus apps will provide great home-practice sessions that every student needs in order to excel in math class.
Comments & Suggestions
Have a suggestion for an educational app for this category you think we should feature? Let us know.
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Matrices, Geometry & Mathematica
This is not your parents' linear algebra course. The focus is on matrix
action, the geometry of matrix action, and the underlying reasons for what
we see, how we solve, and what makes it all work. The foundation is the
singular value decomposition of matrices.
Here's the list of lessons.
Perpendicular Frames
Ill-conditioned Matrices and Roundoff
2D Matrix Action
Subspaces, Spans, Dimension, etc.
Using Aligners, Stretchers and Hangers
Eigensense: Diagonalization, Exponential, etc.
SVD Analysis of 2D Matrices
The Spectral Theorem for Symmetric Matrices
3D Matrices
Function Spaces and RMS Approximation
Beyond 3D
Here are some pages with snapshots of problems from the course.
Be careful if you look at these. They are
chock full of graphics, and may take very long to download.
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points of nondierentiability for the function graphed be15
More Trigonometric Identities
Concepts:
The Addition and Subtraction Identities for Sine and Cosine
The Cofunction Identities for Sine and Cosine
Identities That You Should Learn
15.1
Addition and Subtraction Identities for Sine and Cosine
Theorem 1
13
Trigonometric Graphs
Concepts:
Period
The Graph of the sin, cos, tan, csc, sec, and cot Functions
Applying Graph Transformations to the Graphs of the sin, cos, tan, csc, sec, and cot
Functions
Using Graphical Evidence to Make Conjectures about Iden
17
Triangle Trigonometry
Concepts:
Trigonometry for Acute Angles - The Right Triangle Perspective
Trigonometry for Acute and Obtuse Angles
The Law of Cosines
The Law of Sines
The Problem with SSA
Solving Application Problems that Involve Acute and O
19
Parametric Equations And Polar Coordinates
Concepts:
Sketching Graphs of Parametric Equations
Converting Between Polar Coordinates and Cartesian Coordinates
Sketching Graphs of Polar Equations
(Sections 10.5-10.6)
There are a lot of graphs which doRates of change and derivatives Chapter 2: Practice/review problems
The collection of problems listed below contains questions taken from previous MA123 exams.
Average rates of change (Word Problems) [1]. A train travels from A to B to C. The distance froMA109, Activity 1: Modeling the Real World (Section P.1, pp. 4-9) Today's Goal:
Date:
Assignments:
Distribution of the syllabus & discussion of course policy. We then study simple examples of how the methods of Algebra allow us to describe various You - Elementary Calculus FINAL EXAM
SPRING 2008 04/29/2008SPRING 2007 04/30/2007FALL 2006 12/12/2006 Elementary Calculus THIRD MIDTERM
FALL 2008 11/19/2008 THIRD MIDTERM
FALL 2006 11/15 SECOND MIDTERM
SPRING 2007 03/07/2007 Elem. Calculus FINAL EXAM
SPRING 2007 30 b
MA 123 Elem. Calculus 3rd MIDTERM
SPRING 2007 11
MA 123 Elem. Calculus
FIRST MIDTERM
SPRING 2007
02/07/2007
Name:
Sec.:
Do not remove this answer page you will turn in the entire exam. You have two hours to do this
exam. No books or notes may be used. You may use a graphing calculator during the exam, bFall - Elementary Calculus FINAL EXAM
FALL 2008 12/17/2008 points of nondierentiability for the function graphed be
Computing Derivatives Using the Denition of the Derivative
1. You would like to know f (2). Suppose you dont have a formula for f (x) (Thus, none of the shortcut
formulas can be applied ) but you happen to know
3 x2 h + 15 x h2 + 19 h
f (x + h) f (x) =
x2
Computing Some Integrals determined by the right e
Related Rates (page 21), Solutions
1. Two trains leave a train station at 1:00 PM. One train travels north at 70 miles per hour. The
other train travels east at 50 miles per hour. How fast is the distance between the two trains changing
at 4:00 PM?
Soluti
Related Rates
1. Two trains leave a train station at 1:00 PM. One train travels north at 70 miles per hour. The other
train travels east at 50 miles per hour. How fast is the distance between the two trains changing at 4:00
PM?
2. Suppose the height of a
Computing Derivatives With Formulas Some More (pages 14-15), Solutions
This worksheet focuses on computing derivatives using the shortcut formulas, including the power
rule, product rule, quotient rule, chain rule, and exponential functions. We will make
More Derivative Formulas
This worksheet focuses on computing derivatives using the shortcut formulas, including the power
rule, product rule, quotient rule, chain rule, and exponential functions. We will make constant use of
these techniques throughout th
Maximum and Minimum Values (page 18), Solutions wh
Limits (pages 8-9), Solutions
This worksheet focuses on limits and the related idea of continuity. Many limits can be computed
numerically (through a table of values), graphically, and algebraically. When possible, try to compute
each of the limits below
Limits
This worksheet focuses on limits and the related idea of continuity. Many limits can be computed
numerically (through a table of values), graphically, and algebraically. When possible, try to compute
each of the limits below using all three methods
Introduction to Integration (page 22), Solutions
sample point.
(b
Introduction to Integration sample
point.
(b) Divide [0, 4] into
Exponential Function Word Problems
Exponential growth is modelled by
y = y0 ekt
There are four variables, the initial amount, y0 , the time t, the growth factor k, and the current amount
y. You should be comfortable with nding any one of these four, givenComputing Derivatives With Formulas (pages 12-13), Solutions
This worksheet focuses on computing derivatives using the shortcut formulas, including the power
rule, product rule, and quotient rule. We will make constant use of these techniques throughout t
Formulas for Derivative
This worksheet focuses on computing derivatives using the shortcut formulas, including the power
rule, product rule, and quotient rule. We will make constant use of these techniques throughout the rest
of the semester. Invest the t
Computing Derivatives With Graphs (page 10), Solutions
1. The graph of the function y = f (x) is shown below, along with the graph of the tangent line to
this curve at x = 2. Determine f (2).
Solution: f (2) is the slope of the tangent line to y = f (x) a
Computing Derivatives Using the Denition of the Derivative (page 11),
Solutions
1. You would like to know f (2). Suppose you dont have a formula for f (x) (Thus, none of the
shortcut formulas can be applied ) but you happen to know
3 x2 h + 15 x h2 + 19 hComputing Some Integrals (page 25), Solutions dete 9: Computing some integrals (pp. 189-205, Gootman)
Understand how to use basic summation formulas to evaluate more complex sums.
Chapter
Goals:
Understand how to compute limits of rational functions at innity.
Understand how to use the b
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Nutley Excel course is designed to build on algebraic and geometric concepts. It develops advanced algebra skills such as systems of equations, advanced polynomials, imaginary and complex numbers, quadratics, and concepts and includes the study of trigonometric functions. Algebra 2 is vital for students? success on the ACT, SAT 2 Math, and college mathematics entrance exams.
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Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only... more...
"For high school seniors or college freshmen with a background in algebra and trigonometry, the book should provide a good introduction to matrices, vector algebra, analytical geometry, and calculus. The work's solid modern mathematical content and its personality recommend consideration as a text or as stimulating supplementary reading." ? American... more...
This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics. Focusing upon problems with one independent variable, the text connects the abstract theory to its use in concrete problems. It offers a working knowledge of relevant techniques, plus an impetus for further study. Starting with an... more...
Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition. more...
Based on a series of lectures given by I. M. Gelfand at Moscow State University, this book actually goes considerably beyond the material presented in the lectures. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Considerable attention is devoted to physical... more...
Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x , and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential... more...
This classic text by a distinguished mathematician and former Professor of Mathematics at Harvard University, leads students familiar with elementary calculus into confronting and solving more theoretical problems of advanced calculus. In his preface to the first edition, Professor Widder also recommends various ways the book may be used as a text... more...
Understanding calculus is vital to the creative applications of mathematics in numerous areas. This text focuses on the most widely used applications of mathematical methods, including those related to other important fields such as probability and statistics. The four-part treatment begins with algebra and analytic geometry and proceeds to an exploration... more...
This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to... more...
Excellent text provides basis for thorough understanding of the problems, methods and techniques of the calculus of variations and prepares readers for the study of modern optimal control theory. Treatment limited to extensive coverage of single integral problems in one and more unknown functions. Carefully chosen variational problems and over 400... more...
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7.95,"ASIN":"1934968390","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":7.95,"ASIN":"1933241586","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":7.95,"ASIN":"1933241578","isPreorder":0}],"shippingId":"1934968390::UmRwyaAr6ZOFXWMyTiNqF%2FPOK%2Fm3GP87mwuuAk5vA8Tl5e27qtk53qchhyg5g9m4PhBraIgDOlc0mU1%2Bc%2BfQlPdnIe0e8EWobkzOMlxyMcM%3D,1933241586::akzHUeWREy%2B7ZI5ybjO%2FLcZp6CAqfBVfLXPH%2F9SPN%2BYeJDP1lSGq3J3rkjAq%2FKM6j0dHrq%2ByIw%2Fe8Co7m6KM8olhukRC4OBySToOrpVq6sU%3D,1933241578::MZfYV%2Bt1FclddikUyBxinhZ%2B0L%2FD750nWvJ5Xj8pGe7E%2F%2BzupIkrFCWiBDe7%2B5kS21RQDsoBaRm0H1a0dCSjPQO7qDMJdFaJCK5P2btumak word problems workbook, I would have expected problems that require more concept-level thinking (what operation is needed here?). The problems provide plenty of repeat practice for basic math functions, but there's not much mix of types of problems in each lesson, so the student isn't really required to do much critical thinking in figuring out what approach to use in solving the problem. Once the student solves the first problem or two, the rest of the problems are pretty predictable. I would prefer to have quicker math functions involved if it meant my daughter had to spend more time critically evaluating the path to the solution.
Will write a second review later; but, just wanted to let parents/readers know that I browsed through the book and it looks great. My daughter did 2 pages of it and the questions in books are already picking her brain!!! It is less boring (better than plain old additions/substractions/multiplication/division exercise rut)! She loves to check on the net to see how many meters are in a kilometer to solve the problems in the book. So far so good; keeping my fingers crossed.
I got this to help my daughter keep up on her math during the summer. I have used the Kumon workbooks since my daughter was in Kindergarten. She is a fifth grader now and I think these books are a great helper in addition to her school studies.
I love the kumon books great work and I recommend it to kids who need practice my son loves the little pictures but its mostly little examples and worksheets I bought almost all they offer in math and love all of them
If your kid has been to Kumon, you know what is involved - yes, the daily grind for the kid and the parents. If you like that grind (each of the Kumon franchise will tell you how essential it is) then of course you do not have to buy this book.
However, for rest of us, who questions that grind, this is an easier way to get the juice of the course but without the endless repetitions - at a fraction of the cost. The problems are not same as what a Kumon franchise offers. But that really did not matter. All problems are very nicely created. The difficulty level progresses through the course. And you can always go back to a previous level if you need to. I suggest you do not let your kid to mark the book to make this last part easier.
The price of the book is right. However, I wish the book should have been thicker with more problems - of course a 80 page book cannot be sufficient for the entire year even if the price goes up a bit.
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Introduction to Maple
Basic Maple Syntax and Operations:
A MAPLE command is a statement of a calculation followed by a either semicolon or a colon. If followed by colon, the result will be stored but not displayed.
Example: 12+20 followed by ; or : in Maple gives:
> 12+20;
32
> 12+20:
colon (:) suppresses the display of the output.
Practice: Download the attached Maple file and follow along!
(To download the maple file, right click on the file, then choose "save link as..".)
Arithmetic operations:
The symbols +, -, * (or . ), /, and ^ denote addition, subtraction, multiplication, division, and exponentiation. When a string of operations are specified in a command, MAPLE first does exponentiations, then multiplications and divisions, then additions and subtractions. To change the order, use parentheses.
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Mathematics Career Profiles A collection of essays whose authors describe a wide variety of careers for which a background in the mathematical sciences is useful. They provide practical answers to the question: "Why should I study math?"
