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Description: The text represents one person's attempt to put the essential ideas of calculus into a short and concise format. It may not appeal to a wide range of mathematicians, but it should provide most students with a good foundation in calculus.
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Find a Southeastern CalA continuation of Algebra 1 (see course description). Use of irrational numbers, imaginary numbers, quadratic equations, graphing, systems of linear equations, absolute values, and various other topics. May be combined with some basic geometry. Emphasis on the ideas that lie behind dates, facts and documents
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Elementary Algebra - 9th edition
Summary: Ideal for lecture-format courses taught at the post-secondary level, ELEMENTARY ALGEBRA, Ninth Edition, makes algebra accessible and engaging. Author Charles ''Pat'' McKeague's passion for teaching mathematics is apparent on every page. With many years of experience teaching mathematics, he knows how to write in a way that you will understand and appreciate. His attention to detail and exceptionally clear writing style help you to move through each new concept with ease, and real-wor...show moreld applications in every chapter highlight the relevance of what you are learning79.03 +$3.99 s/h
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PaperbackshopUS Secaucus, NJ
Used - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000
$97175.70
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For Algebra, Spreadsheets Beat Newer Teaching Tools
You already own better algebra-teaching software than any educational software developer is making.
If you do a search on "from arithmetic to algebra" as a verbatim phrase, you'll get about 600 hits, with the ones from Google Books reaching back into the nineteenth century. About three out of every four will be about helping students make the transition from arithmetic to algebra -- it has been known for a very long time that that's where we lose many people who are never able to advance much further in math.
As I noted before, 25 years ago RAND surveyed the then-nascent field of educational software and found many effective arithmetic teaching programs and practically nothing that taught any of the important aspects of algebra (abstract relations, strategy, fundamental concepts and so on). Even back in 1988, it was clearly understood that arithmetic training programs should not be the model for developing algebra educational software because arithmetic is taught as procedural training. When you teach the quadratic formula, polynomial factoring or Cramer's Rule as if they were mere complex recipes like long division, you miss the fundamental concepts that are the whole point of studying algebra.
Depressingly, my survey of algebra-teaching software revealed that 25 years later the situation remains the same. Plenty of programs will drill a student on algebraic procedures, but most do not even attempt to teach any sort of insight, strategy or deeper understanding. Even the best merely offer supporting text or "guess the next step," the same wrong-headed approach that the pioneering math educator Mary Everest Boole identified about the arithmetic-to-algebra transition in 1909.
Proceduralism is about performing tasks (now write this number here and do this ...), but conceptualism is the heart of mathematics (how are these numbers connected or related?). In the leap from "what do I do?" to "what is it?" we're losing many students who might otherwise have gained not only the higher incomes, but the much better understanding of the world, to which mathematics is the gateway.
Now, there may be an educational software design company out there right now about to fix this problem, but probably there's not. And parents and teachers who need to get a seventh-to-ninth grader across the gap right now can't very well wait until he or she is halfway through college, or longer, for algebra teaching software that actually teaches algebra.
And yet there is a piece of instructional software right on your computer that can be used to teach all levels of algebra to all levels of student, in a fully conceptual way. It's the spreadsheet.
You can find plenty of discussion and advice about how to do this from excellent teachers like Tom Button, Sue Johnston-Wilder and David Pimm, Teresa Rojano and Ros Sutherland, but let's just quickly hit the highlights of how exploring spreadsheets, and then exploring with spreadsheets, can provide a conceptual doorway into algebra. If you're interested, you'll find all but limitless resources for this.
Consider, to begin with, that variables and parameters in spreadsheets are very similar to what they are in ordinary algebra. For that matter, Microsoft Excel notation (and most of the Open Office software notation) is either algebra notation outright, or so close that only simple explanations need to be given ("in algebra the multiplication asterisk is understood, in Excel you have to put it in," "what we call a function in algebra is what a formula is in Excel," etc.).
A basic insight of algebra is that a function can be thought of as a rule OR a table OR a graph. (I'm capitalizing because it's the Boolean logical OR rather than ordinary English "or.") In fact, they are three different ways of looking at the same thing. Similarly, a spreadsheet formula can be used to generate a table of data, and the spreadsheet's graphing features can be used to turn it into a graph.
I found in teaching elementary algebra to disadvantaged adult learners that the progression from table to graph and then to formula/function/equation might have been the most powerful tool for "selling" algebra I ever encountered. Anyone can see intuitively that for many problems, if you just make a table big enough, trying out all the possible values will lead to a solution. From there, it's a short step to, but what if there are millions of values? Then they're ready to graph it and the answers are right there at the intersections. From there it's just the step to, but what if you need an answer more exact than the line you can draw, or more dimensions than two? Well, by then, they're used to the idea of formula/function/equation as description, and if a point satisfies more than one description, it's a solution. And they've crossed over to doing algebra.
The spreadsheet provides a natural bridge from arithmetic procedure to formula/function. At first, students will just input numbers, as if the spreadsheet were a calculator. Then they see that if they input variables, they don't have to type nearly so much, and then that this means having not just this answer this time, but all the answers to all problems of this type, all the time.
It's a wide and easy-to-cross bridge from the specific to the general, and from procedure to concept.
One of the big changes in mathematics in the last 30 years has been the idea of experimental math, i.e., of exploring how numbers work by setting up numerical processes and looking at the results; it's at the heart of chaos research, for example. Just as the computer has become the equivalent of the telescope or microscope for mathematicians, Excel can be used as an amateur "scope" for exploring numbers, in a way very much analogous to the way countless students have gotten a handle on science by finding a planet in the sky or exploring the ecology of pond water. Among other things, I've used Excel to teach how every fraction is a division, and division is equivalent to multiplying by the inverse. It could easily be used for many other projects beginning even from a very early age in arithmetic.
Spreadsheet algebra is such an effective and intuitive idea that it has been re-invented several times in the last 20 years, and some Googling around will turn up immense amounts about it. (Caution: "spreadsheet algebra" is also a term used in advanced mathematics research for a kind of non-linear matrix algebra, so your Googling may very well turn up an article or two that's a bit beyond you. Don't worry, just keep looking!)
Although there still needs to be a human being there to guide the student in exploring and using the spreadsheet, as a teaching device for actual algebra (as opposed to a drilling device for standardized tests) the spreadsheet still beats out thousands of purpose-designed products.
They said that about calculators, graph paper, and probably the abacus. The funny thing is that although the spreadsheet does make it possible to avoid learning procedure, you can't use it effectively unless you learn concepts. So it's really a powerful tool for dragging people over the border from the "do your sums this way" to the real kingdom of mathematics
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97804703844 12Engineers and computer scientists who need a basic understanding of algebra will benefit from this accessible book. The sixth edition includes many carefully worked examples and proofs to guide them through abstract algebra successfully. It introduces the most important kinds of algebraic structures, and helps them improve their ability to understand and work with abstract ideas. New and revised exercise sets are integrated throughout the first four chapters. A more in-depth discussion is also included on Galois Theory. The first six chapters provide engineers and computer scientists with the core of the subject and then the book explores the concepts in more detail.
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Are you looking for information about math for adults? As reported in Overcoming Math Anxiety (1978, 1993, 2nd edition) in 600 interviews with college-age and older returning students, Sheila Tobias found three significant variables in her subjects' inability to do college-level mathematics: fear of mathematics, the conviction that mathematics is a white male domain, and the conviction that one is either good in mathematics or in language arts but never both. The students' lack of coping skills in dealing with mathematics classes and with their own anxieties appeared to be the main barrier to their attempting mathematics one more time. Subsequently, Tobias focused her research on entering college students. Her second book, Succeed With Math: Every Student's Guide to Conquering Math Anxiety (1987) was commissioned by the College Board. What follows is a selection of excerpts from that book.
Two myths about mathematics need to be put to rest. One is that college-level mathematics is too difficult for otherwise intelligent students to master. Another is that without mathematics anyone can live a productive intellectual and professional life.
Mathematics is no longer just an entry-level prerequisite for engineering, the physical sciences, and statistics. Its principles and techniques, along with computers, have become part of almost all areas of work, and its logic is used in thinking about almost everything.
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More About
This Textbook
Overview
Assessment and Learning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained. ALEKS courses are very complete in their topic coverage and ALEKS avoids multiple-choice questions. A student who shows a high level of mastery of an ALEKS course will be successful in the actual course she is taking.
Product Details
Meet the Author
Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.
My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I'd like to see math come alive for my students.
Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics.
I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.
Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years. During this time she taught the full spectrum of courses from developmental math through differential equations. She received a bachelor of science degree in math education from Florida State University and a master's degree in math education from Florida Atlantic University. She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom. In addition to this textbook, she has authored a graphing calculator supplement for College Algebra.
I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics
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The mathematics department at UNCA is reforming the
teaching method and the content of its three semester calculus
sequence. There are two motivations driving this reform --- a low
retention rate (particularly in Calculus I) and the ``successful"
calculus students' lack of understanding of fundamental calculus
concepts. Thus our goals are increasing students' understanding of
limits, derivatives and integrals and increasing retention in Calculus
I. We are integrating computer lab explorations with instructor led
lectures and student led discussions while emphasizing applications
which illustrate and reinforce the fundamental calculus concepts.
This talk will describe the steps taken and the lessons learned in our
reform efforts thus far: i) small scale experiment, ii) successful
NSF-ILI grant proposal, iii) computer classroom renovation, iv)
submitting NSF-CCD grant proposal.
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Precalculus A Make it Real learning mathematics, have you ever asked yourself, "When am I ever going to use this?" If you have--and even if you haven't--this book will help you learn the mathematical concepts behind the procedures, and discover how to apply quantitative thinking in your daily lives. PRECALCULUS: A MAKE IT REAL APPROACH doesn't simply "wrap" a real-world situation around a mathematical concept or procedure. Instead, you'll be immersed in familiar real-world contexts--from parking rates and the higher winter incidence of the flu to Egyptian pyramids--that will help you understand mathematical ideas intuitively. One student commented, "It's like having the teacher standing over my shoulder explaining things to me." With this text as your guide, your comment about precalculus will likely be, "Yes, I get it!"
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Browse related Subjects
Includes more than 1,900 solved problems, examples, and practice exercises to sharpen your problem-solving skills of algebra.Includes more than 1,900 solved problems, examples, and practice exercises to sharpen your problem-solving skills of algebra
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The important ideas of algebra, including patterns, variables, equations, and functions, are the focus of this book. Student activities that introduce and promote familiarity with these ideas include constructing growing patterns using isosceles triangles, analyzing situations with constant or varying rates of change, and observing and representing various patterns in an array. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.
"About this title" may belong to another edition of this title.
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Navigating Through Algebra in Grades 3-5 (Principles and Standards for School Mathematics Navigations Series): Search Results
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Writing Mathlets I: A Call to Math Professionals
Author(s):
Tom Leathrum
This is the first in a planned series of articles intended to encourage working college math instructors to write their own applets, and to share their results with other developers, by providing mathematical incentives for learning how to write applets. I want to show in this series how writing applets related to specific topics in a standard undergraduate math course can lead into some interesting mathematical puzzles which may motivate both you and your students to pursue the topics to a higher level. I will do this by providing a few examples from my own experiences as an applet developer and from several different fields of mathematics. The first example comes from a puzzle I encountered while writing an applet for a specific topic in precalculus algebra: equations for parabolas.
This applet, which explores the connection between two different forms of equation for a parabola, was the very first math applet I completed in Java. When I noticed the visual effect I describe below, I looked again at the formulas for the coefficients of the equations in the different forms, and it wasn't difficult for me to see what was happening. In fact, any precalculus student should be able to work through the algebra. But the effect stuck with me. This was an effect I had not expected, even though I wrote the applet and had taught this material many times. It was a moment of discovery for me.
The connection I found was between the formulas for the coordinates (h,k) for the vertex of a parabola and a set of parametric equations for a parabola. You may object that precalculus students have not seen parametric equations yet, but any precalculus course will make use of the parametric form (cos t, sin t) for points on a unit circle, so I think the students can be expected to make the visual connection here, too. The parameter in this example can be eliminated, by some relatively straightforward algebraic procedures, resulting in a more familiar equation for a parabola.
Begin, in the applet, with the parabola y = x2 - 2x + 1 (so a = 1, b = -2, c = 1), which has its vertex at (h,k) = (1,0). Now use the "+" button under the "b=" label to change the value of b from -2.0 to 2.0. Note the path that the vertex (h,k) follows as you do this.
Underlying Mathematics
The two most common forms for the equation for a parabola are the general form and the standard form:
Here the point (h,k) is the vertex of the parabola.
Formulas relating the coefficients a, b, and c with the coordinates h and k can be found by completing the square in the general form (to rewrite it in standard form) or multiplying out and combining in the standard form:
The applet essentially implements these formulas to update all values when one is changed, and it graphs the parabola using the general form equation (for computational reasons).
In the example starting from y = x2 - 2x + 1, with a = 1 and c = 1, treat b as a parameter in the above formulas for h and k:
To eliminate the parameter b, solve for b in the first equation and b2 in the second:
Plug -2h in for b in the second equation:
And simplify:
Keeping in mind that h is the x-coordinate of the vertex and k is the y-coordinate, make the substitution h = x and k = y:
So the path the vertex follows is along the parabola y = 1 - x2, as shown in the following diagram:
The same algebra can be carried out in a more general context, without plugging values into a and c, to show that this situation is not unique -- in fact, it must happen pretty much the same way for any starting parabola.
So no matter what the starting values for a and c, as b changes, the vertex of the parabola follows a path along the parabola y = c - ax2 -- the vertex of this parabola must be on the y-axis, and its vertical orientation (opening upward or opening downward) must be opposite the starting parabola (because of the appearance of -a).
Conclusion
This example demonstrates much about the practice of mathematical exploration -- using terminology which seems currently fashionable, the exploration follows the steps of experimentation with the applet and changing the values of the b coefficient, conjecture that the path the vertex follows is itself a parabola, proof from the formulas that this is the case, and generalization that it must also be the case for other starting parabolas. All of the mathematics, though, is at a level that a precalculus student can understand. This allows students both to pursue the material more deeply and to experience mathematics as a process.
I will continue this thread in future articles in this series, again using examples from my own experiences developing applets. For example, I will present a puzzle (for which, at this writing, I have yet to find a satisfactory answer) related to three-dimensional graphics and involving a blend of linear algebra and geometry. A student who understands projections should be able to see the challenge in that problem.
So I want to challenge readers to do two things: first, try this exploration (or others available as math applets) with your own students; and second, develop your own applets and explorations for your courses. If my experience has been any indication at all, you will find the experience worth sharing.
In Future Articles
To provide some scope for this series, I need to say what I will and won't be doing in the articles. I will not teach how to write applets. Instead, I want to provide mathematical incentives for learning how to write applets. As in the example above with the "Parabolas" applet, I want to show in this series how writing applets can lead into some interesting mathematical puzzles for you and your students. This example comes from a topic in precalculus algebra -- other articles will look at topics in linear algebra, calculus, and perhaps other fields.
While MathDL and JOMA have taken on the task of collecting and publishing quality math applets, you should not expect any list of math applets to be comprehensive. There may not yet be a good applet for the specific topic you want to cover in your course. But from your own experience teaching the course, you know what a good applet should look like and how it should help your students visualize the material. This series aims to motivate you to begin your own applet development, perhaps with your students, by showing you that there can be some unexpected mathematical benefits.
Many of these examples would work as well in standalone applications as in online applets. Applet-enabled Web browsers provide a new and flexible way of presenting math visualizations, though. This series will not attempt to justify online presentation over other modes. However, online presentation may attract new people to begin developing applets. For example, bandwidth limitations of online material actually encourage developers to write small, topic-specific applets. This is in contrast to the commercial pressures usually involved in writing and publishing math software, which generally lead to large and comprehensive packages. People who otherwise would not be inclined to develop math software, but are frustrated by the cost and size of existing packages, now have an alternative.