Careers in Mathematics A variety of essays by scholars in mathematics that describe a wide variety of careers for which a background in the mathematical sciences is useful. They provide practical answers to the question: "Why should I study math?"
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Chapter 12: Equations and Functions
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Description
Presents information about equations, functions, and probability, including writing expressions and equations, solving equations using addition and subtraction, solving equations using multiplication and division, an introduction to functions and graphing functions, an introduction to probability, finding outcomes, and understanding the probability of independent events
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Use appropriate technology to solve mathematical problems and to judge the reasonableness of results.
Be able to use elementary algebra and geometry concepts in applied problems.
Be able to analyze and interpret data using a variety of graphs and basic statistics.
Alignment with Institutional Core Learning Outcomes
Outcome Assessment Strategies
Intelitek on-line activities including end of section tests and final evaluation.
Quizzes and examinations.
At least 1 project in which real world sustainability scenarios, requiring mathematical solutions, must be successfully analyzed and solved by the individual learner. Solution path must be clearly documented.
Graded homework.
Participation in at least 2 online discussions.
Course Content (Themes, Concepts, Issues and Skills)
Green problem-solving concepts:
Collecting and analyzing data to determine known and unknowns when evaluating energy production, consumption, efficiencies, and environmental impacts.
Demonstrating ability to develop a verbal model of a problem to aid in developing equation(s) to solve energy problems and conduct cost/benefit estimations.
Using formulas to solve for unknowns when evaluating energy alternatives.
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Achieving Tabe Success in Mathematics, Tabe 9 and 10 Level D
9780077044695
ISBN:
007704469X
Publisher: McGraw-Hill/Contemporary
Summary: TheAchieving TABE Successfamily is designed to provide complete skill preparation and practice for TABE 9&10, encompassing Reading, Mathematics and Language, for levels E, M, D and A. This series of books will help students achieve NRA gain through targeted instruction that specifically addresses TABE 9&10 skills. Achieving TABE Success ...workbookscontain the following features: TABE 9&10 Correlation Charts Each tex...t contains a TABE 9&10 Correlation Chart that links each question to targeted skill lessons, enabling instructors and students to build a personalized study plan based on skill level strengths and weaknesses. Pre-tests and Post-tests Each workbook begins with a pre-test and a skills correlation chart to help diagnose strengths and weaknesses and determine TABE readiness. The format of each pre- and post-test matches that of the actual TABE test. Targeted TABE Skill Lessons Each lesson specifically targets a TABE skill. Students work with the innovative lesson format that provides step-by-step instruction to help insure success. The Mathematics lessons offer plenty of instruction and practice to help master each TABE skill. In the Reading and Language workbooks, the lessons are divided into four parts for a graduated approach to learning: Introduceclearly defines, explains, and illustrates the skill, and includes examples. Practicepresents work related to the skill just introduced. Applyreinforces the skill through activities and exercises. Check Upevaluates student comprehension. Unit Reviews and Math Glossary Unit reviews are divided into two parts: Review, which summarizes unit content, and Assessment, to determine student understanding. Mathematics texts contain a Glossary of Common Terms to help students with the language of math. Achieving TABE Success in Reading ...Readersare coordinated with their respective Reading workbooks, to strengthen skills by applying examples and questions that are pertinent to the skill covered in the workbook. Text/TABE Level Content Level Level E 2.0 - 3.9 Level M 4.0 - 5.9 Level D 6.0 - 8.9 Level A 9.0 - 12.9
Contemporary is the author of Achieving Tabe Success in Mathematics, Tabe 9 and 10 Level D, published under ISBN 9780077044695 and 007704469X. One hundred Achieving Tabe Success in Mathematics, Tabe 9 and 10 Level D textbooks are available for sale on ValoreBooks.com
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Description
Algebra Helper is a great tool for any students from upper elementary to college. It provides concise flip cards to summarize important algebraic formulas so you don't need to worry about the formula you always forget. Algebra Helper includes a powerful tool, Quadratic equation solve, which has amazing capabilities to solve any quadratic equations, even with complex roots. Scratch Pad is also included so you would no longer need to scramble for paper and pencil while doing your math. In additional to solve math problems, Algebra Helper also provides a sophisticated organizing tool. Of course, you are going to have some fun with voice recognition toy so that you and your friends can have some fun while doing your homeworkFor bug reports or general feedback, email us to appfeedback@chegg.com or tweet @Chegg #androidapp problemGot a problem with homework? Get the Brainly app and ask questions about what's causing you trouble! Now, when you have a problem with some subject, you can, free of charge, quickly and from everywhere use your smartphone to get help with your homework focuses•4th Grade Math Genius includes both practice mode and quiz mode. Both modes include extensive numbers of real test questions in association with learning expectations for 4th grader.
•4th Grade Math Genius is a part of successful test prep series, which provides gradual and consistent approaches in math learning and teaching.
•For each question, you can look up the learning goal and expectation of skill mastery. Each question is also an exemplary tool for a specific learning category.
•4th Grade Math Genius is a must-have reference and incredible resource for any parents, teachers and students both at school and at home.
•4th Grade Math Genius is a integrated component of math series, widely viewed as an innovative series addressing various components of math learning from elementary school to college.
•Standardized tests are playing increasingly important roles at school and career development. The most effective ways to improve scores on standardized tests is to constantly expose the student to the test at all learning levels. 4th Grade Math Genius provides a wonderful opportunity for students to practice and prepare for standardized tests.
• Easy to read and share God's Word • Advanced and friendly interface to make reading God's Word fun and interesting • Read in a number of languages • Single click to move from verse to verse, or chapter to chapter • Easy Page Turner to navigate to any verses with ease • Bookmark function to remember your cherished verses
Talking Bible, Gospels is a fabulous and innovative tool to study and share God's Word. Talking Bible series made reading Bible a fun and interesting adventure.
Taking Bible series is an innovative application with many effective functions and user-friendly features.
It can read the Bible in a number of languages. With a simple touch, you can navigate instantly from verse to verse, or from chapter to chapter. With one click bookmark function, you can easily remember your cherished verse and return to the verse whenever you prefer.
• Algebra Tests and Solutions is an incredible algebra learning, testing and teaching resources for any parents, teachers and students.
• Algebra Tests and Solutions is a comprehensive Algebra reference book and a collection of necessary tools for algebra learning and teaching. Algebra Tests and Solutions can be used by any students, parents and teachers.
• Algebra Test Problems and Solution section is a wonderful and necessary resource for any teachers, parents and students at school and at home. There are a large number of test problems and solutions. For each test problems, there is a knowledge check at the end to summerize the goals and expectation for this specific problem.
• Algebra Tests and Solutions also includes a collection of algebraic tools, which make it easy to do algebra homework or check your answers. Quadratic Equation Solver, Linear Equation Solver, Linear System Solver and Circle Problem Solver are four amazing features with tremendous capabilities.
• Quadratic Equation Solver can solve any quadratic equations, even with complex roots.
• Linear System Solver and Circle Problem Solver are two very popular features and are frequently used in problem solving.
• Algebra References and Formulas section is a great reference source and is an incredibly efficient way to summarize important algebraic formulas. Just swipe your way through many useful references and formulas.
• Scratch pad is included so you would no longer need to scramble for paper and pencils while doing your math.
• Note Creator is a sophisticated organizing and planning tool. You can use this tool to keep track your progress, take notes and more.
• Free We Talk Pro • Professional Synthetic Voice Engine with great user flexibility • Set your preferred voice by adjusting speech pitch and speech • Includes preset male voice, female voice and child voice • Simple type and it talks for you • Wonderful utility tool for many speech impaired or with medical conditions • Many language packages are included in the app, e.g. American English, British English, Italian, French, German, Chinese, Japanese and Korean etc. Simply pick the language and enter the text in that language, it talks with perfect local accents. • Surprise your friend with your own special voice setting • Useful, but could be hours of fun as well. • Enjoy and make good use of this powerful voice engine
• Five levels of Sight Words from pre-K to 3rd grade • Most effective by learning sight words in a sentence setting • Present both lower case and upper case sight words at the same time • Simply touch to hear sound of words and sentences • Easy Word List Browser, using slider to scan all words in the list • Change voice setting to match your favorite male or female voice • Change speech setting to make the reading go fast or slow. To ensure gradual improvement, you can set the speech slow in the beginning, then move up to normal speech. • Happy learning and practicing
3rd Grade Math offers incredible resources for any parents, teachers and students at school and at home. It clearly stated math learning goals for any 3rd graders and provides very effective examples on how to achieve the goals.
3rd Grade Math is a necessary reference manual for any parents, teachers and students.
3rd Grade Math is a part of comprehensive reference manuals for parents, teachers and students.It provided extensive description of math learning goal for 3rd graders. Along with the goals, there are examples on how to achieve the goals.
3rd Grade Math is a part of Math Goals and Examples series. The series offers gradual and consistent approaches in math learning. This innovative series addresses various components of math learning from elementary school to college.
Scratch pad included is a great tools to work with young students. The students can use the scratch pad to do math, write, and have fun with drawings when they get bored with math.
Standardized tests are playing increasingly important roles at school and career development. One of the most effective ways to improve scores on standardized tests is to constantly expose the student to the test at all learning levels. Standardized Test Samples section provides a number of sample questions and answers.
One of the most valuable features is Super Practice Machine. It provides unlimited practices and tests. This practice machine has 5 levels of difficulties so students can practice their way up.
• Talking Bible, Ephesians is a fabulous and innovative tool to study and share God's Word. Talking Bible series made reading Bible a fun and interesting adventure. • Taking Bible series is an innovative application with many effective functions and user-friendly features. With a simple touch, you can navigate instantly from verse to verse, or from chapter to chapter. • With one click bookmark function, you can easily remember your cherished verse and return to the verse whenever you prefer.
Quiz Creator - 3rd Grade Vocabulary Friendly and elegant design with simply layout Create your own quiz or edit the list for a quiz Automatically generate both Practice and Quiz modes Practice mode will help to narrow down the answers Quiz mode will keep the scores and auto advance Interactive and interesting; So much better than regular flashcards... Built-in vocabulary list for unlimited practice and quiz Most effective learning tool.
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Course Abstract Details
MATH-124, Precalculus Part 2:Trigonometry and Advanced Algebra
Course Description
MATH-124, Precalculus Part 2: Trigonometry and Advanced Algebra, is the second course in a two-course sequence. It is intensive study of trigonometry and other advanced algebra topics such as conics, parametric equations, and polar coordinates. This course is intended for future mathematics/science majors. Topics include right triangle trigonometry, trigonometric functions, graphs, identities, trigonometric equations, inverse trigonometric functions, Laws of Sines and Cosines, systems of linear equations, conics, parametric equations, polar coordinates, and polar equations. Problems will be solved through analytic, numerical, and graphical approaches with an emphasis on setting up and solving relevant application problems. Students who need to take MATH-135, Calculus of a Single Variable 1, will need to complete both MATH-123 and MATH-124 in a year-long sequence or the rigorous one semester MATH-130 course. Prerequisites: exemption/completion of READ-A-F and a satisfactory score on the placement exam, or MATH-123 with a "C" grade or better. Credit by exam available. Graphing calculator required. See Mathematics Department web site for details. Three hours lecture each week. Three credits. Three billable hours. Credit cannot be earned in both MATH-124 and MATH-130. GENERAL EDUCATION
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Publisher's Description
The first step in complex math is now the easiest.
Alpha Teach Yourself Algebra I in 24 Hours provides readers with a structured, self-paced, straight-forward tutorial to algebra. It's the perfect textbook companion for students struggling with algebra, a solid primer for those looking to get a head start on an upcoming class, and a welcome refresher for parents tasked with helping out with homework, all in 24 one-hour lessons.
• Algebra is the second-most popular mathematic course for college- bound high school students
• Nearly all college-bound high school students now take algebra
Author Bio
Jane Cook is an accomplished math teacher with a Master's degree in secondary administration. She currently teaches algebra and geometry at Moravian Academy in Bethlehem, PA.
My daughter loves this book! It not only teaches the principles of Algebra, but teaches why it is important to know it and how to use it in everyday life. It has made Algebra so easy for her, that she said she wants to do ALL of her schoolwork this way. She was so disappointed to find out that Geometry is not offered by this company. I hope Alpha continues to add to the courses they offer! We also ordered the Spanish 1 book and are currently getting started on it.