I personally use the Java™ platform when writing applets, and my examples will be Java™ applets, but nothing I will say in these articles will be specific to that platform. Any platform with the same computational and graphical capabilities can be used with the same results. In fact, I will include as little code as possible in the discussions, although the source code for the example applets will be available for those interested. The discussions of some examples may lead to issues of performance and computational feasibility, especially when comparing different ways of solving problems, but I will keep the formal computer science to a minimum and instead emphasize the mathematical aspects of the solutions. Other parts of the Developers' Area may provide links to the resources you will need once you decide to learn and write applets.
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Computational Excursions in Analysis andExplanations are thorough but not easy to understand. Nevertheless, they can be understood by the determined graduate student in mathematics. However, the ideal mix would be a collection of mathematics and computer science students, as the level of computer expertise needed to code the solutions to the problems is at the upper division level…Research mathematicians often need to be able to write code to attack specific problems when no appropriate software tool is available. This book is ideal for a course designed to teach graduate students how to do that as long as they have or can obtain the necessary programming knowledge."
P. Borwein
Computational Excursions in Analysis and Number Theory
"Borwein has collected known results in the direction of several related, appealing, old, open problems (Integer Chebyshev, Prouhet-Tarry-Escott, Erdos-Szekeres, Littlewood). Far from narrow, this interdisciplinary book draws on Diophantine, analytic, and probabilistic techniques. Also, by dint of the celebrated lattice reduction algorithm, some aspects of these problems admit attack by computer; a handful of intriguing computer graphics offer visceral evidence of the intrinsic complexity of the underlying phenomena. Pisot and Salam numbers make terrific enrichment material for undergraduates. As in all Borwein's books, we get beautiful mathematics gracefully explained."—CHOICE
"This extraordinary book brings together a variety of old problems – old, but very much alive - about polynomials with integer co-efficients. … The necessary background is also presented, which makes the book self-contained … . this book is suitable for advanced students of analysis and analytic number theory. It is very well written, rather concise and to the point. … Strongly recommended for specialists in computational analysis and number theory." (R. Stroeker, Nieuw Archief voor Wiskunde, Vol. 7 (3), 2006)
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A distinguished mathematician and educator enlivens abstract discussions of arithmetic, algebra, and analysis by means of graphical and geometrically perceptive methods. His three-part treatment begins with topics associated with arithmetic, including calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers. Algebra-related subjects constitute the second part, which examines real equations with real unknowns and equations in the field of complex quantities. The final part explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 edition. 125 figures.
More editions of Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis (Dover Books on Mathematics):
Four volumes in one: Famous Problems of Elementary Geometry, by Klein. A fascinating, simple, easily understandable account of the famous problems of Geometry--The Duplication of the Cube, Trisection of the Angle, Squaring of the Circle--and the proofs that these cannot be solved by ruler and compass. Suitably presented to undergraduates, with no calculus required. Also, the work includes problems about transcendental numbers, the existence of such numbers, and proofs of the transcendence of $e$. From Determinant to Tensor, by Sheppard. A novel and simple introduction to tensors. ``An excellent little book, the aim of which is to familiarize the student with tensors and to give an idea of their applications. We wish to recommend the book heartily ... The beginner will find the book a valuable introduction and the expert an interesting review with a refreshing novelty of presentation.'' --Bulletin of the AMS Chapter headings: 1: Origin of Determinants; 2: Properties of Determinants; 3: Solution of Simultaneous Equations; 4: Properties; 5: Tensor Notation; 6: Sets; 7: Cogredience, etc. 8: Examples from Statistics; 9: Tensors in Theory of Relativity. Introduction to Combinatory Analysis, by MacMahon. An introduction to the author's two-volume work. Three Lectures on Fermat's Last Theorem, by Mordell. This famous problem is so easy that a high-school student might not unreasonably hope to solve it: it is so difficult that as of the 1962 publication date of this book, tens of thousands of amateur and professional mathematicians, Euler and Gauss among them, failed to find a complete solution. Mordell himself had a solution (as he said he did). This work is one of the masterpieces of mathematical exposition.
More editions of Famous Problems and Other Monographs (AMS Chelsea Publishing):
Widely regarded as a classic of modern mathematics, this expanded version of Felix Klein's celebrated 1894 lectures uses contemporary techniques to examine three famous problems of antiquity: doubling the volume of a cube, trisecting an angle, and squaring a circle. Today's students will find this volume of particular interest in its answers to such questions as: Under what circumstances is a geometric construction possible? By what means can a geometric construction be effected? What are transcendental numbers, and how can you prove that e and pi are transcendental? The straightforward treatment requires no higher knowledge of mathematics. Unabridged reprint of the classic 1930 second edition.
More editions of Famous Problems of Elementary Geometry (Dover Phoenix Editions):
Founder of the National Society for Graphology, Felix Klein began his study of graphology in his birthplace, Vienna, Austria, at the age of thirteen. He was a practicing graphologist all of his life and lectured and gave seminars throughout the United States and in Canada, England, Germany, Israel and Mexico. Mr. Klein came to the United States in 1940 after spending six months each in the concentration camps at Dachau and Buchenwald. While in those camps he formulated his theory of directional pressure as a result of studying changes in the handwriting of his fellow inmates. Mr. Klein did extensive work in personnel selection for major companies and banks, vocational guidance, and individual analyses, as well as forensic document examination for such entities as the U.N., AT&T, and a major political figure in Ghana, Africa. It was probably as a teacher that Felix was most known and loved. He held classes and offered correspondence courses in all levels of graphology: elementary, intermediate, advanced, Master Research, and Psychology for Graphologists. Wherever Felix spoke, his warm, caring personality and his naturalness and keen sense of humor generated enthusiastic responses from young and old alike.
More editions of Gestalt Graphology: Exploring the Mystery and Complexity of Human Nature Through Handwriting Analysis:
In the late summer of 1893, following the Congress of Mathematicians held in Chicago, Felix Klein gave two weeks of lectures on the current state of mathematics. Rather than offering a universal perspective, Klein presented his personal view of the most important topics of the time. It is remarkable how most of the topics continue to be important today. Originally published in 1893 and reissued by the AMS in 1911, we are pleased to bring this work into print once more with this new edition. Klein begins by highlighting the works of Clebsch and of Lie. In particular, he discusses Clebsch's work on Abelian functions and compares his approach to the theory with Riemann's more geometrical point of view. Klein devotes two lectures to Sophus Lie, focussing on his contributions to geometry, including sphere geometry and contact geometry. Klein's ability to connect different mathematical disciplines clearly comes through in his lectures on mathematical developments. For instance, he discusses recent progress in non-Euclidean geometry by emphasizing the connections to projective geometry and the role of transformation groups. In his descriptions of analytic function theory and of recent work in hyperelliptic and Abelian functions, Klein is guided by Riemann's geometric point of view. He discusses Galois theory and solutions of algebraic equations of degree five or higher by reducing them to normal forms that might be solved by non-algebraic means. Thus, as discovered by Hermite and Kronecker, the quintic can be solved ""by elliptic functions"". This also leads to Klein's well-known work connecting the quintic to the group of the icosahedron. Klein expounds on the roles of intuition and logical thinking in mathematics. He reflects on the influence of physics and the physical world on mathematics and, conversely, on the influence of mathematics on physics and the other natural sciences. The discussion is strikingly similar to today's discussions about ``physical mathematics''. There are a few other topics covered in the lectures which are somewhat removed from Klein's own work. For example, he discusses Hilbert's proof of the transcendence of certain types of numbers (including $\pi$ and $e$), which Klein finds much simpler than the methods used by Lindemann to show the transcendence of $\pi$. Also, Klein uses the example of quadratic forms (and forms of higher degree) to explain the need for a theory of ideals as developed by Kummer. Klein's look at mathematics at the end of the 19th Century remains compelling today, both as history and as mathematics. It is delightful and fascinating to observe from a one-hundred year retrospect, the musings of one of the masters of an earlier era.
This well-known work covers the solution of quintics in terms of the rotations of a regular icosahedron around the axes of its symmetry. Its two-part presentation begins with discussions of the theory of the icosahedron itself; regular solids and theory of groups; introductions of (x + iy); a statement and examination of the fundamental problem, with a view of its algebraic character; and general theorems and a survey of the subject. The second part explores the theory of equations of the fifth degree and their historical development; introduces geometrical material; and covers canonical equations of the fifth degree, the problem of A's and Jacobian equations of the sixth degree, and the general equation of the fifth degree. Second revised edition with additional corrections.
More editions of Lectures on the Icosahedron (Dover Phoenix Editions):
This collection of essays by a distinguished mathematician and teacher examines important issues of dynamics from the viewpoint of the theory of functions of the complex variable. Based on a series of lectures delivered by Felix Klein in conjunction with Princeton Universitys 150th anniversary, these presentations center on the problem inherent in the motion of a topthat is, a rigid body rotating about an axiswhen a single point in this axis other than the center of gravity is fixed in position. The contents of this volume render discussions of dynamics-related issues simpler, more attractive, and relevant not only to mathematicians but also to engineers, physicists, and astronomers. Unabridged republication of the classic 1897 edition.
More editions of The Mathematical Theory of the Top (Dover Phoenix Editions):
Originally published in 1897 Mathematical Theory of the Top: Lectures Delivered on the Occasion of the Sesquicentennial Celebration of Princeton [ 1897 ]:
A consideration of the investigations in the first part of Riemann's Theory of Abelian Functions, this volume introduces Riemann's approach to multiple-value functions and the geometrical representation of these functions by what later became known as Riemann surfaces. It further concentrates on the kinds of functions that can be defined on these surfaces, confining the treatment to rational functions and their integrals, and then demonstrates how Riemann's mathematical ideas about Abelian integrals can be arrived at by thinking in terms of the flow of electric current on surfaces. Deeply significant in the area of complex functions, this work constitutes one of the best introductions to the origins of topological problems. Unabridged republication of the classic 1893 edition. 43 figures. Glossary.
More editions of On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises (Dover Books on Mathematics):
The lecture series on the Theory of the Top was originally given as a dedication to Göttingen University by Felix Klein in 1895, but has since found broader appeal. The Theory of the Top: Volume I. Introduction to the Kinematics and Kinetics of the Top is the first of a series of four self-contained English translations that provide insights into kinetic theory and kinematics.
More editions of The Theory of the Top. Volume I: Introduction to the Kinematics and Kinetics of the Top:
The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. The Theory of the Top: Volume III. Perturbations: Astronomical and Geophysical Applications is the third installment in a series of four self-contained English translations that provide insights into kinetic theory and kinematics.
More editions of The Theory of the Top Volume III: Perturbations. Astronomical and Geophysical Applications:
The Theory of the Top. Volume II. Development of the Theory in the Case of the Heavy Symmetric Top is the second in a series of four self-contained English translations of the classic and definitive treatment of rigid body motion. Graduate students and researchers interested in theoretical and applied mechanics will find this a thorough and insightful account. Other works in this series include Volume I. Introduction to the Kinematics and Kinetics of the Top, Volume III. Perturbations. Astronomical and Geophysical Applications, and Volume IV. Technical Applications of the Theory of the Top.
More editions of The Theory of the Top. Volume II: Development of the Theory in the Case of the Heavy Symmetric Top:
The two volumes collected here represent what were to be the first two parts of Klein's plan to write a complete history of the mathematics of the 19th Century. This remarkable book was written by Klein during the last years of his life, a time coinciding with exciting mathematical activity and also the first World War. It is his personal view of the significant developments in mathematics in the 1800s (and early 1900s), especially those connected with the German school. This period includes the time of Klein's greatest activity and influence as a mathematician. The selection of topics reflects Klein's own interests in mathematics. The topics in the first volume include: Gauss's work in pure and applied mathematics; mathematics in France during the early decades of the 19th Century; the contributions of Mobius, Plucker and Steiner to the development of algebraic geometry; mechanics and mathematical physics in England and Germany up to the 1880s; complex analysis according to Riemann and according to Weierstrass; automorphic functions and the interplay between group theory and function theory. The second volume focuses on invariants and their applications in mathematical physics, with particular emphasis on special relativity. Both volumes were published after Klein's death. The final draft for the first volume was prepared by Courant and Neugebauer. The second volume was prepared by Courant and Cohn-Vossen
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The study of geometry—whether taught as a stand-alone or as a series of topics integrated within other courses—develops core ideas, concepts, and habits of mind that students will need as users of mathematics and as lifelong learners.
Connect the process of problem solving with the content of the Common Core. The first of a series, this book will help mathematics educators illuminate a crucial link between problem solving and the Common Core State StandardsThis book focuses on essential knowledge for teachers about proof and the process of proving. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings.
A valuable resource to any mathematics teacher, this rich collection of mathematical tasks will enliven students' engagement in mathematical thinking and reasoning and help them succeed in the classroom.
How do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)?
This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for high school. Discover what students should learn and how they should learn it, including deep support for the Mathematical Modeling conceptual category of the CCSS. Comprehensive and research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency. You'll also learn how fundamental shifts in collaboration, instruction, curriculum, assessment, and intervention can increase college and career readiness in every one of your students. Extensive tools to implement a successful and coherent formative assessment and RTI response are included.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Basic Probability Theory elementary probability theory with interesting and well-chosen applications that illustrate the theory
Main results in elementary probability, random variables, random vectors and the central limit theorem are covered
Applications in reliability theory, basic queuing models, and time series are presented
Over 400 exercises reinforce the material and provide students with ample practice
Introductory chapter reviews the basic elements of differential calculus which are used in the material to follow
This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the all important central limit theorem, are treated next. The last three chapters concentrate on applications of this theory in the areas of reliability theory, basic queuing models, and time series. Examples are elegantly woven into the text and over 400 exercises reinforce the material and provide students with ample practice.
This textbook can be used by undergraduate students in pure and applied sciences such as mathematics, engineering, computer science, finance and economics.
A separate solutions manual is available to instructors who adopt the text for their course.
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The
student will have a basic understanding of the concept of a continuous
function. (L1)
The
students will be able to compute derivatives of polynomial, rational,
exponential, logarithmic, and trigonometric functions. (L1)
The
student will be able to use implicit differentiation to find derivatives.
(L1)
The
student will be able to apply differential calculus to related rate,
maximum-minimum, and curve sketching problems. (L1)
The
student will understand the definition of the indefinite and definite
integral. (L1)
The
student will understand and be able to apply the Fundamental Theorem of
Calculus. (L1)
Grading Procedure :
Tests (300
points): There will be four 50-minute tests, each worth 100 points. The
lowest of these four test scores will be dropped.
Quizzes (100
points): There will be approximately twelve short quizzes, each worth 10
points. Only the highest ten quiz scores will be counted. Thus, the highest
possible number of points earned from the quizzes is 100.
Final Exam
(200 points):There will be a
comprehensive final exam, worth 200 points.
For your grade
in the course, the following grading scale will be used:
(note that the
highest possible number of points is 600)
·540-600 points earns a grade of A
·480-539 points earns a grade of B
·420-479 points earns a grade of C
·360-419 points earns a grade of D
·below 360 points earns a grade of F
Test and
Quiz Policy:The lowest of your
four 50-minute test scores will be dropped.
Only your
highest ten quiz scores will be counted. No make-up tests or quizzes will
be given. If one test is missed, this will be
considered as the test with the lowest
score, and will be the test that is
dropped.A second (or more) missed test
will be
given a grade of F. Missed quizzes get a
grade of 0 out of 10.
Homework:Homework
will be assigned during each class meeting. It is to be completed by the next
class meeting.Although homework will
not be collected or graded, it is ESSENTIAL to your success in the course that
you do the
homework regularly, and on time. Part of each homework assignment is to read
the corresponding material in the text.