I have returned to school after graduating thirty years ago. I never took algebra in high school. This book breaks down the problems,so it can be understood. I have always struggled with math and I find this product is working for me.
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Designed to help students improve their skills in algebra and geometry. Topics include: first and second degree equations, polynomials and factoring, ratios and proportions through similar geometric figures, areas and volumes of plane and solid figures, coordinate geometry and exponents and radicals. Required for students who have not satisfied the Preliminary Mathematics Requirement. Does not satisfy Mathematics Foundation or any General Education requirement. Falls. Prerequisite(s): provisionally admitted students or permission of the Department Chair.
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Solving equations and inequalities
3 videos
1 skill
The core underlying concepts in algebra are variables, expressions, equations and inequalities. You will see them throughout your math life (and even life after school). This tutorial won't give you all the tools that you'll later learn to analyze and interpret these ideas, but it'll get you started thinking about them. Common Core Standards: 6.EE.B.5, 6.EE.B.6, 6.EE.B.7
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Merchandising math is a multifaceted topic that involves many levels of the retail process, including assortment planning; vendor analysis; markup and pricing; and terms of sale. A Practical Approach to Merchandising Mathematics, Revised 1st Edition, brings each of these areas together into one comprehensive text to meet the needs of students who will be involved with the activities of merchandising and buying at the retail level. Students will learn how to use typical merchandising forms; become familiar with the application of computers and computerized forms in retailing; and recognize the basic factors of buying and selling that affect profit.
Author Biography
Linda M. Cushman is an associate professor of Retail Management in the Department of Marketing at Whitman School of Management, Syracuse University. Her research appears in journals such as the Journal of Fashion Marketing and Management, Customer Relationship Management, and the Journal of Shopping Center Research.
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The Definition of a Function, Evaluating a Function, Domain and Range. Evaluating a Function, Average Rate of Change, Even and Odd Functions. Arithmetic Combinations, Function Composition, Inverse Functions
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A university mathematics professor offers a comprehensive guide to elementary mathematics in this new book released by Dog Ear Publishing.
In addition to assisting students interested in more advanced, college-level courses, the book describes real-world uses for math skills.
Indianapolis (PRWEB) November 20, 2012
Those who break out into a sweat at the mere mention of quadratic equations or proportions can breathe a sigh of relief. A new book by a longtime mathematics professor breaks down basic math step by step, helping fill in any gaps in mathematical training. In addition to assisting students interested in more advanced, college-level courses, the book describes real-world uses for math in science, technology, finance and other fields.
"Math Overboard!" emphasizes both computational skills and comprehension of math. Its format allows for both reviewing all standard elementary math skills and honing specific topics. A diagnostic test to identify problem areas, together with review problems at the end of each chapter, further directs readers to ascertain which topics require more study. Topics range from basic addition, subtraction, multiplication and division, to scientific notation, proportions, speed and acceleration, algebra, Euclidean plane geometry and analytic geometry.
This comprehensive resource reveals math history and presents logical approaches to calculations with a sprinkle of humor, as well as tips for avoiding math errors. Extensive sample problems, review sections at the end of every chapter and a detailed index add up to an invaluable tool for learning the ins and outs of basic, school-level mathematics.
Author Colin Clark, professor emeritus of mathematics at the University of British Columbia, wishes his students had been able to use a book like this as they tried – and struggled – to grasp calculus after their previous math education. He also wrote "Mathematical Bioeconomics – The Mathematics of Conservation," and "Dynamic State-Variable Models in Ecology." He and his wife, Janet, live in a suburb of Vancouver, Canada.
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For additional information, please visit
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More About
This Textbook
Overview
The Mathematics of Finance: Modeling and Hedging explains the process of computing derivative prices in terms of underlying equity prices, while at the same time provides readers with the mathematical tools and techniques to carry out that process. The authors help readers understand the process, develop insights into how derivatives are used, and comprehend the risk associated with creating or trading these assets. These insights into derivative trading provide extra knowledge of how modern equity markets work.
Editorial Reviews
Booknews
Explains basic financial and mathematical concepts used in modeling and hedging. Each topic is introduced with the assumption that the reader has little to no previous exposure to financial matters or to the activities that are common to major equity markets. Contains chapters on financial markets, binomial trees, tree models for stocks and options, using spreadsheets to compute stock and option trees, and continuous models and the Black-Scholes formula. Other chapter topics are hedging, bond models and interest rate options, computational methods for bonds, currency markets and foreign exchange risks, and international political risk analysis. Includes exercises and selected answers. The authors are affiliated with Indiana
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Product Description
The Algebra 2 Tutor DVD Series teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry, providing students with essential skills for understanding advanced mathematics.
This lesson teaches students how to solve a system of equations using the addition method. In this technique, one equation of the system is added to the other equation in order to eliminate one of the variables. This allows the solution to be found without any graphing required. Grades 8-12. 27 minutes on DVD.
DVD Playable in Bermuda, Canada, United States and U.S. territories. Please check if your equipment can play DVDs coded for this region. Learn more about DVDs and Videos
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Cheyney CalculusPrecalculus is that last step in the Algebraic sequence of math taken at the high school level. It takes all the skills learned in Algebra 1&2 to a much deeper level, while at the same time advances several concepts begun in Geometry. The goal of Precalculus is to prepare students for Calculus ...
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Math
Q: What courses should be taken during the first year?
Analytical, computational and technological skills have become increasingly important in many disciplines and professional careers. We therefore encourage students to improve and further develop those skills, independent of their intended majors, by taking courses in Mathematics and Computer Science in their first year in college.
To enroll in an introductory mathematics course, students (with the exception of those with advanced-placement credit in calculus) must take the Mathematics Placement Test given during preregistration. Based on placement test scores, students are place into Precalculus, Calculus, or Honors Calculus. Students are encouraged to enroll in the course according to their placement . Students may challenge their placement by taking a backup placement test once.
Two Calculus tracks are open to students with appropriate scores in the Mathematics Placement Test: the regular track MATH 120-MATH 121, and the Honors track MATH 124-MATH 125. Both tracks start in the Fall. Students who do not place into Calculus, but place into Precalculus (MATH 119), can start with MATH 119, to prepared for Calculus and continue with MATH 120 the following year.
The regular track is the less theoretical Calculus sequence (MATH 120-MATH 121). It is geared toward students interested in the natural and social sciences, as well as Computer Science. Many of those studetns will not continue with upper level mathematics classes. Students in this sequence who plan to continue to study mathematics in the future are encourage to take MATH 121 in the Spring semester of their first year.
Honors Calculus (MATH 124-MATH 125) is the more theoretical track and prepares students for intermediate and upper level mathematics classes. It is therefore recommended that students with a strong mathematical background, who intend to take higher-level mathematics classes in the future, start with MATH 124-MATH 125. Those students are usually interested in Mathematics, Physics, Computer Science, and Economics.
Students with a sufficiently high score on the AP (AB) Calculus test receive credit for MATH 120. This credit fulfills the prerequisite for MATH 121, but not for MATH 125. It is recommended that these students start with MATH 124 and continue into MATH 125 if they are interested in taking higher-level mathematics classes in the future.
Students with a sufficiently high score on the AP (AB/BC) Calculus test receive credit for MATH 121 and may continue with MATH 130. In the exceptional circumstances, first-year students without credit for MATH 121 may enroll in MATH 130 with permission fo the instructor.
Q: What courses should first year students steer clear of?
Most mathematics courses have to be taken in a particular sequence. Students are not allowed to register for courses without fulfilling the necessary prerequsities first. For this reason, a mathematics major cannot be completed in less than three years.
Q. Does the deparment offer a First-Year Intensive course?
The department offers 2 FYI courses: 1) Diving into Mathematics Research (MATH 110); 2) Diving into Computer Science Research (CSci 110). It is a 5th class for all students, and it is spread over the course of the year with 0.5 credits per semester. It gives first-year students a unique opportunity to work with faculty and peers on interesting current research projects and to become a part of an intellectual and social community of students with similar interests. Both courses are by permission only and there is a limited number of spaces. With few exceptions, only students with a strong background in Mathematics who register for Honor Calculus or have credit for Calculus with be allowed to join in the class. Students interested in Mathematics research should contact Professor Gideon Maschler (gmaschler@clarku.edu). Students interested in Computer or Computational Science should contact Professor Natalia Sternberg (nsternberg@clarku.edu).
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Classic graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition. more...
Stan Gibilisco has authored or co-authored more than 50 nonfiction books in the fields of electronics, general science, mathematics, and computing. Stan has worked as a technical writer in industry, as a shortwave radio broadcast station technician, as a radio-frequency design engineer, and as a magazine editor. One of his books, the Encyclopedia... more...
From angles to functions to identities - solve trig equations with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear - this hands-on-guide focuses on helping you solve the many types of trigonometry equations you encounter in a focused, step-by-step manner.... more...
Sales Handle
A no-nonsense practical guide to trigonometry, providing concise summaries, clear model examples, and plenty of practice, making this workbook the ideal complement to class study or self-study, preparation for exams or a brush-up on rusty skills.
About the Book
Established as a successful practical workbook series with over 30... more...
This encyclopedia contains trigonometric identity proofs for some three hundred identities. The book is presented in the form of mathematical games for the reader's enjoyment and includes a concordance of trigonometric identities, enabling easy reference. Trig or Treat is a must-have for:. • every student of trigonometry, to find the proofs... more...
Trigonometry has always been an underappreciated branch,... more...
Boost Your grades with this illustrated quick-study guide. You will use it from high school all the way to graduate school and beyond. Clear and concise explanations. Difficult concepts are explained in simple terms. Illustrated with graphs and diagrams. Search for the words or phrases. Access the guide anytime, anywhere - at home, on the train, in... more...
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9780321759665 12/27A Survey of Mathematics with Applications:
4 out of
5
stars based on
1 user reviews.
Summary
In a Liberal Arts Math course, a common question students ask is, "Why do I have to know this?" A Survey of Mathematics with Applicationscontinues to be a best-seller because it shows students howwe use mathematics in our daily lives and why this is important. The Ninth Edition further emphasizes this with the addition of new " Why This Is Important" sections throughout the text. Real-life and up-to-date examples motivate the topics throughout, and a wide range of exercises help students to develop their problem-solving and critical thinking skills. Angel, Abbott, and Runde present the material in a way that is clear and accessible to non-math majors. The text includes a wide variety of math topics, with contents that are flexible for use in any one- or two-semester Liberal Arts Math course.
Author Biography
Allen Angel received his BS and MS in mathematics from SUNY at New Paltz. He completed additional graduate work at Rutgers University. He taught at Sullivan County Community College and Monroe Community College, where he served as chairperson of the Mathematics Department. He served as Assistant Director of the National Science Foundation at Rutgers University for the summers of 1967 - 1970. He was President of The New York State Mathematics Association of Two Year Colleges (NYSMATYC). He also served as Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). Allen lives in Palm Harbor, Florida but spends his summers in Penfield, New York. He enjoys playing tennis and watching sports. He also enjoys traveling with his wife Kathy.
Christine Abbott received her undergraduate degree in mathematics from SUNY Brockport and her graduate degree in mathematics education from Syracuse University. Since then she has taught mathematics at Monroe Community College and has recently chaired the department. In her spare time she enjoys watching sporting events, particularly baseball, college basketball, college football, and the NFL. She also enjoys spending time with her family, traveling, and reading
Dennis Runde has a BS degree and an MS degree in Mathematics from the University of Wisconsin--Platteville and Milwaukee respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for more than fifteen years at State College of Florida–Manatee-Sarasota and for almost ten years at Saint Stephen's Episcopal School. Besides coaching little league baseball, his other interests include history, politics, fishing, canoeing, and cooking. He and his wife Kristin stay busy keeping up with their three sons--Alex, Nick, and Max.