Other:It is strongly recommended
that you allow at least four hours outside of class, before each class meeting,
for homework and study (more would be better). Remember - we will be covering
more than two weeks worth of material (as covered in a Fall or Spring semester
course) each week.Also remember: this
is a 4-credit course. This means that each week we will be covering the
equivalent of more than eight 50-minute class meetings.
It is strongly
recommended that you do not take this course if your grade in 1113 or 1112
was not C or better.
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Summary: ... with animations.[Expand Summary] input signal with the systems impulse response.
The files attached demonstrate the convolution process with animations.[Collapse Summary]
Keywords:axis of symmetry, general form of a quadratic function, quadratic formula, roots, standard form of a quadratic function, vertex, vertex form of a quadratic function, zeros
Summary:In this section, you will:
Recognize characteristics of parabolas.
Understand how the graph of a parabola is related to its quadratic function.
Determine a quadratic function's minimum or maximum value.
Solve problems involving a quadratic function's minimum or maximum value.
Summary:By the end of this section, you will be able to:
Discuss the fundamental difference between anaerobic cellular respiration and fermentation
Describe the type of fermentation that readily occurs in animal cells and the conditions that initiate that fermentation
Keywords:coefficient, continuous function, degree, end behavior, leading coefficient, leading term, polynomial function, power function, smooth curve, term of a polynomial function, turning point
Summary:In this section, you will:
Identify power functions.
Identify end behavior of power functions.
Identify polynomial functions.
Identify the degree and leading coefficient of polynomial functions.
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an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes.
Key Topics and Features:
* Solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem
* Solid treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals
* First treatment in book form of the AKS algorithm that shows that primality testing is of polynomial time
* Many interesting side topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers
The book's user-friendly style, historical context, and wide range of exercises from simple to quite difficult (with solutions and hints provided for select ones) make it ideal for self study as well as classroom use. Intended for upper level undergraduates and beginning graduate students, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced in the book.
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Not certain what level is right for your child? We have a Placement Test to help with the decision making process. You may also call 888-272-3291 and discuss your situation with our friendly and helpful customer service staff.
What is the Complete Elementary Kit?
This package has everything needed to teach RightStart™ Mathematics Level A through Level E first edition. This is perfect for multiple children going through the program.
The Complete Kit includes five Lesson manuals, Worksheets, Transition Lessons and Worksheets, Math Card Games book, along with all the manipulatives used in these five levels. Level G, RightStart™ Mathematics; A Hands-On Geometric Approach, is not included in this kit.
What about a High School curriculum?
We recommend VideoText Interactive for high school algebra, geometry, trigonometry, and pre-calculus. This program uses the same philosophy as RightStart™ Mathematics; students are taught to think mathematically and, consequently, develop an excellent understanding of the material.
VideoText comes in twelve modules, six in Algebra (includes pre-algebra, algebra I, algebra II) and six in Geometry (includes formal geometry, trigonemtry, and pre-calculus). All modules are available via DVD or online.
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Elements of Matrix Modeling and Computing with MATLAB
Publisher:
Chapman & Hall/CRC
Number of Pages:
402
Price:
79.95
ISBN:
1584886277
This book is meant to provide "math-on-time" for second-year students of science and engineering and is intended as the text for a two- or three-credit course concurrent with a second semester of calculus.
There are seven basic applications that provide motivation for the mathematics being illustrated: circuits, trusses, mixing tanks, heat conduction, data modeling, motion of a mass, and image filters. The mathematical tools needed to handle these applications are developed quickly. The reader is introduced to complex numbers and basic complex-valued functions, vectors and matrices, curve fitting, linear ordinary differential equations, Laplace and Fourier transform methods, and some computational methods. As is typical for such texts, the emphasis is more on skills than on theory. MATLAB® is used as the main computing tool.
The twelve-item bibliography includes some standalone web sites and some URLs associated with referenced books. The link to the NASA Mars Rover site seems to be broken.
Although I sometimes cringe at attempts to cram more etiolated mathematical content into an engineering curriculum, I find that the book under review has some redeeming features. For example, data modeling is applied to some interesting examples — the influence of cross-border shopping on the price of goods, the effect of various home attributes (age, the number of bathrooms…) on real estate appraisal, and various population questions. Detailed MATLAB® function and code files are provided for most applications. In addition to its intended use, this book might serve as a source of some examples/problems for a linear algebra, differential equations, or applied mathematics course.
Henry Ricardo (henry@mec.cuny.edu) is Professor of Mathematics at Medgar Evers College of The City University of New York and Secretary of the Metropolitan NY Section of the MAA. His book, A Modern Introduction to Differential Equations, was published by Houghton Mifflin in January, 2002; and he is currently writing a linear algebra text.
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Where can you find answers for the problems in McDougal Litell's geometry book?
A:
Quick Answer
It is possible to find geometry answer guides online, but it is important to recognize that as mathematics textbooks are updated, details in problems sometimes change. It is necessary to ensure that the editions match.
Generally, answer guides for geometry and other mathematics topics are not readily available to students in order to promote learning rather than cheating; however, parents sometimes find that access to an answer key is helpful for understanding how to work out a problem. Because geometry includes the challenging concept of proofs, parents may find that it is helpful to maintain good communications with a teacher in order to address concerns and difficulties.
Related Questions
The "Workbook/Studyguide, Vol. 2: To Accompany Destinos, Lecciones 27-52, 2nd Edition (Spanish Edition) (Paperback)" has an answer key for Destinos worksheets. As of 2014, you can also take quizzes online about the Destinos video series at the McGraw-Hill Higher Education website and receive immediate feedback.
Answers to MathXL questions are not independently available because of the computer-based nature of the program. However, supplemental materials and tutoring support may be available through the publisher's website.
The answers for worksheets in Marcy Mathworks educational products are found in the Answer section, located in the back of each book. Students receiving an individual Marcy Mathworks worksheet for homework should check with their teacher for access to the answer key.
The answers to "Vocabulary Workshop" are available online for teachers at the publisher's website (Sadlier-Oxford.com). In order to access the material, users will need a log-in code, and teachers can create these for themselves.
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Where Can You Find Saxon Math Course 3 Answers?
Answer
The cool thing about math books is that they normally have an answer key in the back of the book. You should be able to find answers in the back of your Saxon Math book. Keep in mind, the answer keys in math books only usually contain answers to the odd problems. The purpose of the answer key is to help you check your answers and figure out how to do the problems.
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Precalculus - 10 edition
Summary: Engineers looking for an accessible approach to calculus will appreciate Young's introduction. The book offers a clear writing style that helps reduce any math anxiety they may have while developing their problem-solving skills. It incorporates Parallel Words and Math boxes that provide detailed annotations which follow a multi-modal approach. Your Turn exercises reinforce concepts by allowing them to see the connection between the exercises and examples. A five-step problem solving ...show moremethod is also used to help engineers gain a stronger understanding of word4717582.39 +$3.99 s/h
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Excursions in Modern Mathematics -Std. Resource Gd - 7th edition
Summary: In addition to the worked-out solutions to odd-numbered exercises from the text, this guide contains selected hints that point the reader in one of many directions leading to a solution and keys to student success, including lists of skills that will help prepare for the chapter examsTextbooksPro Dayton, OH
7th edition. Book is in overall good condition!! Cover shows some edge wear and corners are lightly worn. Pages have a minimal to moderate amount of markings. FAST SHIPPING W/USPS TRACKING!!!23.49 +$3.99 s/h
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Andes: An Intelligent Tutor Homework System
Andes is an intelligent tutor homework system designed
for use in a standard two-semester introductory physics course.
It has been used in the classroom at the US Naval Academy since 2000
and has been used sucessfully at other colleges and at the high-school
level.
Several semester-long evaluations of Andes showed that students
who did their homework on it learned significantly more
than students who did the same homework problems on paper.
In this demo, you will solve a typical Andes problem while watching
an example solution (in case your physics is a little rusty).
During this exploration, we will introduce you to some of the
important features of Andes: emphasis on good problem solving technique,
immediate feedback, hinting strategies, model tracing strategy, and
grading policies.
Figure 1: The Andes screen has areas for the problem statement and
student-drawn diagrams, defining quantities, and entering equations.
The lower left area is where the tutor gives hints. Student entries
turn green if it is correct or red if incorrect. In this example,
the equation has turned red and the student has subsequently asked for a
number of hints.
The Andes user interface is designed to behave like pencil and paper.
A typical physics problem and a partially completed solution
are shown in Figure 1.
Students read the problem (upper left area), draw vectors and coordinate axes
(also upper left area), define variables (upper right area) and enter
equations (lower right area).
These are the actions that students should perform when solving the
same problem with pencil and paper.
Unlike paper, however, variables are defined by filling out a dialogue
box. Vectors and other graphical objects are first drawn by clicking
on the tool bar on the left edge of the window, drawing the object
using the mouse, and filling out a dialogue box. Dialogue boxes
require students to precisely define the semantics of variables and
vectors.
Good problem solving technique
Andes encourages students to use the problem solving strategies that
physics instructors value: student must define quantities, draw
diagrams, use units, and write down intermediate steps in a solution.
It encourages students to work with algebraic (rather than numerical)
expressions. When solving a problem, students must identify implicitly
which principle of physics they are using by writing down an equation that
is isomorphic to the equation associated with that principle.
Immediate feedback
Unlike a piece of paper, as soon as an action is completed, Andes gives
immediate feedback.
Entries are colored green if they are correct and red if they are
incorrect. In Figure 1, all the entries
are green except for the equation, which is red.
Hinting strategies
Andes provides three different kinds of instructional assistance:
Andes pops up an error message whenever the error is likely to be a
slip, which is defined as an error due to a lack of attention
rather than a lack of knowledge. Leaving a
blank entry in a dialogue box is an example of a slip. When
an error is not recognized as a slip, Andes colors the entry
red.
Students can request help on a red entry by selecting it and
clicking on a help button. Since the student is essentially
asking, "what's wrong with that?" we call this What's Wrong
Help.
If students are not sure what to do next, they can click on a button
that will give them a hint. This is called Next Step Help.
Thus, for errors that are likely to be careless mistakes, Andes gives
unsolicited help, while for errors where some learning is possible,
Andes gives help only when asked.
What's Wrong Help and Next Step Help usually generate a hint
sequence consisting of pointing hints, teaching hints, and bottom-out
hints.
For example, in Figure 1, the student has forgotten to
draw one of the vectors.
These are the What's Wrong hints that Andes gives:
There is a force acting on the ball at T0 that you
have not yet drawn.
Notice that the ball is supported by a surface: wall2.
When an object is supported by a surface, the
surface exerts a normal force on it. The normal force
is prpendicular to the surface.
Because wall2 supports the ball, draw a normal
force on the ball due to wall2 at an angle of 40
degrees.
After each of the first three hints, Andes displays two buttons labeled
"Explain more" and "OK." If the student presses "Explain more,"
they get the next hint in the sequence.
Model tracing strategy
The hints in Andes are generated by comparing the student actions to
a model solution of the problem. The model solution (or set of
solutions)
is supposed to represent the way an expert thinks about a problem.
Thus, for "Next Step Help," it matches the student entries to a
model solution to determine how
much of the model solution has been completed and provides hints associated
with the first uncompleted step in the model solution.
Grading
As the student solves a problem, Andes computes and displays a score.
The score is based on the number of correct entries with penalties
for the number of incorrect (red) entries and the number of bottom-out hints
received. The penalty on the bottom-out hints encourages the student
to use the help but discourages help abuse.
Andes puts little weight on the final answer, encouraging students to
"show their work."
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Linear 350 exercises and a self-contained exposition makes the book suitable for both classroom use and self-study
Presents simplified proofs, as well as improvements, of known results
An exhaustive bibliography and the inclusion of a 'Sources and comments' section at the end of each chapter provides the reader with ample links to further literature
It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience.
Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further 'Sources and Comments' section.
The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices.
A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.
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Village Of Palmetto Bay, FL PrecalculusConcepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations
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...Most American students begin their study of algebra with an introductory unit in their middle school or junior high math courses. In this unit, they are usually exposed to very basic algebraic equations, such as X + 3 = 8, and taught how to solve these equations for X. In Algebra 1, in addition...
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At the beginning of W.M. Priestley's book, Calculus: A Liberal Art, is a page titled For Anyone Afraid of Mathematics. Here's the first paragraph:
Maturity, it has been said, involves knowing when and how to delay succumbing to an urge, in order by doing so to attain a deeper satisfaction. To be immature is to demand, like a baby, the immediate gratification of every impulse.
Gabriel Median, 2014 winner of the Van's Triple Crown of Surfing, maturely surfs a wave at the Banzai Pipeline. Maturity, whether in surfing, learning math, etc., involves knowing when and how to delay succumbing to an urge.
I am learning to surf, and every session reminds me how immature I am at this sport! I need instruction, and lots of it. I make bad choices on which waves I should try to catch and which ones I should let pass. More often than not, I do not know when and how to delay succumbing to that urge to ride a wave. But with repeated practice and instruction, I hope to gain a better sense of making mature wave selections.
In a similar way, an immature math student has many urges to overcome. One of the biggest is fear of failure, and when students feel that urge, they often respond immaturely by cheating, asking for help too soon, or just giving up. Do you want to be a mature math student? Here are some suggestions to help you achieve that goal.
Failure is an option. In a math course, there is a reason that you are the student, and not the teacher! Students are the ones who need instruction. So when you are learning, humble yourself and be ready to make lots of mistakes.
Learn from your mistakes. Homework is your time to practice new concepts and to expect some mistakes. When you grade your homework though, and you miss a problem, don't just mark it wrong. Correct it. Review your lesson and your notes. Look for similar examples in the book. How were those examples solved? If your course has a solutions manual, study the solution carefully and work the problem again.
Set a time limit. Some students give up too easily. Others don't know when to give up. Both responses are immature. There is a difference between taking 10 minutes to solve a complex problem that you know how to do, and spending 10 minutes searching aimlessly for clues on how to solve a problem. If you can't figure a problem out after 10 minutes or so, move on. Try it again later. Sometimes, after you've rested, you will find that you can figure a problem out.
Pray for maturity. Ask God to make you a humble, dedicated learner. Math is a tool for studying His creation, and He definitely wants you to use it to know Him better, so talk to Him, and ask Him to lead you. Some students will spend all their years of schooling blaming others for their poor math performance. They will blame the teacher, the textbook, their parents, everything but themselves. If that is you, well, most likely, the main problem is you. Ask God to show you how to have a grateful attitude for the gift of education. Ask Him to help you know when and how to maturely succumb to that urge to know the answer to a problem, and do your work in a way that gives Him glory!
Do you have any other suggestions on how to be a mature student? Feel free to leave a comment.
I never cease to be amazed by the technology of today's digital cameras. By pushing a few buttons, anyone crazy enough to bob around in a 6-8′ high shore break can capture some amazing beauty in God's creation! But as the photos above reveal, the beauty only lasts for an instant.
It seems impossible that things can change from beauty to chaos, or vice-versa, in so short a time. But big changes can and do occur in even less time than the tenth of a second that elapsed between these two photos.
Strangely enough, instantaneous change, something us humans really can't fully comprehend, is behind almost every major technological achievement of the past 300+ years! How can that be? How can something we will never fully understand help us make all sorts of useful devices? Well, some things we just have to take on faith. Faith is at the heart of the branch of mathematics known as calculus. And calculus is all about the study of instantaneous change.
Subjects like calculus are easier to grasp when we consider the Author of every instant of time, and Creator of the biggest and best instantaneous changes of all. Paul writes in 1 Corinthians 15:52 how we will be changed "in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised imperishable, and we shall be changed."
Leonhard Euler (1707-1783), a devout Christian man considered the best mathematician ever, wrote that "it is God, therefore, who places men, every instant, in circumstances the most favourable, and from which, they may derive motives the most powerful, to produce their conversion; so that men are always indebted to God, for the means which promote their salvation."