Table of Contents
1. Critical Thinking Skills
1.1 Inductive Reasoning
1.2 Estimation
1.3 Problem Solving
2. Sets
2.1 Set Concepts
2.2 Subsets
2.3 Venn Diagrams and Set Operations
2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets
2.5 Applications of Sets
2.6 Infinite Sets
3. Logic
3.1 Statements and Logical Connectives
3.2 Truth Tables for Negation, Conjunction, and Disjunction
3.3 Truth Tables for the Conditional and Biconditional
3.4 Equivalent Statements
3.5 Symbolic Arguments
3.6 Euler Diagrams and Syllogistic Arguments
3.7 Switching Circuits
4. Systems of Numeration
4.1 Additive, Multiplicative, and Ciphered Systems of Numeration
4.2 Place-Value or Positional-Value Numeration Systems
4.3 Other Bases
4.4 Computation In Other Bases
4.5 Early Computational Methods
5. Number Theory and the Real Number System
5.1 Number Theory
5.2 The Integers
5.3 The Rational Numbers
5.4 The Irrational Numbers and the Real Number System
5.5 Real Numbers and Their Properties
5.6 Rules of Exponents and Scientific Notation
5.7 Arithmetic and Geometric Sequences
5.8 Fibonacci Sequence
6. Algebra, Graphs, and Functions
6.1 Order of Operations
6.2 Linear Equations in One Variable
6.3 Formulas
6.4 Applications of Linear Equations In One Variable
6.5 Variation
6.6 Linear Inequalities
6.7 Graphing Linear Equations
6.8 Linear Inequalities In Two Variables
6.9 Solving Quadratic Equations By Using Factoring and By Using the Quadratic Formula
6.10 Functions and Their Graphs
7. Systems of Linear Equations and Inequalities
7.1 Systems of Linear Equations
7.2 Solving Systems of Linear Equations by the Substitution and Addition Methods
7.3 Matrices
7.4 Solving Systems of Linear Equations by Using Matrices
7.5 Systems of Linear Inequalities
7.6 Linear Programming
8. The Metric System
8.1 Basic Terms and Conversions Within the Metric System
8.2 Length, Area, and Volume
8.3 Mass and Temperature
8.4 Dimensional Analysis and Conversions To and From the Metric System
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Today's Mathematics: Concepts, Methods, and Classroom Activities 13th Edition, Today's Mathematics: Concepts, Methods, and Classroom Activitiess helps readersthoroughly understand today's NCTM standards and how to present them in the most effective way possible. Readers will find improved and increased coverage of technology while benefiting from a new feature that addresses math anxiety. A new chapter on developments in Common Core State Standards, PARCC and SBAC assessments is included. Elementary math teachers will quickly discover how to put the principles of mathematics to work in the classroom. This text includes increased coverage of diversity while integrating the latest NCTM guidelines. Today's Mathematics: Concepts, Methods, and Classroom Activities 13th Edition provides teachers with a resource that provides a valuable set of ideas and reference materials for actual classroom use.
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Abstract
[Abstract]: Mathematical literacy and competence in mathematics of engineering students are defined and
analysed through the structure of conceptual understanding on both levels. The paper provides a view on technology integration in the teaching process, in particular, the ways how technology can contribute to learning needs of engineering students and what difficulties we can expect on
that way. Examples that show relationships between different mathematical concepts and using technology are discussed. One of the most important concepts of calculus, limit is considered in detail with applications in MATLAB to identify possible obstacles in learning and students'
misconceptions. Potential of conceptual understanding in mathematics for development of students' abilities in engineering applications and computerised calculations is shown. The current situation of the mathematics education of engineers in Australia in the context of the
questions raised in the paper is briefly outlined.
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Browse related Subjects ...Read More In the Sixth Edition, new worksheets in MyMathLab-developed from the authors' experience in the classroom-provide mixed review for students who having trouble reconciling various topics, and also give students an opportunity to show their work. The "Are You Prepared?" section openers focus on students mastering the prerequisite material before beginning a new topic, and for the first time, those exercises are assignable in MyMathLab. Concept and Vocabulary exercises are also now assignable in MyMathLab as reading quizzes.Read Less
Good. 6e Item may show signs of shelf wear. Pages may include limited notes and highlighting. Includes supplemental or companion materials if applicable. Access codes may or may not work. Connecting readers since 1972. Customer service is our top priority.
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This book was initially derived from a set of notes used in a university chemistry course. It is hoped it will evolve into something useful and develop a set of open access problems as well as pedagogical material.
For many universities the days when admission to a Chemistry, Chemical Engineering, Materials Science or even Physics course could require the equivalent of A-levels in Chemistry, Physics and Mathematics are probably over for ever. The broadening out of school curricula has had several effects, including student entry with a more diverse educational background and has also resulted in the subject areas Chemistry, Physics and Mathematics becoming disjoint so that there is no co-requisite material between them. This means that, for instance, physics cannot have any advanced, or even any very significant mathematics in it. This is to allow the subject to be studied without any of the maths which might be first studied by the A-level maths group at the ages of 17 and 18. Thus physics at school has become considerably more descriptive and visual than it was 20 years ago. The same applies to a lesser extent to chemistry.
This means there must be an essentially remedial component of university chemistry to teach just the Mathematics and Physics which is needed and not too much, if any more, as it is time consuming and perhaps not what the student of Chemistry is most focused on. There is therefore also a need for a book Physics for Chemistry.
The origin of surds goes back to the Greek philosophers. It is relatively simple to prove that the square root of 2 cannot be a ratio of two integers, no matter how large the integers may become. In a rather Pythonesque incident the inventor of this proof was put to death for heresy by the other philosophers because they could not believe such a pure number as the root of 2 could have this impure property.
(The original use of quadratic equations is very old, Babylon many centuries BC.) This was to allocate land to farmers in the same quantity as traditionally held after the great floods on the Tigris and Euphrates had reshaped the fields. The mathematical technology became used for the same purpose in the Nile delta.
When you do trigonometry later you will see that surds are in the trigonometric functions of the important symmetrical angles, e.g. and so they appear frequently in mathematical expressions regarding 3 dimensional space.
The notation used for recording numbers in chemistry is the same as for other scientific disciplines, and appropriately called scientific notation, or standard form. It is a way of writing both very large and very small numbers in a shortened form compared to decimal notation. An example of a number written in scientific notation is
with 4.65 being a coefficient termed the significand or the mantissa, and 6 being an integer exponent. When written in decimal notation, the number becomes
.
Numbers written in scientific notation are usually normalised, such that only one digit precedes the decimal point. This is to make order of magnitude comparisons easier, by simply comparing the exponents of two numbers written in scientific notation, but also to minimise transcription errors, as the decimal point has an assumed position after the first digit. In computing and on calculators, it is common for the ("times ten to the power of") to be replaced with "E" (capital e). It is important not to confuse this "E" with the mathematical constant e.
Engineering notation is a special restriction of scientific notation where the exponent must be divisible by three. Therefore, engineering notation is not normalised, but can easily use SI prefixes for magnitude.
Remember that in SI, numbers do not have commas between the thousands, instead there are spaces, e.g., (an integer) or . Commas are used as decimal points in many countries.
Consider a number , where is the base and is the exponent. This is generally read as " to the " or " to the power of ". If then it is common to say " squared", and if then " cubed". Comparing powers (exponentiation) to multiplication for positive integer values of n , it can be demonstrated that
When an expression contains different operations, they must be evaluated in a certain order. Exponents are evaluated first. Then, multiplication and division are evaluated from left to right. Last, addition and subtraction are evaluated left to right. Parentheses or brackets take precedence over all operations. Anything within parentheses must be calculated first. A common acronym used to remember the order of operations is PEMDAS, for "Parentheses, Exponents, Multiplication, Division, Addition, Subtraction". Another way to remember this acronym is "Please Excuse My Dear Aunt Sally".
Keep in mind that negation is usually considered multiplication. So in the case of , the exponent would be evaluated first, then negated, resulting in a negative number.
Take note of this example:
, let x=5.
If evaluated incorrectly (left-to-right, with no order of operations), the result would be 16. Three plus five gives eight, times two is 16. The correct answer should be 13. Five times two gives ten, plus three gives 13. This is because multiplication is solved before addition.
Partial fractions are used in a few derivations in thermodynamics and they are good for practicing algebra and factorisation.
It is possible to express quotients in more than one way. Of practical use is that they can be collected into one term or generated as several terms by the method of partial fractions. Integration of a complex single term quotient is often difficult, whereas by splitting it up into a sum, a sum of standard integrals is obtained. This is the principal chemical application of partial fractions.
An example is
In the above must equal since the denominators are equal. So we set first to +1 giving . Therefore B = -1/2. If we set instead , therefore . So
We can reverse this process by use of a common denominator.
The numerator is , so it becomes
which is what we started from.
So we can generate a single term by multiplying by the denominators to create a common denominator and then add up the numerator to simplify. A typical application might be to convert a term to partial fractions, do some calculus on the terms, and then regather into one quotient for display purposes. In a factorised single quotient it will be easier to see where numerators go to zero, giving solutions to , and where denominators go to zero giving infinities.
A typical example of a meaningful infinity in chemistry might be an expression such as
The variable is the energy E, so this function is small everywhere, except near . Near a resonance occurs and the expression becomes infinite when the two energies are precisely the same. A molecule which can be electronically excited by light has several of these resonances.
Here is another example. If we had to integrate the following expression we would first convert to partial fractions:
so
let then
let then
therefore the expression becomes
Later you will learn that these expressions integrate to give simple expressions.
This can be easily differentiated, and integrated. If this is differentiated with the quotient formula it is considerably harder to reduce to the the same form. The same procedure can be applied to partial fractions.
This is an example of simplification. It would actually be possible to differentiate this with respect to either or using only the techniques you have been shown. The algebraic manipulation involves differentiation of a quotient and the chain rule.
Evaluating gives
Expanding this out to the s and s would look ridiculous.
Substitutions like this are continually made for the purpose of having new, simpler expressions, to which the rules of calculus or identities are applied.
(Notice the line over the square root has the same priority as a bracket. Of course we all know by now that is not equal to but errors of priority are among the most common algebra errors in practice).
There is a formula for a cubic equation but it is rather complicated and unlikely to be required for undergraduate-level study of chemistry. Cubic and higher equations occur often in chemistry, but if they do not factorise they are usually solved by computer.
Solve:
Notice the scope or range of the bracket.
Notice here that the variable is a concentration, not the ubiquitous .
It is usually necessary in chemistry to be familiar with at least three systems of units, Le Système International d'Unités (SI), atomic units as used in theoretical calculations and the unit system used by the experimentalists. Thus if we are dealing with the ionization energy, the units involved will be the Joule (J), the Hartree (Eh, the atomic unit of energy), and the electron volt (eV).
These units all have their own advantages;
The SI unit should be understood by all scientists regardless of their field.
The atomic unit system is the natural unit for theory as most of the fundamental constants are unity and equations can be cast in dimensionless forms.
The electron volt comes from the operation of the ionization apparatus where individual electrons are accelerated between plates which have a potential difference in Volts.
An advantage of the SI system is that the dimensionality of each term is made clear as the fundamental constants have structure. This is a complicated way of saying that if you know the dimensionality of all the things you are working with you know an awful lot about the mathematics and properties such as scaling with size of your system. Also, the same system of units can describe both the output of a large power station (gigaJoules), or the interaction of two inert gas atoms, (a few kJ per mole or a very small number of Joules per molecule when it has been divided by Avogadro's number).
In SI the symbols for units are lower case unless derived from a person's name, e.g. ampere is A and kelvin is K.
An approximation of how much of a chemical bond each energy corresponds to is placed next to each one. This indicates that light of energy 4 eV can break chemical bonds and possibly be dangerous to life, whereas infrared radiation of a few cm-1 is harmless.
The labelling of tables and axes of graphs should be done so that the numbers are dimensionless, e.g. temperature is ,
and energy mol / kJ etc.
This can look a little strange at first. Examine good text books like Atkins Physical Chemistry which follow SI carefully to see this in action.
The hardest thing with conversion factors is to get them the right way round. A common error is to divide when you should be multiplying, also another common error is to fail to raise a conversion factor to a power.