Euler understood God's relationship with man and creation very well. He also understood mathematics really well, too! Much of the way we teach mathematics today comes from Euler's textbooks on the subject.
In our new Shormann Mathematics curriculum, we believe that all 10 major topics covered, including and especially calculus, are best understood by connecting the study of mathematics to Jesus Christ, the founder of all knowledge, and the founder and perfecter of our faith (Hebrews 12:2).
The following is the sixthShormann Math teaches students that mathematics is the language of science, and therefore an important tool for unlocking mysteries and revealing the amazing beauty found in God's creation. It is also an important tool for interacting with others, such as when buying and selling things. Shormann Math will train students to become skillful at using mathematics in a way that will help them become productive members of God's world, using their talents to serve Him and serve others.
Shormann Math teaches students what mathematics is, and how to solve problems using mathematical concepts. Problem solving is simply the application of mathematical concepts in new situations. It is about building on foundations that have already been laid, using mathematical tools developed over the centuries and applying those in new situations to solve problems. This is the essence of deductive reasoning, which is simply about applying rules. Mathematics is primarily deductive in nature, while scientific investigations are inductive (about finding rules).
What follows is a partial list of areas that mathematics is used, and that you may see covered in a Shormann Math Practice Set. At least one problem in each Practice Set will be about one of these areas. If you don't see an area you think we should cover, let us know. One thing is for certain, Shormann Math students will not be asking the "what am I ever gonna use this for" question regarding math!
Electricity generated by geothermal powerplants is expected to increase by 73% between 2010 and 2015. Image source: geothermal-energy.org.
Most of the world's electricity is generated using steam. Water is heated, generating high-pressure steam, which blasts out and spins a turbine. The turbine system creates motion of a magnet relative to wires, which in turn generates an electrical current, a phenomena Michael Faraday discovered in the 1830's.
Powerplants mainly differ in the heat sources they use to generate steam. The most common heat sources are currently coal, natural gas, nuclear, and oil. A schematic of a steam turbine powerplant is shown below, courtesy of the South Texas Nuclear Project.
Schematic of a nuclear power plant. Notice how a closed loop of water is heated, passed over a turbine, cooled, and reheated. Image source: South Texas Nuclear Project.
In the 21st Century, a growing trend is developing towards using geothermal heat sources. The amount of electricity generated by geothermal powerplants is expected to increase by 73% between 2010 and 2015. While geothermal powerplants are less efficient, they do have several advantages. The #1 advantage is they use the Earth's heat. And beneath our feet lies an almost infinite supply of heat.
Current geothermal powerplants are located where magma sources rise close to the surface. However, with improvements in technology, we should be able to access deeper and deeper heat sources. And, we can also vastly improve geothermal powerplant efficiency by using supercritical water(high pressure/high temperature) instead of steam. This was the goal of the Iceland Deep Drilling Project. In this first-of-its-kind system, they actually drilled into the magma, creating what is known as a magma-enhanced generating system. While the system is not currently operating, the project showed it is possible to use water near the supercritical phase, resulting in a much more efficient powerplant.
The search for alternative energy sources continues as people become increasingly aware of the negative environmental impact of covering vast expanses of Earth's surface with wind turbines and solar reflectors. God commanded us to be good stewards of His creation, and covering the land with windmills and solar reflectors is not a good management solution. Hopefully, cities and states will continue looking more and more at geothermal systems, with their small environmental footprint and low emissions.
The following is the fifthAfter years of teaching mathematics, researching math curricula and math history, and applying mathematics as a scientist and engineer, I concluded mathematics can be taught by covering 10 major concepts. The 10 major concepts are: number, ratio, algebra, geometry, analytical geometry, measurement, trigonometry, calculus, statistics, and computer math. While all 10 concepts can be taught in any K-12 course, specific concepts will be emphasized more or less at appropriate times. For example, number and ratio will be emphasized in younger grades, algebra in Algebra 1 and 2, etc.
I know what you are thinking right now, and that is "But CALCULUS is one of the 10 major concepts! How can you possibly teach calculus to an Algebra 1 student?!" Well, if you have even an 8th grade level of math proficiency, you know that if it took you exactly one hour to drive 60 miles, your average speed would be 60 mph. If you understand that, you already understand something about calculus, because calculus is really nothing more than studying rates of change. And yes, it gets more complicated than that example, but it also gets less complicated, too, so much so that there are things about calculus you could teach a kindergartner!
Most state mathematics standards do not include calculus, and none that I know of require calculus in high school. And the federal Common Core math standards include no calculus, and almost no precalculus either! However, the discovery of calculus is one of the greatest mathematical achievements ever! All the great technological achievements of the last 300+ years are in some way or another related to calculus! And proficiency in calculus opens the door for a student to choose any college major, while an inability to pass calculus limits a student to about 20% of college majors.
For high school mathematics, most home schools and private schools simply parrot whatever their state standards are, which means they complete Algebra 1, 2, and Geometry, and check off math on their transcript, not really knowing why they did math this way. With Shormann Math though, we want you to know why you are doing math differently. We are going to paint a broader brush than most math curricula, teaching math like a language, while at the same time helping you become proficient in standard Algebra 1, 2 and Geometry concepts. Along the way, rather than avoiding calculus because you heard it was scary, you are gently introduced to it. And, before you know it, you will be understanding more calculus than all your peers, and probably even your parents, ever did! Rather than an afterthought or a scary thought, Shormann Math makes calculus a normal, natural part of the curriculum, and culminates with a formal (and yes, it's optional!) calculus course that will prepare students to receive college credit via CLEP or AP Calculus.
Done in a thoughtful and age-appropriate way, all 10 major concepts listed above can most definitely be represented in one way or another in a K-12 mathematics curriculum.
The following is the fourthWhat does Leonardo DaVinci's famous painting, "The Last Supper", have to do with geometry? Use Shormann Mathematics and find out!
History helps connect students to their world and their Creator.
Most modern mathematics curricula ignore math history. But core ideas have consequences, and studying history often reveals which ideas are worth repeating and which ones aren't. Did you know that Isaac Newton, author of the most famous science book ever written (The Principia), based the format of his book off of Euclid's Elements, the most famous math book ever written? Did you know Shormann Math bases its format off Euclid's and Newton's famous works, stating rules and definitions up front, and using these as the building blocks to learn new concepts? Did you know that modern mathematics has a rich Christian heritage? Well, if you use Shormann Math, you will learn all about these things and more! Whether or not you are using a classical, trivium/quadrivium approach to your child's education, understanding mathematics within a biblical, historical framework will help students make more sense out of what they are learning and why they are learning it.
Screenshot of a part of Lesson 9 from Shormann Mathematics, Algebra 1. Did you know there is a connection between the U.S. Declaration of Independence and Euclid's famous geometry text, "The Elements?" Did you know Scripture predates Euclid's main idea of "self-evident truths?" Shormann Mathematics uses history to connect students to their world and their Creator.
The following is the thirdJesus Christ is the "Common Core" of Shormann Math
Perhaps you have heard of the United States government's "Common Core" curriculum. Perhaps you have also heard that a lot of people are concerned about it. Leading experts believe the Common Core's mathematics standards will not prepare students to study science, technology, engineering, and math (STEM) in a selective four-year college. And a white paper by the Pioneer Institute concludes by saying
"At this time we can conclude only that a gigantic fraud has been perpetrated on this country, in particular on parents in this country, by those developing, promoting, or endorsing Common Core's standards."
Unfortunately, man and his ever-changing ideas are at the core of this curriculum. At DIVE, we strive to place Jesus Christ at the core of all our products, and we pray that this will result in students learning math and science for His glory and the service of others. So, even though our primary goal is NOT to prepare students for STEM, we believe by putting Christ at the foundation, just like the world's original universities did, students will naturally learn to use mathematical tools that will connect them to their world and their Creator.
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Classes
MTH 067: Foundations of Mathematics
This is the first of two courses in the developmental math sequence. The focus of this course is to develop students' problem-solving and basic algebra skills. Topics for this course include applications involving integers, decimals and fractions, as well as applications of percents, proportions and consumer credit, algebraic expressions, algebraic properties, algebraic operations and multi-step equation-solving. The Cartesian Coordinate system and applications of algebra are also introduced. Students who complete this course, and demonstrate competency on an exit test, are eligible to enroll in the second course
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Survey of Mathematics With Application - With Access - 9th edition
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 Applications continues to be a best-seller because it shows students how we 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 motiv...show moreate the topics throughout, and aUsed - Good Hardcover. Textbook Only! 9Hardcover Good 03218375
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Calculus Early Vectors
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Introduces vectors along with their basic operations, such as addition, scalar multiplication, and dot product. This title gives the definition of vector functions and parametric curves, using a two-dimensional trajectory of a projectile as motivation.Introduces vectors along with their basic operations, such as addition, scalar multiplication, and dot product. This title gives the definition of vector functions and parametric curves, using a two-dimensional trajectory of a projectile as motivation
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Math Connects: Concepts, Skills and ..., Crs. 2 - 09 edition
Summary: Math Connects: Concepts, Skills, and Problem Solving was written by the authorship team with the end results in mind. They looked at the content needed to be successful in Geometry and Algebra and back mapped the development of mathematical content, concepts, and procedures to PreK to ensure a solid foundation and seamless transition from grade level to grade level. The series is organized around the new NCTM Focal Points and is designed to meet most state standards....show more Math Connects focuses on three key areas of vocabulary to build mathematical literacy, intervention options aligned to RtI, and a comprehensive assessment system of diagnostic, formative, and summative assessments. ...show lessYankee Clipper Books Windsor Locks, CT
Sail the Seas of ValueHardcover Fair 0078740460 00787404607.35 +$3.99 s/h
Acceptable
Quality School Texts OH Coshocton, OH
2008-01-02
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Chartley Trigon If algebra is the foundation of mathematics, then calculus is the foundation of physics, statistics, and applied mathematics. It is not an exaggeration to say that our modern world exists thanks to Liebnitz and Newton, who separately invented calculus at the same time.The (The open response section involves answering two multipart problems. The section score eva
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Proof and Proving in Mathematics covering a wide range of aspects related to the teaching and learning of proof
Provides illustrative examples of proof practices and activities in different contexts and levels
Extensive survey of available research findings, and indicating directions for future research
One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels.
Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification.
This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as:
The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice.
The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades.
The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving.
The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
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HermitianMany examples and hundreds of exercises are provided to promote understanding
Uses the concept of orthogonality to unify various mathematical topics
Includes accessible content designed to lead students from undergraduate- to research-level mathematics
Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book: geometric considerations in several complex variables. The final chapter includes complex differential forms, geometric inequalities from one and several complex variables, finite unitary groups, proper mappings, and naturally leads to the Cauchy-Riemann geometry of the unit sphere. The book thus takes the reader from the unit circle to the unit sphere.
This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. It will also be useful for students in physics and engineering, as it includes topics in harmonic analysis arising in these subjects. The inclusion of an appendix and more than 270 exercises makes this book suitable for a capstone undergraduate Honors class.
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Last Updated 1/31/2015 1:20 AM
Individualized and/or small group instruction for students with documented learning disabilities to improve adaptive skills in the following areas: basic arithmetic computational skills and word problems, basic and intermediate computational skills and word problems in algebra, and higher level mathematical concept development. This class will assist learning disabled students to transition from concrete to conceptual math.
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This paper describes and discusses the activity of grade 8 students on two word
problems, using a spreadsheet. We look at particular uses of the spreadsheet, namely
at the students' representations, as ways of eliciting forms of algebraic thinking
involved in solving the problems. We aim to see how the spreadsheet allows the solution of formally impracticable problems at students' level of algebra knowledge,
by making them treatable through the computational logic that is intrinsic to the
operating modes of the spreadsheet. The protocols of the problem solving sessions
provided ways to describe and interpret the relationships that students established
between the variables in the problems and their representations in the spreadsheet.
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Numerous pedagogical features help students learn and retain the information: boldface type explains difficult steps; a large number of drill exercises are presented where they are needed the most; marginal annotations; important concepts boxed and labeled; and marginal labels.
An emphasis on applications in examples and exercises show students how to use what they learn in TTthe r...show moreeal world.TT
The author stresses problem-solving strategy rather than reliance on set formulas, helping to build students' mathematical intuition and maturity
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Algebra 2 expands upon the principles students learned in Algebra 1, including rules of operations and relations. The topics studied in Algebra 2 include equations and inequalities, quadratic functions, powers and polynomials. Students who study Algebra 2 work to solve equations using matrices
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Modern Algebra: An Introduction
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Designed to help students learn the basic fundamentals of modern algebra, this textbook demonstrates how to handle abstract ideas. It has been revised and updated to include additional examples, problems and recent mathematical advances in the field.Designed to help students learn the basic fundamentals of modern algebra, this textbook demonstrates how to handle abstract ideas. It has been revised and updated to include additional examples, problems and recent mathematical advances in the field.Read Less
Very good. Hardcover. Has minor wear and/or markings. SKU: 9780470384435Fine. Hardcover. Almost new condition. SKU: 9780470384435
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About the book:
This textbook demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen program: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case they carefully explain key results and discuss the relationship among geometries. This richly illustrated and clearly written text includes full solutions to over 200 problems and is suitable both for undergraduate courses on geometry and as a resource for self study.
Softcover, ISBN 0521597870 Publisher: Cambridge University Press, 2009521597870 Publisher: Cambridge University Press1597870 Publisher: Cambridge University1597870 Publisher: Cambridge University Press, 1999 Used - Very Good, Usually dispatched within 1-2 business days, In very good little used condition. We despatch from the UK daily. Buy with confidence here.
Softcover, ISBN 0521597870 Publisher: Cambridge University Press, 1999 Used - Very Good, Usually ships in 1-2 business days, Wear to the bottom of front cover. Otherwise excellent condition. Sales tax included in price.
Softcover, ISBN 0521597870 Publisher: Cambridge University Press, 1999
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College Algebra: A Graphing Approach
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...Read More teaching easier and help students succeed. Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set. The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles
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Get a good grade in your precalculus course with Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH and it's accompanying CD-ROM! Written in a clear, student-friendly style and providing a graphical perspective so you can develop a visual understanding of college algebra and trigonometry, this text provides you with the tools you need to be successful in this course. Preparing for exams is made easy with iLrn, an online tutorial resource, that gives you access to text-specific tutorials, step-by-step explanations, exercises, quizzes, and one-on-one online help from a tutor. Examples, exercises, applications, and real-life data found throughout the text will help you become a successful mathematics student!
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45This book is an introduction to digital image processing from an elementary perspective. Providing a broad introduction to the discipline, the book covers topics that can be introduced with simple mathematics so students can learn the concepts without getting overwhelmed by mathematical detail. The first three chapters set the scene for the rest of the book by exploring the nature and use of digital images and how they can be obtained, stored, and displayed. By using MATLAB and its Image Processing Toolbox, students will be able to apply the theory they have learned into practiceAlasdair McAndrew is Senior Lecturer in the School of Computer Science and Mathematics at Victoria University of Technology. His research interests include digital topology, applications of image processing, error control coding, mathematical inequalities and applications, pedagogy, and learning. His teaching interests include image processing, elementary undergraduate mathematics, coding, and cryptography.
Most Helpful Customer Reviews
I have looked for an intro book for long time, until I found this one. this is by far the best. it covers the material with sufficient level of detail and once you are done reading it, you will know a wealth of info and will be reafy for more advanced books. it is a shame on the publisher to stop printing this book. the info is only in few places dated but mostly accurate and valid as of 2013. look no further.
Bought this book because I needed a crash course on image processing using MATLAB and it did just that. It is an amazing book. Though some of the codes for the worked example needed some slight modification when using MATLAB 2011b, most of them were just fine.
This book does an *excellent* job of both explaining and demonstrating each and every step in image processing. Being a newbie to Matlab myself, I found the book extremely informative and most importantly very helpful in getting the things I needed to get done, done. Perhaps the simple things more advanced Matlab users take for granted, the newbie can easily grasp. I had a couple of things I wanted to do related to my research and this book saved me hours of frustration.
I was looking for a book to help me analyze images in Matlab and I found this book. The book lives up to its title and was an easy read. Luckily for me this book covered every topic I was interested in and by the time I finished reading it I had manipulated my images as needed!
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Pass the Test (Standalone) for Beginning and Intermediate Algebra with Applications &Visualization
Summary
KEY MESSAGE:Gary Rockswold and Terry Kriegerfocus on teaching algebra in context, giving students realistic and convincing answers to the perennial question, "When will I ever use this?" The authors'consistent use of real data, graphs, and tables throughout the examples and exercise sets gives meaning to the numbers and equations as students encounter them. This new edition further enhances Rockswold and Krieger's focus on math in the real world with a new features and updated applications to engage today's students. KEY TOPICS: Introduction to Algebra, Linear Equations and inequalities, Graphing Equations, Systems of Linear Equations in Two Variables, Polynomials and Exponents, Factoring Polynomials and Solving Equations, Introduction to Rational Expressions, Linear Functions and Models, Matrices and Systems of Linear Equations, Radical Expressions and Functions, Quadratic Functions and Equations, Exponential and Logarithmic Functions, Conic Sections, Sequences and Series MARKET: For all readers interested in algebra.
Author Biography
Gary Rockswold is a professor of mathematics at Minnesota State University—Mankato. He received his BA in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State. He was elected to the honor societies of Phi Beta Kappa, Phi Kappa Phi, and Sigma Xi. He has been a principal investigator at the Minnesota Supercomputer Institute and has published several research articles discussing parallel processing and numerical analysis. He is also the author or coauthor of more than 10 current textbooks. At regional and national meetings, he has given numerous presentations related to teaching mathematics. During his thirty-five-year career, Gary has taught mathematics, physical science, astronomy, and computer science at a variety of student levels, ranging from junior high to graduate. Making mathematics meaningful and relevant for students at the developmental and precalculus levels is of special interest to him. He also has a passion for professing mathematics and for communicating the amazing impact that mathematics has on our society.
Terry Krieger has taught mathematics for over fifteen years at the middle school, high school, vocational, community college, and university levels. He graduated summa cum laude from Bemidji State University in Bemidji, Minnesota with a BA in secondary mathematics education. He received his MA in mathematics from Minnesota State University—Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Outside of teaching, Terry enjoys wilderness camping, trout fishing and home improvement projects. His past experiences include running two marathons, climbing Mt. Kilimanjaro, and watching the sunset from the banks of the Nile. He currently resides in Rochester, Minnesota with his wife and family. Terry has been involved with various aspects of mathematics textbook publication for more than ten years.
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College Mathematics for the Managerial, Life, and Social Sciences
College Mathematics for the Managerial, Life, and Social Sciences (with CengageNOW Printed Access Card)
Enhanced WebAssign - Start Smart Guide for Students
College Mathematics for the Managerial, Life, and Social Sciences
College Mathematics for the Managerial, Life, and Social Sciences, 7th Edition
Summary
In this revision of his best-selling text, Soo Tan builds on the features that have made his texts best-sellers: a problem-solving approach, accurate mathematical development, a concise yet accessible writing style, and a wealth of interesting and appropriate applications. These features are combined with practical pedagogical tools to help students understand and comprehend the material. Tan also now includes innovative use of technology that is optional, yet well integrated throughout the book.
Table of Contents
Straight Lines and Linear Functions
2
(76)
The Cartesian Coordinate System
4
(9)
Straight Lines
13
(20)
Using Technology: Graphing a Straight Line
30
(3)
Linear Functions and Mathematical Models
33
(14)
Portfolio: Carol Busa
37
(7)
Using Technology: Evaluating a Function
44
(3)
Intersection of Straight Lines
47
(14)
Using Technology: Finding the Points of Intersection of Two Graphs
58
(3)
The Method of Least Squares (Optional)
61
(15)
Using Technology: Finding an Equation of a Least-Squares Line
68
(5)
Summary of Principal Formulas and Terms
73
(1)
Review Exercises
74
(2)
Systems of Linear Equations and Matrices
76
(104)
Systems of Linear Equations-Introduction
78
(9)
Solving Systems of Linear Equations I
87
(19)
Using Technology: Solving Systems of Linear Equations I
102
(4)
Solving Systems of Linear Equations II
106
(13)
Using Technology: Solving Systems of Linear Equations II
116
(3)
Matrices
119
(13)
Using Technology: Matrix Addition and Subtraction, Scalar Multiplication, and the Transpose of a Matrix
130
(2)
Multiplication of Matrices
132
(16)
Using Technology: Matrix Multiplication
144
(4)
The Inverse of a Square Matrix
148
(17)
Using Technology: Finding the Inverse of a Square Matrix
160
(5)
Leontief Input-Output Model (Optional)
165
(15)
Using Technology: The Leontief Input-Output Model
172
(5)
Summary of Principal Formulas and Terms
177
(1)
Review Exercises
178
(2)
Linear Programming: A Geometric Approach
180
(38)
Graphing Systems of Linear Inequalities in Two Variables
182
(9)
Linear Programming Problems
191
(10)
Portfolio: Leanne Jenkins
198
(3)
Graphical Solution of Linear Programming Problems
201
(17)
Summary of Principal Terms
216
(1)
Review Exercises
216
(2)
Linear Programming: An Algebraic Approach
218
(48)
The Simplex Method: Standard Maximization Problems
220
(26)
Portfolio: Harley Lance Kaplan
241
(1)
Using Technology: The Simplex Method: Solving Maximization Problems
242
(4)
The Simplex Method: Standard Minimization Problems
246
(20)
Using Technology: The Simplex Method: Solving Minimization Problems
260
(4)
Summary of Principal Terms
264
(1)
Review Exercises
264
(2)
Mathematics of Finance
266
(52)
Compound Interest
268
(14)
Using Technology: Finding the Accumulated Amount of an Investment and Finding the Effective Rate of Interest
280
(2)
Annuities
282
(12)
Using Technology: Finding the Amount of an Annuity
292
(2)
Amortization and Sinking Funds
294
(12)
Portfolio: John Decker
300
(4)
Using Technology: Amortizing a Loan
304
(2)
Arthmetic and Geometric Progressions (Optional)
306
(12)
Summary of Principal Formulas and Terms
315
(1)
Review Exercises
316
(2)
Sets and Counting
318
(48)
Sets and Set Operations
320
(12)
The Number of Elements in a Finite Set
332
(7)
The Multiplication Principle
339
(6)
Portfolio: John L. Higgins
342
(3)
Permutations and Combinations
345
(21)
Using Technology: Evaluating n!, P(n, r), and C(n, r)
360
(2)
Summary of Principal Formulas and Terms
362
(1)
Review Exercises
363
(3)
Probability
366
(96)
Experiments, Sample Spaces, and Events
368
(10)
Definition of Probability
378
(11)
Rules of Probability
389
(10)
Use of Counting Techniques in Probability
399
(9)
Conditional Probability and Independent Events
408
(16)
Bayes' Theorem
424
(11)
Markov Chains (Optional)
435
(27)
Using Technology: Finding Distribution Vectors
454
(4)
Summary of Principal Formulas and Terms
458
(1)
Review Exercises
459
(3)
Probability Distributions and Statistics
462
(76)
Distributions of Random Variables
464
(12)
Using Technology: Graphing a Histogram
472
(4)
Expected Value
476
(15)
Portfolio: Lilli Meiselman
489
(2)
Variance and Standard Deviation
491
(13)
Using Technology: Finding the Mean and Standard Deviation
502
(2)
The Binomial Distribution
504
(12)
The Normal Distribution
516
(10)
Applications of the Normal Distribution
526
(12)
Summary of Principal Formulas and Terms
535
(1)
Review Exercises
536
(2)
Precalculus Review
538
(32)
Exponents and Radicals
540
(4)
Algebraic Expressions
544
(9)
Algebraic Fractions
553
(8)
Inequalities and Absolute Value
561
(9)
Summary of Principal Formulas and Terms
567
(1)
Review Exercises
568
(2)
Functions, Limits, and the Derivative
570
(122)
Functions and Their Graphs
572
(21)
Using Technology: Graphing a Function
588
(5)
The Algebra of Functions
593
(9)
Portfolio: Michael Marchlik
598
(4)
Functions and Mathematical Models
602
(18)
Using Technology: Finding the Points of Intersection of Two Graphs and Modeling
614
(6)
Limits
620
(25)
Using Technology: Finding the Limit of a Function
640
(5)
One-Sided Limits and Continuity
645
(20)
Using Technology: Finding the Points of Discontinuity of a Function
660
(5)
The Derivative
665
(27)
Using Technology: Graphing a Function and Its Tangent Lines
686
(3)
Summary of Principal Formulas and Terms
689
(1)
Review Exercises
689
(3)
Differentiation
692
(94)
Basic Rules of Differentiation
694
(14)
Using Technology: Finding the Rate of Change of a Function
702
(6)
The Product and Quotient Rules
708
(13)
Using Technology: The Product and Quotient Rules
718
(3)
The Chain Rule
721
(13)
Using Technology: Finding the Derivative of a Composite Function
728
(6)
Marginal Functions in Economics
734
(16)
Higher-Order Derivatives
750
(9)
Using Technology: Finding the Second Derivative of a Function at a Given Point
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solutions manual and test bank foraccounting principles using excel for success international edition 2nd edition solutions manual and test bank by james reeve, jonathan duchac and carl warrenget it now by emailing us ...
solution manual foraccounting information systems, 7th edition by james a. hall. solution manualget it now by emailing us at: solutionsmanualonline@gmail.com we respond fast!!! includes solutions to all cases!
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discover how you can easily multiply your learning ability by 1000 times and have incredibly powerful recall of anything you read or listen to within the next 72 hours...without learning a complicated memory system! ...
top 50 universities in the uk an interesting website that would be handy for anyone whowould like details of the top 50 unis in the uk.you get photographs and details of the universities includingaddresses, email address...
this college algebra online course provides students with a working knowledge of college-level algebra and its applications, emphasizing methods for solving linear and quadratic equations, word problems, and polynomial, ...
students gain a working knowledge of precalculus and its applications in this online precalculus course. the course begins with a review of algebraic operations and emphasizes the solving and graphing of equations that i...
this general calculus i course is designed to acquaint students with calculus principles such as derivatives, integrals, limits, approximation, applications and modeling, and sequences and series. during this course stud...
online business communication is a practical course that examines principles of communication in the workplace. it introduces you to common formats, such as the memo, letter, and report. it helps you review your writing ...
online english composition i course in english composition i, students learn how to develop better writing skills by identifying and understanding the steps involved in the writing process-all in this one online english...
economics i: macroeconomics online course macroeconomics economics looks at the big-picture performance of the national economy and its links to the global economy. designed to examine many of the basic tools economists...
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Beginning Algebra - With CD - 5th edition
Summary: KEY MESSAGE:Elayn Martin-Gay'sdevelopmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes greatly to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues this focus on students and what they need to be successful. Martin-Gay also strives t...show moreo provide the highest level of instructor and adjunct support. Review of Real Numbers; Equations, Inequalities, and Problem Solving; Graphing; Solving Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Roots and Radicals; Quadratic Equations For all readers interested in algebra, and for all readers interested in learning or revisiting essential skills in beginning algebra through the use of lively and up-to-dateSusies Books Garner, NC
2008 Hardcover Fair This book is in acceptable conditon. It is a good reading copy for personal use if you want to save some money but do not try and give as a giftBooksForGoodwillGetJobs St Paul, MN
Fair Cover has some rubbing and edge wear. The CD is included
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Tutor Training Workshop
Math Center
Tutor Training Manual
Last Updated August 9, 2007
Table of Contents
What is Tutoring?
What Does a Math Tutor Do? …………………………………………………………………………...…..…….3
The Tutoring Session…………….…………………………………………………………………………...…...4
The Tutorial Creed……………………………………………………………………………………...….….......5
10 Benefits of Tutoring…………………………………………………………………………...…………..…...5
Math Center Procedures
Math Center: A Guide for Math Tutors………………………………………..…………………………………………….6
Math Center Policies………………………………………………………………………………………………………..10
TutorTrac
How to Register for NKU TutorTrac…………………………………………………………………………….11
Entering the Realm of NKU TutorTrac………………………………………………………………………….12
Tutoring Tips
Questioning as an Effective Tutoring Technique………………………………………………………………..13
What to Do When You Get Stuck……………………………………………………………………………… 14
Tips for Tutors…………………………………………………………………………………………………...15
How to Promote Active Learning………………………………………………………………………………..16
Learning Styles
Learning Styles…………………………………………………………………………………………………..17
Tutoring Tips Based on Learning Styles……………………………………………………………………...…18
Math Anxiety
Some Causes of Math Anxiety…………………………………………………………………………………..19
Mathematics Anxiety Bill of Rights……………………………………………………………………………..20
Overcoming Anxiety……………………………………………………………………………………………..21
Math Test Anxiety Reduction Checklist………………………………………………………………………....22
Study Skills
21 Ways to Get More Done in Less Time……………………………………………………………………….23
Math Study Skills Inventory……………………………………………………………………………………..24
20 Tips for Academic Success…………………………………………………………………………………...25
Word Problems
Differences between English Language and Math Language……………………………………………………26
Steps for Solving a Word Problem………………………………………………………………………………27
Natural Human Learning Process
Summary of Natural-Learning Stages…………………………………………………………………………...28
Major Points about Learning…………………………………………………………………………………….29
2
What Does a Math Tutor Do?
The tutor assists students as they practice, review or prepare material for class. This role includes helping
students identify error, reminding them of mathematical concepts and finding additional practice problems. We
always instruct students that are extremely behind to see their professors.
Tutoring Do's:
Do always be on time for appointments and do your best not to have appointments run
over.
Do greet students as they come to the door and help them with logging in to TutorTrac.
Do offer to help students who come in to the Math Center without an appointment if you
do not have an appointment.
Do exchange names with the student and take a minute to understand where the student is
having problems.
Do pay attention to the body language of the student.
Do find out how the student's professor would like a problem worked.
Do help the student with note taking skills.
Do help the student with test taking skills.
Do help the student with overcoming math anxiety.
Do go with the student to get clarification from a professor.
Do let me know if you have any questions.
Do be relaxed. It helps set people at ease.
Do work your self out of a job.
Tutoring Don'ts:
Don't be late or allow appointments to run over.
Don't ignore students when they enter the Math Center.
Don't do the problems for the student.
Don't do the problems the way you learned them. (Unless it will help the students to see
it a different way)
Don't focus only on completing the homework assignments.
Don't work all problems with the student. Leave some for the student to do on their own
and move on to other topics.
Don't "teach" the student a topic the professor has not covered in class yet.
Don't help a student with a quiz unless cleared with me or their professor.
Don't be afraid to say that you don't know the answer, or can't think of another way to
explain it.
Don't criticize the instructor no matter how challenging the instructor or difficult his/her
English for the student to understand.
3
The Tutoring Session
How to begin a tutoring session:
Have the student sign in to TutorTrac.
Begin filling out the tutoring session form and ask the student what they would like to
work on.
Take the time to ask the student what they have been going over in class and what
specifically the student has had problem with.
Decide, with the student, the best plan of action.
In the Middle:
If at all possible, have the student work the problem.
Only work a problem if necessary and then work one and allow the student to work a
similar problem.
Have the student tell you what they are doing, as they do it.
Ask the student questions.
Have the student think about what makes the problem different then other problems they
have worked.
Have the student think about what makes the problem the same as other problems they
have worked.