1 eV = 96.48530891 kJ mol-1
1 cm-1 = 0.01196265819 kJ mol-1
To convert eV to cm-1, first convert to kJ per mole by multiplying by 96.48530891 / 1. Then convert to cm-1 by multiplying by 1 / 0.01196265819 giving 8065.540901. If we tried to go directly to the conversion factor in 1 step it is easy to get it upside down. However, common sense tell us that there are a lot of cm-1s in an eV so it should be obviously wrong.
1 inch = 2.54 centimetres. If there is a surface of nickel electrode of 2 * 1.5 square inches it must be 2 * 1.5 * 2.542 square centimetres.
To convert to square metres, the SI unit we must divide this by 100 * 100 not just 100.
One of the reasons powers of variables are so important is because they relate to the way quantities scale. Physicists in particular are interested in the way variables scale in the limit of very large values. Take cooking the turkey for Christmas dinner. The amount of turkey you can afford is linear, (power 1), in your income. The size of an individual serving is quadratic, (power 2), in the radius of the plates being used. The cooking time will be something like cubic in the diameter of the turkey as it can be presumed to be linear in the mass.
(In the limit of a very large turkey, say one the diameter of the earth being heated up by a nearby star, the internal conductivity of the turkey would limit the cooking time and the time taken would be exponential. No power can go faster / steeper than exponential in the limit. The series expansion of goes on forever even though gets very small.)
Another example of this is why dinosaurs had fatter legs than modern lizards. If dinosaurs had legs in proportion to small lizards the mass to be supported rises as length to the power 3 but the strength of the legs only rises as the area of the cross section, power 2. Therefore the bigger the animal the more enormous the legs must become, which is why a rhino is a very chunky looking version of a pig.
There is a very good article on this in Cooper, Necia Grant; West, Geoffrey B., Particle Physics: A Los Alamos Primer, ISBN 0521347807
The most basic relationship between two variables and is a straight line, a linear relationship.
The variable is the gradient and is a constant which gives the intercept. The equations can be more complex than this including higher powers of , such as
This is called a quadratic equation and it follows a shape called a parabola. High powers of can occur giving cubic, quartic and quintic equations. In general, as the power is increased, the line mapping the variables wiggles more, often cutting the -axis several times.
without complex numbers does not exist. However the number behaves exactly like any other number in algebra without any anomalies, allowing us to solve this problem.
The solutions are .
is an imaginary number. is a complex number.
Two complex numbers are added by .
Subtraction is obvious: .
Division can be worked out as an exercise. It requires as a common denominator. This is , (difference of two squares), and is .
This means
In practice complex numbers allow one to simplify the mathematics of magnetism and angular momentum as well as completing the number system.
There is an apparent one to one correspondence between the Cartesian plane and the complex numbers, . This is called an Argand diagram. The correspondence is illusory however, because say for example you raise the square root of to a series of ascending powers. Rather than getting larger it goes round and round in circles around the origin. This is not a property of ordinary numbers and is one of the fundamental features of behaviour in the complex plane.
Remember this is a consequence of Pythagoras' theorem where the length of the hypotenuse is 1.
The difference of two angles can easily be generated by putting and remembering and . Similarly, the double angle formulae are generated by induction. is a little more complicated but can be generated if you can handle the fractions! The proofs are in many textbooks but as a chemist it is not necessary to know them, only the results.
Identities and equations look very similar, two things connected by an equals sign. An identity however is a memory aid of a mathematical equivalence and can be proved. An equation represents new information about a situation and can be solved.
For instance,
is an identity. It cannot be solved for . It is valid for all . However,
is an equation where .
If you try and solve an identity as an equation you will go round and round in circles getting nowhere, but it would be possible to dress up into a very complicated expression which you could mistake for an equation.
Check you are familiar with your elementary geometry. Remember from your GCSE maths the properties of equilateral and iscoceles triangles. If you have an iscoceles triangle you can always dispense with the sin and cosine rules, drop a perpendicular down to the base and use trig directly. Remember that the bisector of a side or an angle to a vertex cuts the triangle in two by area, angle and length. This can be demonstrated by drawing an obtuse triangle and seeing that the areas are .
Remember that the interior angles of a -sided polygon are n * 180 -360,
().
For benzene there are six equilateral triangles if the centre of the ring is used as a vertex, each of which having an interior angle of 120 degrees. Work out the the angles in azulene, (a hydrocarbon with a five and a seven membered ring), assuming all the C-C bond lengths are equal, (this is only approximately true).
Imagine you make a rail journey from Doncaster to Bristol, from where you travel up the West of the country to Manchester. Here you stay a day, travelling the next morning to Glasgow, then across to Edinburgh. At the end of a day's work you return to Doncaster. Mathematically this journey could be represented by vectors, (in 2 dimensions because we are flat earthers on this scale). At the end of the 2nd journey (D-B) + (B-M) you are only a short distance from Doncaster, 50 miles at 9.15 on the clockface. Adding two more vectors, (journeys) takes you to Edinburgh, (about 250 miles at 12.00). Completing the journey leaves you at a zero vector away from Doncaster, i.e. all the vectors in this closed path add to zero.
Mathematically we usually use 3 dimensional vectors over the 3 Cartesian axes , and .
It is best always to use the conventional right handed axes even though the other way round is equally valid if used consistently. The wrong handed coordinates can occasionally be found erroneously in published research papers and text books. The memory trick is to think of a sheet of graph paper, is across as usual and up the paper. Positive then comes out of the paper.
A unit vector is a vector normalised, i.e. multiplied by a constant so that its value is 1. We have the unit vectors in the 3 dimensions:
so that
The hat on the i, j, k signifies that it is a unit vector. This is usually omitted.
Our geographical analogy allows us to see the meaning of vector addition and subtraction. Vector products are less obvious and there are two definitions the scalar product and the vector product. These are different kinds of mathematical animal and have very different applications. A scalar product is an area and is therefore an ordinary number, a scalar. This has many useful trigonometrical features.
The vector product seems at first to be defined rather strangely but this definition maps onto nature as a very elegant way of describing angular momentum. The structure of Maxwell's Equations is such that this definition simplifies all kinds of mathematical descriptions of atomic / molecular structure and electricity and magnetism.
If A and B have no common non-zero components in , and the value is zero corresponding to orthogonality, i.e. they are at right angles. (This can also occur by sign combinations making zero. corresponding to non axis-hugging right angles.)
The minus sign on the middle term comes from the definition of the determinant, explained in the lecture. Determinants are defined that way so they correspond to right handed rotation. (If you remember our picture of going round the circle, as one coordinate goes up, i.e. more positive, another must go down. Therefore rotation formulae must have both negative and positive terms.) Determinants are related to rotations and the solution of simultaneous equations. The solution of simultaneous equations can be recast in graphical form as a rotation to a unit vector in -dimensional space so therefore the same mathematical structures apply to both space and simultaneous equations.
If we have 2 equations of the form we may have a set of simultaneous equations. Suppose two rounds of drinks are bought in a cafe, one round is 4 halves of orange juice and 4 packets of crisps. This comes to 4 pounds 20. The thirstier drinkers at another table buy 4 pints of orange juice and only 1 packet of crisps and this comes to 6 pounds 30. So we have:
and
i.e.
If you plot these equations they will be simultaneously true at and .
Notice that if the two rounds of drinks are 2 pints and 2 packets of crisps and 3 pints and 3 packets of crisps we cannot solve for the prices! This corresponds to two parallel straight lines which never intersect.
If we have the equations:
If these are simultaneously true we can find a unique solution for both and .
By subtracting the 2 equations a new equation is created where has disappeared and the system is solved.
Substituting back gives us .
This was especially easy because had the same coefficient in both equations. We can always multiply one equation throughout by a constant to make the coefficients the same.
If the equations were:
and
things would go horribly wrong when you tried to solve them because they are two copies of the same equation and therefore not simultaneous. We will come to this later, but in the meantime notice that 3 times 8 = 4 times 6. If our equations were:
we can still solve them but would require a lot of algebra to reduce it to three (2x2) problems which we know we can solve. This leads on to the subject of matrices and determinants.
Simultaneous equations have applications throughout the physical sciences and range in size from (2x2)s to sets of equations over 1 million by 1 million.
because it breaks down into a (2x2) and is not truly a (3x3). (In the case of the benzene molecular orbitals, which are (6x6), this same scheme applies. It becomes two direct solutions and two (2x2) problems which can be solved as above.)
but cannot exist. To be multiplied two matrices must have the 1st matrix with the same number of elements in a row as the 2nd matrix has elements in its columns.
where the s are the elements of .
Look at our picture of and as represented by a unit vector in a circle. The rotation of the unit vector about the -axis can be represented by the following mathematical construct.
In two dimensions we will rotate the vector at 45 degrees between and :
This is if we rotate by +45 degrees. For and . So the rotation flips over to give . The minus sign is necessary for the correct mathematics of rotation and is in the lower left element to give a right handed sense to the rotational sign convention.
As discussed earlier the solving of simultaneous equations is equivalent in some deeper sense to rotation in -dimensions.
The first matrix is the inverse of the 2nd. Computers use the inverse of a matrix to solve simultaneous equations.
If we have
In matrix form this is....
In terms of work this is equivalent to the elimination method you have already employed for small equations but can be performed by computers for simultaneous equations.
(Examples of large systems of equations are the fitting of reference data to 200 references molecules, dimension 200, or the calculation of the quantum mechanical gradient of the energy where there is an equation for every way of exciting 1 electron from an occupied orbital to an excited, (called virtual, orbital, (typically equations.)
This takes a long time to get all the signs right. Elimination by subtracting equations is MUCH easier. However as the computer cannot make sign mistakes it is not a problem when done by computer program.
The following determinant corresponds to an equation which is repeated three times giving an unsolvable set of simultaneous equations.
Matrix multiplication is not necessarily commutative, which in English means does not equal all the time. Multiplication may not even be possible in the case of rectangular rather than square matrices.
I will put a list of the properties and definitions of matrices in an appendix for reference through the later years of the course.
The above determinant is a special case of simultaneous equations which occurs all the time in chemistry, physics and engineering which looks like this:
This equation in matrix form is and the solution is .
This is a polynomial equation like the quartic above. As you know polynomial equations have as many solutions as the highest power of i.e. in this case . These solutions can be degenerate for example the orbitals in benzene are a degenerate pair because of the factorisation of the polynomial from the 6 Carbon-pz orbitals. In the 2nd year you may do a lab exercise where you make the benzene determinant and see that the polynomial is
from which the 6 solutions and the orbital picture are immediately obvious.
The use of matrix equations to solve arbitrarily large problems leads to a field of mathematics called linear algebra.
They are all the same! This exemplifies a deeper property of matrices which we will ignore for now other than to say that complex numbers allow you to calculate the same thing in different ways as well as being the only neat way to formulate some problems.
The derivative of a function times a constant is just the same constant times the derivative.
The derivative of a sum of functions is just the sum of the two derivatives.
To get higher derivatives such as the second derivative keep applying the same rules.
One of the big uses of differentiation is to find the stationary points of functions, the maxima and minima. If the function is smooth, (unlike a saw-tooth), these are easily located by solving equations where the first derivative is zero.
Notice when differentiating a product one generates two terms. (Terms are mathematical expression connected by a plus or minus.) An important point is that terms which represent physical quantities must have the same units and dimensions or must be pure dimensionless numbers. You cannot add 3 oranges to 2 pears to get 5 orangopears. Integration by parts also generates an extra term each time it is applied.
is the tangent or gradient. At a minimum is zero. This is also true at a maximum or an inflection point. The second gradient gives us the nature of the point. If is positive the turning point is a minimum and if it is negative a maximum. Most of the time we are interested in minima except in transition state theory.
If the equation of is plotted, is is possible to see that at there is a third kind of point, an inflection point, where both and are zero.
Plot between -4 and +3, in units of 1. (It will speed things up if you factorise it first. Then you will see there are 3 places where so you only need calculate 5 points.) By factorising you can see that this equation has 3 roots. Find the 2 turning points. (Differentiate once and find the roots of the quadratic equation using . This gives the position of the 2 turning points either side of zero. As the equation is only in it has 3 roots and 2 maxima / minima at the most therefore we have solved everything. Differentiate your quadratic again to get . Notice that the turning point to the left of zero is a maximum i.e. and the other is a minimum i.e..