Once the student has mastered a topic, move on to the next. It is not necessary for the
student to do all their homework with you watching.
How to end a tutoring session:
About 5 minutes before the end of the appointment, finish working the problem you are
currently working on.
Finish filling out the tutoring session form.
Have the student log out of TutorTrac.
Help the student with scheduling another appointment (if necessary).
4
The Tutorial Creed
By Paul Ellis
I. I will try to help you make sense of what you do not understand, but I will not be your
instructor.
II. I will try to show you how to find the right answer, but I will not just give you the answer.
III. I will review with you the homework that you have completed so that you can see your
successes and failures, but I will not do your homework for you.
IV. I will help you learn how to read your textbook for understanding, but I will not explain to
you something that you have not read.
V. I can meet with you one hour per week (sometimes two, in special circumstances and with
permission from the LAP) and help you achieve learning goals that we have set together,
VI. I will always expect your best effort, and you should too!
10 Benefits of Tutoring
By Paul Ellis
1. Successful work with others is a necessary skill for most careers.
2. Students learn strategies and habits for success by working with a peer role model.
3. Working as part of a team or community enhances students' motivation and confidence.
4. Students working with a tutor are free to ask questions as they come up, which they may be
inhibited to ask in the classroom.
5. Ideally, the tutoring session allows students enough time to master an idea or concept. A
tutor is in a good position to identify what the student still needs work on and when it's time
to move on.
6. A tutor can guide a student to other available and appropriate resources (Supplemental
Instruction (SI) / Structured Learning Assistance (SLA), Steely Library, Academic Advising
Resources Center (AARC), Student Support Services (SSS), Financial Aid, Career
Development Center (CDC), Health, Counseling, and Prevention Services, etc.
7. For students from non-academic backgrounds, the tutor functions as a bridge between the
student's community and the academic community.
8. In a diverse setting like NKU, tutoring allows us to learn about each other's cultures,
experiences, and languages in an accepting and supportive environment.
9. The tutor and the instructor have the same goals for the student, but the tutor can approach
things from a different, often more individualized way.
10.Working with a tutor can provide a bridge into a learning community for students who have
been used to working on their own. The environment in a tutoring center encourages
collaborative work and support of fellow students.
5
Math Center
A Guide for Math Tutors
Center Goals
The Math Center is designed to aid the developmental math students as well as the student in selected general
studies math courses (i.e. 110, 111, 115, 205). The goal is to help the student develop the learning and study
skills necessary to prepare for homework and tests as well as develop the problem solving skills that will allow
the student to work efficiently, confidently, and effectively not only in mathematics but throughout life.
Tutor Role
The tutor assists students as they practice, review, or prepare material for class. This role includes helping
students identify error, reminding them of mathematical concepts and finding additional practice problems. We
always instruct students that are extremely behind to see their instructors. As a tutor, you should:
Great all students that enter the Math Center, if you are with a student and there is no free tutor stop for a
second and ask the student to wait.
Help students register, set up appointments and login/out of TutorTrac.
Show the student that you are interested.
Start where the student is.
Encourage the student to be an active learner.
Model and promote effective study skills and support classroom instruction. Use student"s notes, course
textbooks, and solution methods used by student"s instructor during tutoring session.
WORK YOURSELF OUT OF A JOB
Helpful Hints
There are many common trouble areas that the tutor will begin to recognize when working with the tutees. Here
are some hints for dealing with those problems before they become a major hindrance to learning.
Try to determine exactly what kind of difficulties your student is having:
Is your student able to remember basic skills?
Does your student understand the text?
Are the instructor"s lectures causing problems?
Does your student lack basic study skills?
Does your student suffer from test anxiety?
Negative self-talk (i.e. "I"m stupid", "I can"t learn", "I"m too old") is to be considered obscene and
unacceptable.
There is to be no waste of time in allowing students to qualify the question they are about to ask you with
phrases such as "Can I ask you something?" or "This may sound stupid". You are a tutor and are thus
present to answer any question of the tutee relating to math. The tutee should be aware of this and feel
comfortable in asking any question.
6
The tutee should keep his/her hand off the pencil until he/she has read the problem and understands the
problem. If the tutor is working example problems, the tutee should follow along by listening, not by
writing.
The tutee should never be allowed to skip steps in working problems (no short cuts should be allowed).
If you are working problems on the board, use colored chalk to color-code work.
Positive and directional internal dialogue should be used, but concepts need to be understood and rote
memorization should be discouraged.
Always work on the opposite side of the hand the student uses (i.e. if the student is left-handed, work on
his/her right side).
Don"t tell the student if he/she is right or wrong. Instead, let the student finish the entire problem, then if a
question arises, ask, "What do you think?" "Is it reasonable?" "How did you arrive at that answer?"
Use a sequential approach to problems to help the student build on what he/she already knows.
Some students have trouble communicating with their instructors. Encourage the student to ask questions in
class and to go see his/her professor during their office hours. Also, some courses have pooled office hours
where a student can go to the office hours of another professor who is teaching (or has taught) the same
course.
The Textbook as a Learning Tool
Students sometimes forget that the text is very important to their total understanding of the math problems they
are working. Encourage the use of the Text.
The MAH 095, 099 textbooks are color coded to aid the student in reaching a better understanding of each
section of material covered. The following is a breakdown of those color codes for the Bittinger/Beecher
textbooks.
PINK - Section Objectives
TAN - Margin Exercises
ORANGE (arrow in box) - Rules
GRAY - Calculator Spotlight
Most textbooks use a similar scheme to aid the student. Help the student identify the scheme in his/her
specific Text and learn to use it.
Make certain that the student carefully reads the introduction of each section, carefully studies the example
problems present, works the practice exercises contained in the section, and understands the concepts that
are presented. Reading along with the student can often be helpful, especially if the tutor asks pertinent
questions throughout the reading.
Have the student read the next day"s material the night before. This way, the student will have a better
understanding of the material covered in the lecture and the material will not be completely new to them.
Some students have a better understanding of new concepts if they get a "Birdseye view" of the material
before they begin. Encourage these students to read the chapter summary, present at the end of each
chapter, before starting a new chapter. This will allow them to get the big picture by observing the structure
of the chapter before entering it in greater detail.
Encourage students to try to work the margin exercises as they read the chapter. Each solution for the
margin exercises is given in the back of the book. Margin exercises are similar to the examples that are
worked out step by step in the chapter. This enables the students to have a more active involvement while
they read.
7
Word Problems
Word problems are one of the biggest causes of distress for most students. Here are some tips to pass along to
the tutee for working word problems.
Use a highlighter to highlight keywords in the problem itself.
Write out the equations in words then fill in the numbers.
Make certain the student identifies the variable in the problem.
Put the solution to the problem in the form of a sentence.
Help the student develop a word problem solving routine.
Organizational Skills
The tutor should convey the importance of organizational skills to the tutee. Here are some skills that can be
passed along.
Line up the equal signs in the work and use one equal sign per line.
Use a #2 pencil or dark pencil and always have a good eraser.
Straight edges should be used to draw lines (if a straight edge isn"t present, use your driver"s license or
student I.D. card).
Flash cards can be stored in small sandwich bags for safe keeping.
The tutor should look at a student"s notes to give suggestions for better organization. Encourage the student
to actively take organized notes during the lecture.
Remind the tutee to date his/her notes.
Encourage the student to use a binder with separators to keep notes and work. Use separate sections for
class notes, homework, extra practice and test/quizzes. Discourage the use of spiral notebooks.
Encourage the use of a scientific calculator, especially a graphing calculator (when the professor allows it) if
he/she can afford it. A graphing calculator can be checked out from the Learning Resource Center.
Tests
The one subject that causes the most anxiety of almost any math student is tests. Share the following ideas to
help students fight test-taking anxiety.
Before the test:
Know the difference between a "test" and a "quiz".
Go to class--Do NOT skip the class right before the test.
Eat breakfast, but avoid acidic foods such as orange juice.
Close the book and put away the notes about 30 minutes before bed and do something enjoyable.
Use breathing exercises to calm down before the test.
Review old tests and quizzes.
Have the student choose problems from the text to make up their own test. Notecards work nicely for this,
see "proven study method."
Have the tutees say, "I"m going to do my best", discourage them from saying, "I"m going to fail".
8
During the Test: (Instruct the tutee to)
Read through the whole test. Pay close attention to the directions.
Do the easy problems first.
Don"t spend any enormous amount of time on any one problem.
Don"t leave anything blank.
Sit back for a moment and take a deep breath should you find yourself tensing up.
Go back and check their work, if there is time.
After the Test: (Instruct the tutee to)
Don"t be discouraged if you didn"t get the grade you wanted.
Work all problems you got wrong.
Save the tests and quizzes to study from later.
Use your text to review concepts missed on the test.
Resources
The tutor should let the tutee know of the resources on campus.
Math videotapes are available from the Steely library or are available to be viewed in the Math Center;
however, they should be actively and not passively viewed. The student should take notes and carefully
follow through the examples presented not simply watch, as one would watch a movie. They should think of
it as a lecture that they can control the pace of.
Computer aided assistance is available through software (MathMax is the software that comes with the
MAH 095,099 book) and a list of helpful websites is available on the Math Center"s Webpage
(
9
Math Center Policies
Cell phone ringers should be turned off as to not disturb other
students. Cell phones should not be answered in the Math Center. If
a call must be taken, please take it outside the center. (This policy is
for both students and tutors, if a student is not abiding by this policy let
me know.)
The computer directly next to the door should only be used for
TutorTrac purposes such as logging students in or out and making
appointments.
If the lab is not busy, you may work on your own homework. However,
students using the lab must not get the impression that you are "busy"
and not available to assist them if they need you. Students must
always be helped first.
The two computers on the wall with the printer may be used by tutors
for personal business if and only if there is not a student who needs
help or who needs to use Minitab (computer to the right of the printer).
Tutors who are not working with a student should always be aware of
students coming into the center. The tutor should welcome the student
and then assist them (log them in, help them make an appointment,
tutor them).
If all tutors are working with students, greet the student and either get
me or ask them to wait for a moment and help them when you come to
a stopping point in the tutoring session.
If a student comes in looking for help but does not have an
appointment and a tutor is available, a tutor should help them until the
tutor's next appointment shows up or the tutor is scheduled to leave.
Please let me know of an absence as soon as possible. When a tutor
calls off, it is possible that I will need to cancel a student's
appointment, so please make every attempt to come in.
Please check your email at least every 48 hours.
10
How to Register For NKU TutorTrac
NKU TutorTrac is a web-based program that allows NKU students to make Writing Center consultations and/or
Math Center tutoring appointments on-line, or to access contact information of Academic tutors. First, however,
you must register. Follow the directions below to register for NKU TutorTrac.
1. Access NKU TutorTrac via Norse Express.
2. In User Name box, type "new"; click "Login."
3. NKU TutorTrac invites you to register. Your ID is your Social Security #. Your Account (or User)
Name is your NKU email prefix—what comes before the @. Your Password should be your
SS#—the same as your ID, easily remembered.
Please complete the form:
ID: SS#
First Name: Jane
Last Name: Doe
Account Name: doej1 (NKU email prefix)
Password: same as NKU email password
Confirm Password: same as NKU email passwor
Click on "Confirm"
4. The next screen requests information about you. We need this information so we know what NKU
student population groups we are serving and how well we are serving them. Complete the form,
using drop down boxes when available. Be sure to click on Save!
ID: SS#
Last Name:
First, Middle Name: Referred by:
Gender: Age:
Phone: (optional) Permanent Residence:
Cell: (optional) Live on campus?
Major: (optional) Currently member of Student
Email: Support Services (SSS)?
Ethnic Background: Admitted to NKU with
College: conditions?
Class: Tutoring selected for …?
Click on "Save"
5. The next screen should be the Student Main Menu, with your name on it. You are now ready to
make tutoring appointments on-line or to access tutor contact information on-line!
11
Entering the Realm of NKU TutorTrac:
Student Instructions
[If you have any questions please contact the Math Center (FH 201; 859-572-5779).]
1. Once you are registered, you can access Tutortrac remotely by using any browser (Explorer, Netscape);
type in the web address Bookmark or mark it as a favorite!
2. Enter your login user name and password and click the Login button. [Your user name is your NKU
email name. (Ex: paule – Do Not include @nku.edu.) Your password will be the same as your NKU
email password.
3. On the Student Main Menu page, you will see your name and all upcoming appointments you have
scheduled, as well as other messages, including reminders of tomorrow"s appointments, if any. You may
cancel an appointment by clicking on its Date, then clicking Delete.
4. Near the top of the Main Menu page are the buttons: More Info | Make Appointment | Find Resources
| Edit Information | Exit. Click on Edit Information if you need to update biographical information,
like a change in your email address, class status, etc.
5. Click on Make Appointment if you wish to book an appointment.
6. At the Availability Search screen, you may search for an appointment during the upcoming week in one
of two ways: You may select a specific center and a specialty area (course), OR you may select specific
Tutor. NOTE: Not every tutor can help with every course. It is best that you only specify a tutor if
you have already worked with him or her. Verify that the date range is okay (you can change the
dates if it is not); click the Search button.
7. You will need to scroll down to see all the Search Results. Click on an Availability's time that you
want.
8. Select a time, type in location [FH 209 for Writing], verify duration (.5 hour default, 1 hour maximum),
identify "Request Help In" (Prewriting, Revising, Editing for Writing); Click on Save Appointment.
Your new appointment will appear on your Main Menu page.
9. You can cancel an appointment by clicking on its Date, then clicking Delete.
10. Click Exit to quit.
To Login a student:
1. Make sure the computer is on the login screen by going to tutortrac.nku.edu and typing in the login
username and password (found on the black binder in the cabinet.
2. On the login screen, have the student type in either their username or social security number.
3. Have the student select their course, reason for visit and type in their instructor's last name.
4. Click Continue.
To Logout a student:
1. Click the logout button next to the student's name.
2. Select the reason for the visit and the place. Also select the tutor the student was working with.
To Login as a tutor:
Your username is your first name, last initial. (ex. My tutor username is bethw)
12
QUESTIONING as an EFFECTIVE TUTORING TECHNIQUE
*********************************************
Beth Kupper-Herr <bethkh@hawaii.edu>
Writing Specialist / Tutor Supervisor
Learning Resource Center
Leeward Community College
Pearly City, Hawaii
*********************************************
Asking questions is one of the best and most important ways to help others learn. Socrates, the ancient Greek
philosopher, was perhaps the first teach to sue this method. He didn't TELL his students what to think; by
skillful questioning, he guided them along their own path to the truth. This means of teaching is known as the
Socratic Method.
QUESTIONING AT THE BEGINNING OF A TUTORING SESSIONS: Use questions for the diagnosis and
focus – to find out what your tutee needs to work on and to determine what to cover during the session.
QUESTIONING DURING THE SESSION: Questions can be used in many ways during a tutoring session.
Below are three question types. Discuss the effectiveness of these types. Is one type more useful than another?
When should each type be used? Give reasons for your conclusions.
Closed questions – including yes/no and short answer questions:
Do you understand?
In what state is the Yukon River?
Who was the first Prime Minister of India?
Rhetorical questions (no response needed):
Didn't the Chinese reject Western culture for a long time?
Should your introductions include a thesis statement?
Open questions – asking for broadly inclusive statements, assertions, explanations, or opinions:
What's the most important thing you want to tell your reader?
What's the difference between moncotyledons and dicotyledons?
What do historians mean by the Colombian Exchange?
Why do you think that labor issues have been omitted from most history textbooks?
QUESTIONING AT THE END OF A TUTORING SESSION: Use questions for summary, review and to
establish directions for further study.
13
What to do when you get stuck!