What is the solution and the turning point of .
Solve , by factorisation.
(The 3 roots are -3,0 and +2.
Solutions are and , i.e. -1.7863 and 1.1196.
There are 3 coincident solutions at , , at 0 so this is an inflection point.
This works fine for all powers except -1, for instance the integral of
is just
-1 is clearly going to be a special case because it involves an infinity when and goes to a steep spike as gets small. As you have learned earlier this integral is the natural logarithm of and the infinity exists because the log of zero is minus infinity and that of negative numbers is undefined.
§The integration and differentiation of positive and negative powers[edit]
You will be able to work them out easily when you have done more integration. The thing to notice is that the calculus of negative and positive powers is not symmetrical, essentially caused by the pole or singularity for at .
Logarithms were invented by Napier, a Scottish Laird, in the 17th-century. He made many inventions but his most enduring came from the necessity of doing the many long divisions and trigonometric calculations used in astronomy. The Royal Navy in later years devoted great time and expense to developing logarithm technology for the purposes of navigation, leading to the commissioning of the first mechanical stored program computer, which was theoretically sound but could not be made by Charles Babbage between 1833 and 1871.
The heart of the system is the observation of the properties of powers:
This means that if we have the inverse function of we can change a long division into a subtraction by looking up the exponents in a set of tables. Before the advent of calculators this was the way many calculations were done.
Napier initially used logs to the base for his calculations, but after a year or so he was visited by Briggs who suggested it would be more practical to use base 10. However base is necessary for the purposes of calculus and thermodynamics.
nd are undefined but sometimes a large number over a large number can have defined values. An example is the of 90 degrees, which you will remember has a large opposite over a large hypotenuse but in the limit of an infinitesimally thin triangle they become equal. Therefore the is 1.
This is done in many textbooks and Wikipedia. Their notation might be different to the one used here, which hopefully is the most clear. You derive the expression by taking the product rule and integrating it. You then make one of the into a product itself to produce the expression.
(all integration with respect to . Remember by
( gets differentiated.)
The important thing is that you have to integrate one expression of the product and differentiate the other. In the basic scheme you integrate the most complicated expression and differentiate the simplest. Each time you do this you generate a new term but the function being differentiated goes to zero and the integral is solved. The expression which goes to zero is .
The other common scheme is where the parts formula generates the expression you want on the right of the equals and there are no other integral signs. Then you can rearrange the equation and the integral is solved. This is obviously very useful for trig functions where ad infinitum.
First order differential equations are covered in many textbooks. They are solved by integration. (First order equations have , second order equations have and .)
The arbitrary constant means another piece of information is needed for complete solution, as with the Newton's Law of Cooling and Half Life examples.
Provided all the s can be got to one side and the s to another the equation is separable.
This is the general solution.
Typical examples are:
by definition of logs.
(1)
(2)
(3)
This corresponds to:
The Schrödinger equation is a 2nd order differential equation e.g. for the particle in a box
It has taken many decades of work to produce computationally efficient solutions of this equation for polyatomic molecules. Essentially one expands in coefficients of the atomic orbitals. Then integrates to make a differential equation a set of numbers, integrals, in a matrix. Matrix algebra then finishes the job and finds a solution by solving the resultant simultaneous equations.
There are many different ways of expressing the same thing in trig functions and very often successful integration depends on recognising a trig identity.
but could also be
(each with an integration constant!).
When applying calculus to these functions it is necessary to spot which is the simplest form for the current manipulation. For integration it often contains a product of a function with its derivative like where integration by substitution is possible.
Where a derivative can be spotted on the numerator and its integral below we will get a function. This is how we integrate .
Many textbooks go through the proper theory of differentiation and integration by using limits. As chemists it is possible to live without knowing this so we might well not have it as an examinable topic. However here is how we differentiate sin from 1st principles.
You may be aware that you can fit a quadratic to 3 points, a cubic to 4 points, a quartic to 5 etc. If you differentiate a function numerically by having two values of the function apart you get an approximation to by constructing a triangle and the gradient is the tangent. There is a forward triangle and a backward triangle depending on the sign of . These are the forward and backward differentiation approximations.
If however you have a central value with a either side you get the central difference formula which is equivalent to fitting a quadratic, and so is second order in the small value of giving high accuracy compared with drawing a tangent. It is possible to derive this formula by fitting a quadratic and differentiating it to give:
This is calculated data for the shielding in ppm of the proton in HCl when the bondlength is stretched or compressed by 0.01 of an Angstrom (not the approved unit pm). The total shielding is the sum of two parts, the paramagnetic and the diamagnetic. Notice we have retained a lot of significant figures in this data, always necessary when doing numerical differentiation.
Exercise - use numerical differentiation to calculated d (sigma) / dr and d2 (sigma) / dr2 using a step of 0.01 and also with 0.02. Use 0.01 to calculate d (sigma(para)) / dr and d (sigma(dia)) / dr.
Wikipedia has explanations of the Trapezium rule and Simpson's Rule. Later you will use computer programs which have more sophisticated versions of these rules called Gaussian quadratures inside them. You will only need to know about these if you do a numerical project later in the course. Chebyshev quadratures are another version of this procedure which are specially optimised for integrating noisy data coming from an experimental source. The mathematical derivation averages rather than amplifies the noise in a clever way.
The ubiquitous is not always the variable as you will all know by now. One problem dealing with real applications is sorting out which symbols are the variables and which are constants. (If you look very carefully at professionally set equations in text books you should find that there are rules that constants are set in Roman type, i.e. straight letters and variables in italics. Do not rely on this as it is often ignored.)
Here are some examples where the variable is conventionally something other than .
The Euler angles which are used in rotation are conventionally and not the more usual angle names and . The rotation matrix for the final twist in the commonest Euler definition therefore looks like
The energy transitions in the hydrogen atom which give the Balmer series are given by the formula is just a single variable for the energy the tilde being a convention used by spectroscopists to say it is wavenumbers, (cm-1). The H subscript on has no mathematical meaning. It is the Rydberg constant and is therefore in Roman type. is known very accurately as 109,677.581 cm-1. It has actually been known for a substantial fraction of the class to make an error putting this fraction over a common denominator in examination conditions.
In the theory of light is used for frequency and not surprisingly for time. Light is an oscillating electric and magnetic field therefore the cosine function is a very good way of describing it. You can also see here the use of complex numbers. Using the real axis of the Argand diagram for the electric field and the imaginary axis for the magnetic field is a very natural description mathematically and maps ideally onto the physical reality. Here we are integrating with respect to and , the operating frequency if it is a laser experiment is a constant, therefore it appears on the denominator in the integration. In this case we can see a physical interpretation for the integration constant. It will be a phase factor. If we were dealing with sunlight we might well be integrating a different function over in order to calculate all of the phenomenon which has different strengths at the different light frequencies. Our integration limits would either be from zero to infinity or perhaps over the range of energies which correspond to visible light.
This example is a laser experiment called Second Harmonic Generation. There is an electric field , frequency and a property constant . is a fundamental constant. We have an intense monochromatic laser field fluctuating at the frequency , (i.e. a strong light beam from a big laser). Therefore the term contributes to the polarization. We know from trigonometric identities that can be represented as a cosine of the double angle Therefore the polarization is In this forest of subscripts and Greek letters the important point is that there are two terms contributing to the output coming from which multiplies the rest of the stuff. In summary we have is equal to where everything except the trig(t) and trig(2t) are to some extent unimportant for the phenomenon of doubling the frequency. and differ only in a phase shift so they represent the same physical phenomenon, i.e. light, which has phase. (One of the important properties of laser light is that it is coherent, i.e. it all has the same phase. This is fundamentally embedded in our mathematics.)
Notice that the term is positive corresponding to repulsion. The term is the attractive term and is negative corresponding to a reduction in energy. A and B are constants fitted to experimental numbers.
This function is very easy to both differentiate and integrate. Work these out. In a gas simulation you would use the derivative to calculate the forces on the atoms and would integrate Newton's equations to find out where the atoms will be next.
Another potential which is used is:
This has 1 more fittable constant. Integrate and differentiate this.
The is called a Lennard-Jones potential and is often expressed using the 2 parameters of an energy and a distance .
is an energy. Set the derivative of this to zero and find out where the van der Waals minimum is. Differentiate again and show that the derivative is positive, therefore the well is a minimum, not a turning point.
Interaction energy of argon dimer. The long-range part is due to London dispersion forces
In a diatomic molecule the energy is expanded as the bond stretches in a polynomial. We set . At the function is a minimum so there is no term.
Whatever function is chosen to provide the energy setting the 1st derivative to zero will be required to calculate . The 2nd and 3rd derivatives will then need to be evaluated to give the shape of the potential and hence the infra-red spectrum. is usually modelled by a very complicated function whose differentiation is not entered into lightly.
A one-dimensional metal is modelled by an infinite chain of atoms 150 picometres apart. If the metal is lithium each nucleus has charge 3 and its electrons are modelled by the function
which repeats every 150 pm. What constant must this function be multiplied by to ensure there are 3 electrons on each atom? (Hint... integrate between either and or -75pm and +75pm according to your equation. This integral is a dimensionless number equal to the number of electrons, so we will have to multiply by a normalisation constant.)
Here we have modelled the density of electrons. Later in the second year you will see electronic structure more accurately described by functions for each independent electron called orbitals. These are subject to rigorous mathematical requirements which means they are quite fun to calculate.
Another physics problem but a good example of a log-log plot is the radius and time period relations of the planets.
This data is dimensionless because we have divided by the time / distance of the earth. We can take logs of both.
Mercury
Venus
Earth
Mars
Jupiter
Saturn
r
0.3871
0.7233
1
1.524
5.203
9.539
T
0.2408
0.6152
1
1.881
11.86
29.46
Mercury
Venus
Earth
Mars
Jupiter
Saturn
log10r
-0.4122
0
0.9795
log10T
-0.6184
0
1.4692
Try a least squares fit on your spreadsheet program. Using the Earth and Saturn data: (which is extremely bad laboratory practice, to usejust two points from a data set!)
so
so and
This is Kepler's 3rd law. If you use either a least squares fit gradient or the mercury to saturn data you get the same powers. We have got away with not using a full data set because the numbers given are unusually accurate and to some extent tautological, (remember the planets go round in ellipses not circles!).
This test was once used to monitor the broad learning of university chemists at the end of the 1st year and is intended to check, somewhat lightly, a range of skills in only 50 minutes. It contains a mixture of what are perceived to be both easy and difficult questions so as to give the marker a good idea of the student's algebra skills and even whether they can do the infamous integration by parts.
(1) Solve the following equation for
It factorises with 3 and 5 so : therefore the roots are -5 and +3, not 5 and -3!
(2) Solve the following equation for
Divide by 2 and get .
This factorises with 2 and 5 so : therefore the roots are 5 and -2.
(3) Simplify
Firstly so it becomes .
(4) What is
64 = 8 x 8 so it also equals xi.e. is , therefore the answer is -6.
(5) Multiply the two complex numbers
These are complex conjugates so they are minus xi.e. plus 25 so the total is 34.
(6) Multiply the two complex numbers
The real part is -25 plus the . The cross terms make and so the imaginary part disappears.
(7) Differentiate with respect to :
Answer:
(8)
Answer:
(9)
Answer:
(10)
Expand out the difference of 2 squares first.....collect and multiply....then just differentiate term by term giving:
(11)
This needs the product rule.... Factor out the ....
(12)
This could be a chain rule problem.......
or you could take the power 2 out of the log and go straight to the same answer with a shorter version of the chain rule to:.
(13) Perform the following integrations:
must be converted to a double angle form as shown many times.... then all 3 bits are integrated giving .......
(14)
Apart from , which goes to , this is straightforward polynomial integration. Also there is a nasty trap in that two terms can be telescoped to .
(15) What is the equation corresponding to the determinant:
The first term is the second and the 3rd term zero. This adds up to .
(16) What is the general solution of the following differential equation:
where A is a constant..
.
(17) Integrate by parts:
Make the factor to be differentiated and apply the formula, taking care with the signs... .