Math Lab & Tutor Training
Bethel University
3/16/07
It's bound to happen – you are working with students and you get stuck on a problem…
Two Important Ideas:
1. Use the opportunity to model good problem solving skills (do what you do when you get stuck!).
2. Be honest and don't give incorrect answers: giving incorrect answers leads students astray and often
spreads like a disease (they tell someone else, the incorrect material ends up on an exam, etc.). It is much better
to say "I don't know the answer, but let's work to find a solution" than to lead someone down the wrong path.
Some Strategies:
1. Have the student state the problem in their own words.
- Define any unknown terms (use index or current section in book if necessary)
- Write the problem in the form: Given:
Find:
2. Use the student's resources, ask lots of leading questions.
- Find out which pieces of the problem the student understands
- Write out any formulas or theorems that may apply
- See if there is a similar example in the book
- Use their class notes
- Ask them if they have done a similar problem before
3. Other Strategies
- Draw a picture or graph, make a model, or act it out
- Break the problem into smaller parts, solve an easier problem
- Make a numerical example that fits the problem, and solve it first (this is
especially helpful if the problem is full of parameters)
- If possible, estimate a solution, then check with this estimate
- Look for patterns
- Brainstorm - throw out all kinds of ideas
- Incubate! (let it sit for awhile)
4. If you still have not found a solution...
- Ask another student from the same class or another tutor to help.
- Check the answer key (if available)
- Refer the student to their instructor and follow up when you see them again!
14
TIPS FOR TUTORS
1. Use simple language. Remember, there is a difference between understanding a topic and
teaching it.
2. Paraphrase what the student says.
3. Provide information that the student needs, rather than what you know.
4. Ask one question at a time.
5. Use "wait time".
6. Avoid asking "yes" and "no" questions.
7. Check to see if you have been understood.
8.Ask a student to explain back to you the steps that were needed to solve a problem.
9.Admit when you don't know the answer.
10. Avoid being condescending.
11. Refrain from commenting on how easy a problem or concept is to understand.
12. Provide realistic feedback about learning from high school vs. university perspective.
13. Listen actively.
14. Keep a positive attitude about the person you are assisting.
15. Be conscious of your body language.
16. Show enthusiasm for learning.
17. Look for opportunities to encourage and affirm the student's work
18. Actively teach study skills.
From Cornell University's Learning Strategies Center
15
How to Promote Active Learning *
The goal of the tutor is NOT to solve problems, provide answers, or write papers for students. The primary goal
is to show students how to solve problems, how to think through questions, how to work through the writing
process. Tutors should get the students to do the thinking and talking as much as possible. Sometimes it is
important to slow things down so that students can become more aware of what they are doing – more aware of
their thinking processes. This awareness can lead to intellectual change, development, and growth.
Some ways to get students to slow down and reflect on their thinking processes:
Have students read the problem/question/assignment aloud and tell you what is needed before they
start work.
Get students to "think out-loud" as they respond to a problem/question/assignment. Encourage
students to constantly talk about what they are doing and why. This will slow down the thinking
process and make it more explicit – and perhaps more accurate. It will at least allow you to help
students check their own reasoning and find their own mistakes by having them express exactly what
they know about the problem/question/assignment.
Ask questions or make comments that can help students clarify their thinking:
o What are some possible ways you might go about solving this problem/question/assignment?
o Tell me what you know about the problem/question/assignment.
o How might you break the problem/question/assignment into small steps?
o What are you thinking right now?
o I don't understand. Will you please explain?
Sometimes you may find it appropriate to model good problem solving techniques. You may need to
demonstrate how you would go about reading and understanding a question before responding to it. Make sure
that your model or demonstrations is clear (e.g., work step-by-step, back up if necessary when things don't
work out, break a complex task into parts, move from simpler to more complex, construct visual representations
on paper, etc.). After modeling or demonstrating, require that students work through a similar task to make sure
they understand the process.
*Adapted from Beverly Black and Elizabeth Axelson, University of Michigan.
16
Learning Styles
When you.. Visual Auditory Kinesthetic & Tactile
Do you sound out the word or Do you write the word down to
Spell Do you try to see the word?
use a phonetic approach? find if it feels right?
Do you sparingly but dislike Do you enjoy listening but are Do you gesture and use
listening for too long? Do you favor impatient to talk? Do you use expressive movements? Do
Talk
words such as see, picture, and words such as hear, tune, and you use words such as feel,
imagine? think? touch, and hold?
Do you become distracted by Do you become distracted by Do you become distracted by
Concentrate
untidiness or movement? sounds or noises? activity around you?
Do you forget faces but
Meet someone Do you forget names but remember Do you remember best what
remember names or remember
again faces or remember where you met? you did together?
what you talked about?
Do you talk with them while
Contact people Do you prefer direct, face-to-face,
Do you prefer the telephone? walking or participating in an
on business personal meetings?
activity?
Do you enjoy dialog and
Do you like descriptive scenes or Do you prefer action stories or
Read conversation or hear the
pause to imagine the actions? are not a keen reader?
characters talk?
Do you prefer verbal
Do something Do you like to see demonstrations, Do you prefer to jump right in
instructions or talking about it
new at work diagrams, slides, or posters? and try it?
with someone else?
Do you ignore the directions
Put something Do you look at the directions and
and figure it out as you go
together the picture?
along?
Need help with a Do you call the help desk, ask
Do you seek out pictures or Do you keep trying to do it or
computer a neighbor, or growl at the
diagrams? try it on another computer?
application computer?
Adapted from Colin Rose(1987). Accelerated Learning.
17
Tutoring Tips based on Learning Style
AUDITORY LEARNERS TACTILE/KINESTHETIC LEARNERS VISUAL LEARNERS
Encourage them to explain the Encourage them to pick up the book as Let them take notes during the
material to you. they are reading or talking. tutoring session.
Ask them to read Have them write while they are reading or Use a blackboard or notepaper
explanations out loud. talking. for both of you to write questions
and answers.
Ask the student to make up a song Encourage them to walk around the room Encourage the use of color-
using the subject material. The for appropriate books and other resources. coded highlighting.
'crazier' the better.
Tell the students they can review Advise them to sit near the front of their Use graph paper to help them
audio tapes while they drive. classroom and to take notes. This will create charts and diagrams
keep the student focused. that demonstrate key points.
Advise them that when they are Advise them to spend extra time in any Have them use mnemonics,
learning new information, state the labs offered. acronyms, visual chains, and
problem out loud. Reason through mind maps.
solutions out loud.
Ask the student to say words in Encourage them to use the computer to Advise them to use the computer
syllables. reinforce learning using their sense of to organize materials and
touch. to create graphs, tables, charts,
and spreadsheets.
Encourage them to make up and Advise them to write with their fingers in Ask the student to organize the
repeat rhymes to remember facts, sand. material.
dates, names, etc.
Advise the student to join or create Have them write lists repeatedly. Use visual analogies. Use
a study group, or to get a study photographs.
partner.
To learn a sequence of steps, write Advise them to exaggerate lip movements Use visual metaphors.
them out in sentence form, then in front of a mirror.
read them out loud.
Ask the student to use mnemonics Ask them to stand while they explain When you ask them to explain
and word links. something to you. something, suggest they do so
by writing the explanation down.
Involve the student in a discussion Ask them to use rhythm (beats) to Ask them to make flashcards,
of the material. memorize or explain something. then use them during
the session/s.
Make sure they go over all As the student is explaining something, The act of writing (the cards) and
important facts aloud. have the student point to the subject viewing them doubles their
matter in the book, on the board, etc., comprehension.
while reading it out loud.
Ask them to use gestures when giving Encourage them to visualize the
explanations. scene, formula, words, charts,
etc.
Advise them to make models that Refer them to the Book's or other
demonstrate the key concept. (The computer software.
purpose here is the act of making the
model.)
Advise students to use hands-on Use illustrations.
experience when possible.
Make flashcards for each step in the
procedure. Put the cards in order until the
sequence becomes automatic.
Use audio tapes from classes. Play them
while they walk or
exercise.
Ask them to stretch and move in the
chairs.
Adapted from Three Rivers Community College's Tutoring and Academic Success Centers' Website
18
Some Causes of Math Anxiety
1.Inability to handle frustration
2.Poor self-concept
3.Excessive school absence
4.Parental attitudes toward mathematics
5.Teacher attitudes toward mathematics
6.Emphasis on learning mathematics through drill
without understanding
7.Lack of mathematical experiences
8.Negative Math Experiences:
Singled out/embarrassed
Overwhelming pressure
Forced to stay at board
Physical punishment
Verbal messages
Competition with siblings/friends
Moved to new school/teacher
19
Mathematics Anxiety Bill of Rights
By Sandra L. Davis
I HAVE THE RIGHT:
1. to learn at my own pace and not feel put down or stupid if I'm slower than someone else.
2. to ask whatever questions I have.
3. to need extra help.
4. to ask a teacher or a tutor for help.
5. to say "I don't know" or "I don't understand."
6. to not understand.
7. to feel good about myself regardless of my abilities in math.
8. not to base my self-worth on my math skills
9. to view myself as capable of learning mathematics.
10. to seek help in learning math.
11. to be listened to and taken seriously when I ask for math help.
12. to assess my math instructors and how they teach.
13. to seek out the best math instruction possible.
14. to relax.
15. to be treated as a competent adult.
16. to dislike math.
17. to like math.
18. to define success in my own terms.
19. to demand explanations I can understand.
20. to explain what I'm thinking and receive clarification.
21. to ask "Why?"
22. to make mistakes in math and to learn from those mistakes.
23. to protest unfair treatment or criticism when I'm doing math.
24. to remain calm and confident when doing math.
25. to work hard toward achieving success in math.
20
Overcoming Anxiety
Acknowledge your feelings. Admit that you are anxious.
Stop yourself from thinking irrelevant thoughts or putting yourself down.
Rework your negative statements into neutral statements and think in positive terms.
Learn that even failure has a bright side: you can learn from your mistakes. Remember,
if you do not take risks, you are not growing. And taking risks means allowing yourself
the freedom to fail.
Don't worry about what others may be doing or thinking. It's what we say to ourselves
that counts the most. Think, "I can" or "I want" instead of " what if."
Don't worry about everything at once. Set goals that you can accomplish one step at a
time. If you occasionally stray from your goal, don't give up on your self. It's okay to
feel guilty for a little while, but resolve to get back on track.
Practice the situation that makes you anxious. Set up a "dress rehearsal" as closely to the
real life situation as you can. Practice the situation over and over in your mind picturing
how you will succeed.
Picture a time when you felt confident about an accomplishment. Focus on all the details
of how you felt. Now picture the situation that causes you anxiety. Replay the picture
with you feeling confident and succeeding.
And finally, focus your attention away from yourself and toward the task.
21
MATH TEST ANXIETY REDUCTION CHECKLIST
1. ___ I've reviewed and worked out lots of problems so I know my material out of context.
2. ___ I know the format and content of my upcoming math test.
3. ___ I know how many questions will be on my exam and its duration.
4. ___ I've given myself several practice exams.
5. ___ On practice exams, I've noted areas of difficulty so I can strengthen them.
6. ___ I've analyzed my past pattern of typical errors so I can be alert to them on my exam.
7. ___ I've gotten seven to eight hours of sleep in the days prior to the exam.
8. ___ I've kept a regular program of moderate exercise.
9. ___ I've eaten a small meal of low-fat protein one to two hours before the exam and avoided too much
caffeine.
10. ___ I'll arrive at the exam on time and avoid talking with others.
11. ___ Throughout the exam I'll remain calm, relaxed and positive.
12. ___ I will say positive self-statements to myself and push away all disturbing or distracting thoughts.
13. ___ I will write out all my formulae and key ideas on the top corner of my exam sheet before beginning
the test.
14. ___ I'll quickly read through the exam, note point values, and schedule my time accordingly.
15. ___ I'll proceed comfortably throughout the exam, working first on the problems that come most easily
to me.
16. ___ I'll carefully read the directions to all problems and circle significant words to avoid
misinterpretation.
17. ___ After finishing the exam, I'll check my answers, proofread for omissions and check for my typical
errors.
18. ___ I'll leave and reward myself for a job well done!
Adopted from "Conquering Math Anxiety" by Cynthia Arem
22
21 WAYS TO GET MORE DONE IN LESS TIME
1. Monitor your time for a week to see how you actually spend your time. The results are always
surprising.
2. Create a schedule for yourself as a guide - but be willing to be flexible when necessary.
3. Each night prepare a list of things you hope to accomplish the next day.
4. Every morning look at your to-do list. Determine which task you dislike the most, and do it first.
Completing unpleasant task decreases anxiety and gives you a sense of accomplishment.
5. Write things down to eliminate confusion and forgetting.
6. Keep a record of all test dates, assignment deadlines, appointments etc. on a calendar.
7. Improve efficiency by "bunching" activities. For example, plan one afternoon a week for running
errands such as shopping, banking, picking up cleaning, etc.
8. Do specific tasks on specific days.
9. Focus your efforts on items that will have the best long-term benefits.
10. Start off with the most profitable parts of large project. You may often find that it is not necessary to do
the rest.
11. If a project seems overwhelming, divide it into smaller tasks and complete one immediately. Doing the
first task will help dissipate negative feelings and encourage you to go on.
12. Cut off nonproductive activities as quickly as possible.
13. Learn to delegate tasks to others when you can.
14. Use your personal time clock; know you own best working style.
15. Set time limits for projects and activities.
16. Concentrate on one thing at a time.
17. Give yourself time off and special rewards when you've done important things.
18. Make maximum use of short time periods.
19. Keep you study area/desk cleared to prevent distractions while working.
20. Don't waste time regretting your failures.
21. Remember, the less time you feel you have to spare; the more important it is for you to plan your time
carefully.
23
Math Study Skills Inventory
(Taken from Conquering Math Anxiety by Cynthia Arem)
This inventory will help you assess the effectiveness of your math study skills. Read each of the statements
carefully and determine how frequently each applies to you. Enter the correct point score for that item on the
line. (Usually=3, Sometimes=2, and Rarely=1)
1. ____I attend all my math classes.
2. ____I read my math assignments before attending class.
3. ____In class, I mentally follow all explanations, trying to understand concepts and principles.
4. ____In class, I write down main points, steps in explanations, definitions, examples, solutions, and
proofs.
5. ____I review my class notes as soon after class as possible.
6. ____I review my notes again six to eight hours later, or definitely the same day.
7. ____I do weekly and monthly reviews of all my class and textbook notes.
8. ____In reviewing, I use all methods, such as reciting aloud, writing, picturing the material, etc.
9. ____I study math before other subjects, and when I am most alert.
10. ____I take small breaks every 20 to 40 minutes when I study math.
11. ____I work to complete my difficult math assignments in several small blocks of time
12. ____I reward myself for having studied and concentrated.
13. ____I survey my assigned math readings before I tackle them in depth.
14. ____When I read, I say aloud and write out important points.
15. ____I underline, outline, or label the key procedures, concepts, and formulas in my text.
16. ____I take notes on my text and review them often.
17. ____I complete all assignments and keep up with my math class.
18. ____I study math two hours per day, at least five days a week.
19. ____I work on at least ten new problems and five review problems during each study session.
20. ____I work to "overlearn" and thoroughly master my material.
21. ____I retest myself often to fix ideas in memory.
22. ____I work to understand all formulas, terms, rules, and principles before I memorize them.
23. ____I use a variety of checking procedures when solving math problems.
24. ____I study with two or more different math books.
MY GRAND TOTAL IS:_______.
If your score is above 68 points, you have excellent math study skills.
If your score is between 54 and 68 points, you have fair study skills, but you need to improve.
If you score is below 54 points, you have poor math study skills and you need help fast!
24
20 Tips for Academic Success
1. Each night prepare a course of study that you hope to accomplish the next day.
2. Create a schedule for yourself that is flexible but informs you of your weekly time commitments.
3. Plan and schedule some time each day to accomplish your goals.
4. Schedule leisure time the same way you schedule work commitments.
5. Keep a record of all test dates, assignments, deadlines, appointments, etc., on a calendar.
6. Make sure your desk faces a blank wall – not another desk or window.
7. If you are studying at home, find a place that you use only for studying. Keep noise distractions to a
minimum. Keep your door closed; avoid all conversations including unnecessary phone calls.