There is much useful free material relevant to this book, including downloadable DVDs, funded by the HEFCE Fund for the Development of Teaching & Learning and the Gatsby Technical Education Project in association with the Higher Education Academy at Math Tutor.
Maths for Chemistry is an online resource providing interactive context-based resources which explain how various aspects of maths can be applied to chemistry. There are quizzes and downloadable files to check understanding.
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Learn to read, write, and think mathematically with Tussy and Gustafson's PREALGEBRA and its accompanying technology tools designed to help you save time studying and improve your grade. You'll develop your study skills, problem solving, and critical thinking as you master mathematical concepts. A pretest gauges your understanding of prerequisite concepts; problems that make correlations between your daily life and the mathematical concepts; and study skills information to give you the best chance to succeed in the course. The accompanying CD-ROM and access to iLrn Tutorials, MathNOW personalized study system, and live online tutoring with a math expert who has a copy of your textbook help you every step of the way to success. You also have access to TLE Labs, a proven way to master mathematics20310.99
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eChapter 6: Graphing, Exponents, and Polynomials
eChapter 7: Percent
eChapter 8: Ratio, Proportion, and Measurement
eChapter 9: Introduction to Geometry
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MA125 Intermediate Algebra
for U1FF class will be taught using a combination of lecture, demonstration, and discussion of sample math problems and homework. The best way to demonstrate understanding is to explain (teach) the material to a classmate; therefore, students are encouraged to work together on all parts of the course especially homework. Bonus points will be given for news, work, or life events where mathematics is or could/should be used to provide better decision-making information
Learning Outcomes: Core Learning Outcomes
State and use basic terminology and symbols of the discipline appropriately
Solve linear equations and inequalities in one variable and verify solution(s)Solve equations involving radicals
Apply the method of completing the square
Apply the quadratic formula
Graph algebraic equations and inequalities of one and two variables.
Instructor Learning Outcomes
State and use basic terminology and symbols of the discipline appropriately
Solve linear equations and inequalities in one variable and verify solutionClass Assessment: Students are required to complete homework and all chapter quizzes mid-term exam and the final exam. The mid-term exam, final exam, weekly quizzes, homework completion, participation, and attendance will be included in course assessment
Grading:
The course will be graded based on the following allocation:
Attendance, Homework and Participation/Demonstration 20 %;
Chapter Quizzes 30 %;
Mid-Term Exam 25%
Final Exam 25 %.
Total scores of 90 to 100 % will be considered an A. 80 to 89 % will receive a B, 70 to 79 % will receive a C, 60 to 69 % will receive a D. Any score below 60 % will be failing.
In addition, the final exam MUST be passed to receive any grade higher than a D
Late Submission of Course Materials: Late homework will not be accepted without prior coordination with the instructor. Students unable to take a quiz/exam will coordinate with the instructor prior to the period of the exam for an alternate exam time/place. Failure to do this will result in a failing grade on the quiz/exam
Classroom Rules of Conduct: Students should come to class prepared to discuss the subject material scheduled for the day. They are expected to have read the appropriate sections of the textbook and come prepared to ask questions about the topic of the day. The only dumb question is the one that doesn't get asked
Course Topic/Dates/Assignments:
Week 1: Chapter 1
Week 2: Chapter 2/Quiz (Chapters 1 & 2)
Week 3: Chapter 3
Week 4: Chapter 4/Mid-term Exam (Chapters 1-4)
Week 5: Chapter 5
Week 6: Chapters 6 & 7/Quiz (Chapters 5, 6, & 7)
Week 7: Chapters 8 & 9
Week 8: Review/Final Exam (Chapters 1-9Evaluate 4 out of 4 algebraic expressions
Evaluate 3 out of 4 algebraic expressions
Evaluate 2 out of 4 algebraic expressions
Evaluate 0 or 1 out of 4 algebraic expressions
Synthesis Outcomes 1
Simplify and manipulate 4 out of 4 algebraic expressions
Simplify and manipulate 3 out of 4 algebraic expressions
Simplify and manipulate 2 out of 4 algebraic expressions
Simplify and manipulate 0 or 1 algebraic expressions
Analysis Outcomes 2
Solve and check 4 out of 4 algebraic equations
Solve and check 3 out of 4 algebraic equations
Solve and check 2 out of 4 algebraic equations
Solve and check 0 or 1 out of 4 algebraic equations
Application Outcomes 3
Solve 4 out of 4 practical applications
Solve 3 out of 4 practical applications
Solve 2 out of 4 practical applications
Solve 0 or 1 practical applications
Content of Communication Outcomes 4
Graph 4 out of 4 linear equations or inequalities
Graph 3 out of 4 linear equations or inequalities
Graph 2 out of 4 linear equations or inequalities
Graph 0 or 1 linear equations or inequalities
Technical Skill in Communicating Outcomes 4
Find 4 out of 4 slopes of lines
Find 3 out of 4 slopes of lines
Find 2 out of 4 slopes of lines
Find 0 or 1 slopes of lines
First Literacy Outcomes (Formulas) 1, 2, 3
Use and evaluate 4 out
of 4 formulas
Use and evaluate 3 out
of 4 formulas
Use and evaluate 2 out
of 4 formulas
Use and evaluate 0 or 1 out
of 4 formulas
Second Literacy Outcomes (Order of Operations) 1, 2, 3
Apply order of operations to 4 out of 4 algebraic expressions
Apply order of operations to 3 out of 4 algebraic expressions
Apply order of operations to 2 out of 4 algebraic expressions
Apply order of operations to 0 or 1 out of 4 algebraic expressions
Copyright:
This material is protected by copyright
and can not be reused without author permission.
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30 - Mathematics for Liberal Arts
Survey of modern mathematics and applications, historical perspective, and calculator/computer applications with emphasis on the liberal arts. Topics include: sets, probability and statistics, systems of numeration, modern algebraic structures and modern geometries.
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DescriptionMathematica: A Problem-Centered Approach introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked- out problems. Each section starts with a description of a new topic and some basic examples. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations.
While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool.
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9780321559449KEY BENEFIT: TheBittinger Concepts and Applications Seriesextends proven pedagogy to a new generation of students, with updates throughout to help todayrs"s students learn. Bittinger transitions students from skills-based math to the concepts-oriented math required for college courses, and supports students with quality applications and exercises to help them apply and retain their knowledge. New features such as Translating for Success and Visualizing the Graph unlock the way students think, making math accessible to them. KEY TOPICS: Introduction to Algebraic Expressions; Equations, Inequalities, and Problem Solving; Introduction to Graphing; Polynomials; Polynomials and Factoring; Rational Expressions and Equations; Functions and Graphs; Systems of Equations and Problem Solving; Inequalities and Problem Solving; Exponents and Radicals; Quadratic Functions and Equations; Exponential and Logarithmic Functions; Conic Sections; Sequences, Series, and the Binomial Theorem; Elementary Algebra Review MARKET: For all readers interested in algebra.
Table of Contents
Introduction to Algebraic Expressions Introduction to Algebra The Commutative, Associative, and Distributive Laws Fraction Notation Positive and Negative Real Numbers Addition of Real Numbers Subtraction of Real Numbers Multiplication and Division of Real Numbers Exponential Notation and Order of Operations
Polynomials Exponents and Their Properties Negative Exponents and Scientific Notation Polynomials Addition and Subtraction of Polynomials Multiplication of Polynomials Special Products Polynomials in Several Variables Division of Polynomials
Functions and Graphs Introduction to Functions Domain and Range Graphs of Functions (including brief review of graphing) The Algebra of Functions Variation and Problem Solving
Systems of Equations and Problem Solving Systems of Equations in Two Variables Solving by Substitution or Elimination Solving Applications: Systems of Two Equations Systems of Equations in Three Variables Solv
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Prerequisites: No official prerequisites but "Mathematical Maturity" is a must. Linear algebra at the level of MA 405 will be very helpful.
Course Description: Combinatorics is the part of
mathematics concerned with discrete structures and finite sets. Anytime we need to answer the question "how many ways are there to do X?" we are usually solving a combinatorial problem. These discrete structures arise in more than just counting problems, and combinatorial reasoning pervades modern mathematics. This is the first course of a year-long series on combinatorics. The first semester will be on algebraic and enumerative combinatorics and the second semester will focus on geometric combinatorics. Main topics for the fall semester are: Fundamental Counting Problems and Techniques including "Balls in Boxes", Binomial and Multinomial Coefficients, Generating Functions, Partitions, Permutations (6 weeks), Partially Ordered Sets (4 weeks), Matroids (4 weeks)
Learning Objectives (This document will be updated throughout the course and can be used as a study guide.)
Homework: Homework will be assigned weekly and is due in class on Thursday, unless otherwise indicated. Students must write up their own solutions. Working with other students is allowed, however, you must first attempt all problems on your own before discussing solutions with other students. Limit your group size to at most four students. Each student must write up their own solutions.
Please indicate on your homework any sources that you used in preparing
solutions (e.g. if another student helped with a solution, or you found the
solution in a book).
It is acceptable
to use other sources besides the course notes and the text to aid your learning.
However, using other student's homework solutions
from previous courses, online homework solutions from courses at other
universities, or copying the solutions out of books are unacceptable
sources for preparing your homework, and violate the university's academic
integrity policy.
Students are encouraged to prepare homework solutions in LateX. Homework
assignments can be found at the course website as well as information on
preparing your homework in LateX.
A file explaining how to prepare your homework can be found here. Homework assignments can be found here.
Policy on Late Homework: Homework is due in class on Thursdays, unless otherwise indicated. Late homework will be accepted up to Friday at 5 PM of the week it was due, either to my mailbox, delivered to me in person, or by email and will received 80% of the points. Any homework turned in after Friday at 5 PM will receive a zero. If you must miss a class on the day a homework is due and you want full credit, it is your responsibility to get the homework to me by the beginning of class on Thursday. This could be delivered to my mailbox, delivered to me in person, turned in by another student, or by email.
Quizzes: There will be two 20-minute quizzes. Each quiz will be worth 5% of your grade. The quizzes will cover basic definitions and theorem statements only. The quizzes will be on September 24 and November 19.
Exams: There will be one in-class midterm exam and an in-class final exam. The midterm will be on October 8. The final exam will take place in the usual classroom from 1-4 PM on Thursday, December 12.
Grades: Grades will be based on Homework (40%), Quizzes (10%), Midterm (20%), and Final Exam (30%). Grades are based on the following scale: A : (> 85%), B: (70-85 %) C: (60-70%) D-F: (<60%).
Attendance and Participation: Participation in class activities, group work, and class discussions will be a key contributor to your understanding of the material. To encourage your participation, I will provide up to one third of a letter grade "bonus" to students that attend regularly and participate actively in group work in class (fyi: one third of a letter grade means B would become B+, B+ would become A-, etc.).
Adverse Weather: Announcements regarding scheduled delays or the closing of the University due to adverse weather conditions will be broadcast on local radio and television stations and posted on the University homepage.
Electronic Devices: You may use your electronic devices in class as long as it is not distracting to the other students or me. (Warning: I get distracted very easily.) Acceptible: Using a tablet to take notes. Unacceptible: Answering your phone in class, typing on a laptop.
Academic Integrity Statement: Students are required to follow the NCSU policy . "Academic dishonesty is the giving, taking, or presenting of information or material by a student that unethically or fraudulently aids oneself or another on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student's record or academic career.'' (NCSU Code of Student Conduct). The Student Affairs website has more information.
Students with Disabilities: Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disabilities Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.01).
Class Evaluations: Online class evaluations will be available for students to complete during the last two weeks of class. Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations. All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know the ratings for any particular instructors.
| 677.169 | 1 |
7
0
0
Volume 2 of Josiah H. Coggeshall's notebooks of lectures by Tapping Reeve and James Gould, transcribed at the Litchfield Law School. The original notebook is available in the Yale Law Library: This digitization is part of the Litchfield Law School Sources project and funded by The Cromwell Foundation. For further information or permissions, please contact Michael Widener at the Yale Law Library: mike.widener@yale.edu Topics: Litchfield Law School Students, Lecture Notes Connecticut Litchfield
2,274
1
0
Here you will find a series of question and answers from the teacher of this course, Andrew Sutherland, which introduce the course to the user. Topics: Free, open, online, high school, course materials, MIT, Lecture notes, MIT student developed...
355
0
0
A lot of events in our life seem random or impossible to predict. However, with probability theory we can learn more about these things to solve interesting problems that range from the lottery to diagnosing medical diseases. By teaching you basic principles and more advanced topics about theorems and models, this class will give you the tools to see the world in a different way that may not be intuitive but is proved by the math behind it. Topics: open, high school, probability, random, lecture notes, bayes' rule, counting, discrete random...
28,256
6
0
What do one mathematician, one artist, and one musician all have in common? Are you interested in zen Buddhism, math, fractals, logic, paradoxes, infinities, art, language, computer science, physics, music, intelligence, consciousness and unified theories? Get ready to chase me down a rabbit hole into Douglas Hofstadter's Pulitzer Prize winning book Gödel, Escher, Bach. Lectures will be a place for crazy ideas to bounce around as we try to pace our way through this enlightening tome. You... Topics: Free, open, online, high school, course materials, MIT, Lecture notes, MIT student developed...
| 677.169 | 1 |
This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including... more...
This book is an introduction to the arithmetic of complex numbers, and explains their role in solving equations in both plane and non-Euclidean geometry. Exercises with solutions are included in every chapter and the textbook is rounded out with an appendix on calculating with complex numbers and conformal transformations in MAPLE and Cinderella. more...
Twists, Tilings, and Tessellation describes the underlying principles and mathematics of the broad and exciting field of abstract and mathematical origami, most notably the field of origami tessellations. It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding... more...
This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of... more...
Practice makes perfect! Get perfect with a thousand and one practice problems! 1,001 Geometry Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems that deal with core geometry topics, such as points, lines, angles, and planes, as well as area and volume of shapes. You'll also find practice problems on more advanced... more...
This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern... more...
After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries... more...
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the principal... more...
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Basic Math Syntax in the System
The basic syntax for entering mathematical formulas or expressions in
the system enables you to quickly enter expressions using 2-D
notation. You can type formulas using standard mathematical notation (similar
to that used for a graphing calculator) and, in general, the system correctly
interprets it.
For example, the following formula is acceptable.
(x^2-2x+1) 2sin(x) (x^2+1)e^(-x^2)
Note: If
a product includes one or more variables, always use an asterisk "*". For example,
specify 2*$A.
For a Maple
question, you must always include an asterisk (*).
(x^2-2*x+1)*2*sin(x)*(x^2+1)*e^(-x^2)
The most common mistake is to forget parentheses "()".
For example, the expression:
1/(x+1)
is different from:
1/x+1
which the system interprets as:
(1/x) + 1
Alternatively, you can use MathML
expressions, which are supported for both display and content within the
system.
The arguments of trigonometric functions, remember
they are measured in radians.
The square root function, use sqrt(x).
(Alternatively, use x^(1/2) or x^0.5.)
In 2-D
Text Entry Mode the square root function is sqrt(x).
(Alternatively, you can enter x^(1/2) or x^0.5.) In Symbol Mode, use the keyboard shortcut
# for square root, or pick the symbol from
the Tools Palette.
The inverse trigonometric functions, use the standard
abbreviated names (arcsin(x), arccos(x),
and arctan(x)).
Note: The variable
e should not
be assigned as a global variable in Maple
code. It can be used, however, as a local variable.
| 677.169 | 1 |
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An Introduction to Numerical Methods and Analysis, Solutions Manual
Praise for the First Edition
". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math
An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics.
A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth.
The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis
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Education
Practice is the key to improving your algebra skills, and that's what this workbook is all about. This hands-on guide focuses on helping you solve the many types of algebra problems you'll encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, this workbook shows you how to work with fractions, exponents, factoring, linear ... Read More
1001 Algebra II Practice Problems For Dummies takes you beyond the instruction and guidance offered in Algebra II For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in algebra II. Plus, an online component provides you with a collection of algebra problems presented in multiple choice format to further help you test ... Read More
Passing grades in two years of algebra courses are required for high school graduation. Algebra II Essentials For Dummiescovers key ideas from typical second-year Algebra coursework to help students get up to speed. Free of ramp-up material, Algebra II Essentials For Dummies sticks to the point, with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical Algebra II course, from polynomials, conics ... Read More
Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math.
Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems ... Read More
Learn and practice your Algebra II skills with two friendly For Dummies guides for one low price!
This value-priced, two-book bundle brings two popular For Dummies math guides together to offer readers essential Algebra I instruction combined with real-world practice problems to put their knowledge to the test and help reinforce key Algebra I concepts. Each bundle includes full-size editions of Algebra II For Dummies ... Read More
Al
Do you have a grasp of Algebra II terms and concepts, but can't seem to work your way through problems? No fear -- this hands-on guide focuses on helping you solve the many types of Algebra II problems in an easy, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to ... Read More
Want to utilize cleaner, greener types of energy? This plain-English guide clearly explains the popular forms of alternative energy that you can use in your home, your car, and more. Separating myth from fact, this resource explores the current fossil fuel conundrum, the benefits of alternatives, and the energy of the future, such as hydrogen and fuel cell technology. ... Read More
Every year, more than 100,000 degrees are completed in biology or biomedical sciences. Anatomy and physiology classes are required for these majors and others such as life sciences and chemistry, and also for students on a pre-med track. These classes also serve as valuable electives because of the importance and relevance of this subject's content. Anatomy and Physiology For Dummies, 2nd Edition ... Read More
Are you flummoxed by phalanges, stymied by the scapula, or perplexed by pulmonary capillaries? Look no further. Topic by topic and problem to problem, Anatomy & Physiology Workbook For Dummies, 2nd Edition offers hundreds of practice problems, memorization tricks, and study tips to help you score higher in your anatomy and physiology course. With this handy guide you'll be identifying ... Read More
Perfect for those just starting out or returning to Anatomy after some time away, Anatomy Essentials For Dummies focuses on core concepts taught (and tested on!) in a typical Anatomy course. From names and technical terms to how the body works, you'll skip the suffering and score high marks at exam time with the help of Anatomy Essentials For Dummies.
Designed for students who want the key concepts and a few ... Read More
Unravel the history behind of one of the most fascinating ancient civilisations with this engaging, entertaining and educational guide to the ancient Egyptians. With a complete rundown of ancient Egyptian history and culture alongside insights in to the everyday lives of the Egyptians, you'll discover how they kept themselves entertained, the gory details of mummification, the amazing creation of the pyramids, the deciphering of hieroglyphs and much ... Read More
The civilisation of the Ancient Greeks has been immensely influential on the language, politics, educational systems, philosophy, science and arts of Western culture. As well as instigating itself as the birthplace of the Olympics, Ancient Greece is famous for its literature, philosophy, mythology and the beautiful architecture- to which thousands of tourists flock every year.
This entertaining guide introduces readers to the amazing world of the ... Read More
Get a handle on the fundamentals of biological and cultural anthropology
When did the first civilizations arise? How many human languages exist? The answers are found in anthropology - and this friendly guide explains its concepts in clear detail. You'll see how anthropology developed as a science, what it tells us about our ancestors, and how it can help with some of the hot-button issues our world ... Read More
Relax. The fact that you're even considering taking the AP Biology exam means you're smart, hard-working and ambitious. All you need is to get up to speed on the exam's topics and themes and take a couple of practice tests to get comfortable with its question formats and time limits. That's where AP Biology For Dummies comes in.
This user-friendly and completely reliable guide helps you get the most out of any AP biology class and reviews all of the ... Read More
Gearing up for the AP Chemistry exam? AP Chemistry For Dummies is packed with all the resources and help you need to do your very best. This AP Chemistry study guide gives you winning test-taking tips, multiple-choice strategies, and topic guidelines, as well as great advice on optimizing your study time and hitting the top of your game on test day.
This user-friendly guide helps you prepare without perspiration by developing a pre-test plan, organizing ... Read More
Getting ready to tackle the AP U.S. History exam? AP U.S. History For Dummies is a practical, step-by-step guide that will help you perfect the skills and review the knowledge you need to achieve your best possible score! Discover how to identify what the questions are really asking and find out how to combine your history knowledge with context clues to craft thoughtful essays. Try your hand at two true-to-life AP exams, complete with detailed answer ... Read More
Regarded as one of the most difficult languages to learn for native English speakers, Arabic is gaining global prominence and importance. Recent world events have brought more and more English speakers into contact with Arabic-speaking populations, and governments and businesses are increasingly aware of the importance of basic Arabic language skills. ... Read More
Regarded as one of the most difficult languages to learn for native English speakers by the U.S. State Department, Arabic is gaining both prominence and importance in America. Recent world events have brought more and more Americans and other English speakers into contact with Arabic-speaking populations, and governments and businesses are increasingly aware of the importance of basic Arabic language skills. ... Read More
Learn how to speak and understand Modern Standard Arabic quickly and easily with Arabic For Dummies Audio Set, which allows you to practice your skills whether you're at home or on the road. From 3 hours of instructional material on 3 CDs, learn basic greetings, vocabulary, how to ask for directions, get help when you need it most, expressions, grammar, and other essentials that will allow you to start communicating right away. Follow along with the ... Read More
Today readers with the tools to converse with others in Modern Standard Arabic on a basic level. It uses real-world ... Read More
Archaeology continually makes headlines--from recent discoveries like the frozen Copper-Age man in the Italian Alps to the newest dating of the first people in America at over 14,0000 years ago. Archaeology For Dummies offers a fascinating look at this intriguing field, taking readers on-site and revealing little-known details about some of the world's greatest archaeological discoveries ... Read More
Do you know the difference between a red giant and a white dwarf? From asteroids to black holes, this easy-to-understand guide takes you on a grand tour of the universe. Featuring updated star maps, charts, and an insert with gorgeous full-color photographs, Astronomy For Dummies provides an easy-to-follow introduction to the night sky. Plus, this new edition also gives you the latest theories, explanations ... Read More
The Armed Forces Qualifying Test (AFQT) is the most important part of the Armed Services Vocational Aptitude Battery (ASVAB), and you need to start preparing for it early. Your AFQT score determines which branch of the military you can join, and the better your score, the more attractive you become to recruiters. Your AFQT score is determined by your scores on the Verbal Expression, Mathematics Knowledge ... Read More
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Online Math Classes
Economics
Homeschool Entrepreneur
9-week course for teens which provides your budding entrepreneur with information he/she needs to launch a business while learning simple accounting, business skills, and advertising acumen.
Online Math Classes
Unique Math
AN A TO Z AFFILIATE
Unique Math brings together comprehensive math skills assessment with differentiated instruction, all administered in an interactive, online class. Let's Go Learn's Diagnostic Online Math Assessment (DOMA) Basic Math Skills first performs a detailed assessment of each student's basic math abilities across multiple benchmarks. After the initial assessment, the program transitions homeschool students into interactive tutorials and activities that improve essential math skills.
Algebra 1 – High School
This is a self-paced, online course. You have 6 months to finish. An instructor will monitor your progress and assess your body of work at course completion.
A+ TutorSoft
Currently has an online Algebra 1 class. Editions available for students wishing to work alone, and for those with parent support and supervision. Homeschoolers, select Products -> Home School Edition. Free 15-day trial.
eTap Math
Self-paced algebra class completely online, suitable for students in about grades 6-10. Starts with place value and ends with quadratic equations and statistical functions. Students must register, so kids, ask your parents if this is OK and what information you should give out.
Geometry Class for High School
This geometry course is designed for those students, young or old, who need a thorough course in Geometry. This online class is equivalent to the first semester of high school geometry. The class and its sequel, Geometry (second semester) will prepare you well for Algebra 2 and Precalculus. Also taught by Sue.
Kahn Acaedmy
Free online classes in video format. Knowledge map to show you how concepts in math are related. Begin where ever you want.
MathOps
Online pre-algebra and algebra video tutorials. Join our service and explore online classes, video examples, and interactive quizzes. It is like having your own math tutor, but with interactive lessons you access whenever you are ready.
Omega Math
These classes have been online since 1997, and each lesson has been tested by the students for over fifteen (15) years
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