8. Keep the surface of your desk and the space immediately surrounding your study area free of visual
distractions such as photographs, mementos, etc.
9. Keep your desk uncluttered and have all the necessary materials readily available.
10. Have decent lighting and a good straight-back comfortable chair. Avoid studying in bed or stretched out
on a couch.
11. Remember the importance of consistency: the most effective studying is done in the same place at a
regular time.
12. Begin with your hardest subject, while your concentration is at its peak. Remember to take a 15-minute
break every hour. Do not study in segments longer than 3 hours.
13. Begin studying your first subject by briefly surveying the material to be learned.
14. Make sure you understand the material you are studying; otherwise it becomes more difficult to learn.
15. Be a questioning reader. Ask yourself, "What re the main points the author is trying to tell me?" Read to
find the answers to your questions. (Yes, you do need to read a math book!)
16. Become actively involved in your studying. Underline or highlight key words and phrases. Write down
important points and definitions. If you are having a hard time concentrating, begin outlining the
chapter. Remember that you are learning by writing.
17. Don't be afraid to ask your professors for help. NO question is too "dumb."
18. When preparing for a test, make sure you have a clear idea of what is to be covered on your test.
Review copies of old tests if possible.
19. Remember to eat well and get enough sleep and exercise around exam time. An unrested and poorly fed
body has to work harder to do regular things.
20. Arrive for tests early so as to be organized and ready instead of in a panic. Try to go into the test alert
and calm.
25
Differences between English Language and Math Language
SPOKEN AND WRITTEN ENGLISH USES ACTIVE AND PASSIVE VOICE, which
means that it…
1. …has a sense of action or time depending on the context, i.e. narratives require
active voice, but a psychological study would require a passive voice.
2. …sometimes uses emotion but often requires an objective tone, i.e. persuasive
papers might rely on emotional language but summaries need to be neutral.
3. …first-person "I" is used to convey personal experience but when summarizing,
informing or reporting stay unbiased.
4. …follows grammatical conventions depending on the context, discipline, and
format.
5. …prepositions allow us to express relationships betweens ideas particularly time and
space.
6. …is a highly flexible language which varies on purpose and context, which
articulate different language standards depending on the academic discipline.
7. …is a language full of coordinating conjunctions and subordinating conjunctions
which allow us to express complex thoughts.
MATHEMATICAL LANGUAGE USES PASSIVE VOICE, which means that it …
1. …has no sense of action or time.
2. …uses no emotional words.
3. …does not use the first-person "I".
4. …has a different grammar. For example, find the verb in:
"If x = 5, then x + 3 = 8."
5. …puts great emphasis on prepositions. For example, compare: "3 divided by 6" and
"3 divided into 6."
6. …is a high-density language to be read for detail, in which even a two letter word
cannot be missed.
7. …is a propositional language because of its logical structure like the "if-then"
construct.
By Carrie Ann James (English, Urbana U.) and Rose Kleski Hart (Math, OSU-Newark)
26
Steps for Solving a Word Problem
1. Read the problem through quickly.
2. Pick out the question.
3. Read the problem until you have a complete understanding.
4. Write out the important information
5. Organize the information. Draw a picture if relevant.
6. Collect any formulas that may be useful.
7. Define variables. Don't be afraid to stray from the popular "x".
8. Write out the relationship in English.
9. Write out the equation in Algebra.
10. Solve the equation.
11. Check your solution. Is it realistic?
27
The Natural Human Learning Process
Information from presentation and book by Rita Smilkstein, PH.D
We're Born to Learn: Using the Brain's Natural Learning Process
Summary of Natural-Learning Stages
Based on NHLP Research with Approximately 6,000 Children and Adults
STAGE 1: MOTIVATION/Responding to stimulus in the environment: watched, observed, had to, interest,
desire, curiosity
STAGE 2: BEGINNING PRACTICE/Doing it: practice, practice, practice, trial and error, ask questions,
consult others, basics, make mistakes, lessons, some success
STAGE 3: ADVANCED PRACTICE/Increase of skill and confidence: practice, practice, practice, trial and
error, some control, reading, encouragement, experiment, tried new ways, positive attitude, enjoyment, lessons,
feedback, confidence, having some success, start sharing
STAGE 4: SKILLFULNESS/Creativity: practice, doing it one's own way, feeling good about yourself,
positive reinforcement, sharing knowledge, success, confidence
STAGE 5: REFINEMENT/Further improvement: learning new methods, becoming second nature, continuing
to develop, different from anyone else, creativity, independence, validation by others, ownership, habit,
teaching
STAGE 6: MASTERY/Broader application: greater challenges, teaching it, continuing improvement or
dropping it, feeds into other interests, getting good and better and better, going to higher levels
28
Major Points about Learning
FOR STUDENTS
We're Born to Learn, page 103
1. Your brain was born to learn, loves to learn, and knows how to learn.
2. You learn what you practice.
and again.
3. You learn what you practice because, when you are practicing, your brain is growing new
fibers (dendrites) and connecting them (at synapses). This is what learning is.
4. Learning takes time because you need time to grow and connect dendrites.
5. If you don't use it, you can lose it. Dendrites and synapses can begin to disappear if you don't
use them (if you don't practice or use what you have learned).
6. Your emotions affect your brain's ability to learn, think, and remember.
-doubt, fear, etc., prevent your brain from learning, thinking, and remembering.
Remember, you are a natural-born learner.
29
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9780321644909
ISBN:
0321644905
Edition: 3 Pub Date: 2010 Publisher: Prentice Hall
Summary: Martin-Gay, Elayn is the author of Prealgebra & Introductory Algebra (3rd Edition) (The Martin-Gay Paperback Series), published 2010 under ISBN 9780321644909 and 0321644905. Three hundred thirty eight Prealgebra & Introductory Algebra (3rd Edition) (The Martin-Gay Paperback Series) textbooks are available for sale on ValoreBooks.com, one hundred ten used from the cheapest price of $9.45, or buy new starting at $71.52....[ let the beginning chapters be shorter. That content is mainly brushing up on skills that most already have. I would use this book to present new things to teach others.in a field that uses a lot of math.
The book went hand in hand with the course material, so it was easy to understand.
Actually there was nothing in the book that was not helpful. It could not have been better.
This book was very helpful. It was the best algebra and math book I have used. It really explained how to do problems. It was very informative and I actually did well in this class. Math is not my strong suite. I missed an A by 3.6 points.
| 677.169 | 1 |
This fascinating volume contains 344 "challenging" problems partitioned into three major categories: 114 in geometry and trigonometry, 112 in algebra and analysis and 118 in number theory and combinatorics. Actually, the problems themselves comprise only the first 85 pages of this volume. What follow are the solutions.
In the preface, the authors make the distinction between an "exercise" and a "problem"; the latter requiring more time and thought to solve. The questions contained in this volume are definitely problems by this definition. The authors have gathered many problems that have appeared as part of the Mathematical Olympiad and offer a glimpse of the challenge faced by the competitors.
As a regional director for the American Mathematics Competitions (AMC-8,-10 and -12) this reviewer is often asked why students should participate in these competitions. My typical response is that such competition stimulates mathematics students to think "outside the box". The problems one sees on these examinations are not your typical textbook exercises and the problems in this volume represent a good sample.
Where might this text be used? One important audience is the high school teacher who wishes to stimulate interest in mathematics by challenging students with some difficult (but accessible) problems. This might be to help them prepare for a mathematics competition or it may just be for fun.
While these problems originate from a competition among high school students, the problems contained within will be a challenge to some of our brightest college mathematics students, and even for college faculty. I could foresee this volume being used in a number of ways at the college level.
First, one could use it as a text and/or resource for a problem-solving seminar taken by mathematics majors and minors.
Secondly, an institution could use these problems to help prepare a team for the Putnam competition.
Finally, many institutions sponsor a "Problem of the Week". Here are some great candidates!
What did I like about this book? The format of dividing the problems into three broad categories can be helpful to faculty who are looking for problems for specific courses. I am also pleased that complete solutions were given, but the solution is not immediately after the problem. In fact, one could just read the solution section and learn a lot about mathematical problem solving. The problems are well chosen with credit given to the original proposer.
What did I not like? I have only one small concern. The problems are (possibly) too good. Perhaps the inclusion of a few "warm-up" problems would have been appropriate. I want to emphasize that this is a minor drawback and it should not influence ones decision to use this nook. After all, such warm-up problems can be exercises that are found in our "usual" textbooks.
The authors are experienced problem solvers and coaches of mathematics teams. This expertise shows through and the result is a volume that would be a welcome addition to any mathematician's bookshelf.
Herbert E. Kasube (hkasube@hilltop.bradley.edu) is associate professor of mathematics at Bradley University with a particular interest in the history of mathematics. He also serves as regional director for the AMC-8 and AMC-10/12.
| 677.169 | 1 |
Oh, if you're majoring in P-chem, I highly suggest you get this book later on. It has multivariable calculus, but I've never used it for such since I took a separate course on it. It should cover EVERYTHING you could possibly (reasonably) ever run into in the physical sciences related to math (multivariable calculus, vector calculus, linear algebra, prob/stats, the kitchen sink, and more). I know my school used it to cover diff eq for physics majors, and it's a classic resource.
In your case, if you're having trouble with self-studying multivariable calculus from your text, that book by Adams will help you out.
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Introduction to Matrices and Vectors [NOOK Book]Customers Who Bought This Also Bought
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This BookRelated Subjects
Table of Contents
Preface
Chapter 1. Definition, Equality, and Addition of Matrices
1. Introduction
2. What Matrices Are
3. Equality of Matrices. Specification of Matrices. The Zero Matrix
4. Addition of Matrices
5. Addition of Matrices Continued
6. Addition of Matrices Concluded
7. Numerical Multiples of Matrices
Chapter 2. Multiplication of Matrices
1. A Problem Arising in Business Management
2. Formal Definition of Multiplication
3. A Surprising Property of Matrix Multiplication
4. Matrix Multiplication Continued
5. The Unit Matrix
6. The Laws of Matrix Multiplication
7. Powers of Matrices. Laws of Exponents
8. Multiplication of Matrices by Matrices and Multiplication of Matrices by Numbers
9. Polynomials in a Matrix
Chapter 3. Division of Matrices
1. Introduction
2. Using an Equation Satisfied by a Matrix
3. The Least Equation Satisfied by a Matrix
4. Using the Least Equation Satisfied by a Matrix to Solve the Problem of Reciprocals
5. Proof of the Uniqueness of the Least Equation Satisfied by a Matrix
6. Two Theorems about Reciprocals
Chapter 4. Vectors and Linear Equations
1. Definition of Vectors. Notation and Properties
2. Vectors and Directed Segments in the Plane
3. Vectors and Directed Segments in Three-dimensional Space
4. Geometric Applications of the Algebra of Vectors
5. Distances, Cosines, and Vectors
6. More about the Lengths of Vectors
7. Expressing Systems of Linear Equations in Terms of Vectors and Matrices. Solving by Using Reciprocal Matrices
8. Solving Systems of Linear Equations by the Method of Elimination
Chapter 5. Special Matrices of Particular Interest
1. The Complex Numbers as Real Matrices
2. The Quaternion Matrices
3. Matrices with Complex Entries
Chapter 6. More Algebra of Matrices and Vectors
1. The Transpose Matrix
2. The Trace of a Matrix
3. The Cross Product of Matrices
4. 3 x 3 Skew Matrices and Vectors of Size 3
5. Geometry of the Cap Product
Chapter 7. Eigenvalues and Eigenvectors
1. Matrix Reciprocals and Vectors
2. Eigenvalues
Chapter 8. Infinite Series of Matrices
1. The Geometric Series
2. The Size of the Entries in the Powers of A
3. The Exponential Series
| 677.169 | 1 |
gebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?
The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving.
In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes:
A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3
From the 2nd Edition:
"I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry." -The American Mathematical Monthly
| 677.169 | 1 |
Description of Exploring the World of Mathematics by Master Books
Math doesn't have to be difficult, and John Tiner shows that it can actually be fun. Students of different ages and skill levels can use this fascinating book.
Intended as a supplement to a homeschool curriculum, Exploring the World of Mathematics is more than just a math book. Tracing the history of mathematics principles and theory, it includes stories and tips showing math to be practical for everyday use. It also uses many examples of mathematics from the Bible and explains the timekeeping methods used in biblical times.
Included are the following: basic mathematical principles including some simple algebra, geometry, and scientific math; Egyptian and Greek contributions to mathematics; Math involving time; the seasons; and measurements.
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Graphing calculators just want to have fun. The tool used for advanced math can do more than just calculate. Gone are the days when the only creative thing you could do with a calculator was type "HELLO" (or the ever-popular, giggle-inducing "BOOBS")...
Unless something drastic happens, Texas Instruments might be getting ready to eat Casio's dust. The latter consumer electronics company has just released a graphing calculator with a gorgeous color screen and a suite of apps, bringing mainstream math
| 677.169 | 1 |
Introduction to graph theory
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...Read More introduction to the subject for non-mathematicians. The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range of applications. This is followed by two chapters on planar graphs and colouring, with special reference to the four-colour theorem. The next chapter deals with transversal theory and connectivity, with applications to network flows. A final chapter on matroid theory ties together material from earlier chapters, and an appendix discusses algorithms and their efficiency.Read Less
New. It is HARD COVER reprint edition of the book published
| 677.169 | 1 |
CBSE solved test papers for class 9 Mathematics Summative Assessment-I (First Term). Review of representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification. Rational numbers as recurring/terminating decimals. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number. Definition of nth root of a real number. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.) Rationalization (with precise meaning) of real numbers of the type (& their combination).
CBSE solved test papers for class 9 Mathematics Summative Assessment-I (First Term). Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial / equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorization of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Simple expressions reducible to these polynomials.
CBSE solved test papers for class 9 Mathematics Summative Assessment-I (First Term). History - Euclid and geometry in India. Euclid method of formalizing observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem. Given two distinct points, there exists one and only one line through them. (Prove) two distinct lines cannot have more than one point in common.
CBSE solved test papers for class 9 Mathematics Summative Assessment-I (First Term). (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180 degree and the converse. (Prove) If two lines intersect, the vertically opposite angles are equal. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines. (Motivate) Lines, which are parallel to a given line, are parallel. (Prove) The sum of the angles of a triangle is 180 degree. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interiors opposite angles.
CBSE solved test papers for class 9 Mathematics Summative Assessment-I (First Term). (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence). (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence). (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (Prove) The angles opposite to equal sides of a triangle are equal. (Motivate) The sides opposite to equal angles of a triangle are equal. (Motivate) Triangle inequalities and relation between 'angle and facing side' inequalities in triangles.
CBSE solved test papers for class 9 Mathematics Summative Assessment-I (First Term). The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y = mx + c and linking with the chapter on linear equations in two variables.
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Math Survival Guide Tips and Tricks for Science Students
9780471270546
ISBN:
0471270547
Edition: 2 Pub Date: 2003 Publisher: Wiley & Sons, Incorporated, John
Summary: This second edition of 'Math Survival Guide' provides tips for science students in the form of a quick reference/update guide. It uses an approachable tone and appropriate level and includes good problem sets.
Appling, Jeffrey R. is the author of Math Survival Guide Tips and Tricks for Science Students, published 2003 under ISBN 9780471270546 and 0471270547. Three hundred twelve Math Survival Guide Tips and ...Tricks for Science Students textbooks are available for sale on ValoreBooks.com, sixty three used from the cheapest price of $10.03, or buy new starting at $38 [more
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Calculus : Early Transcendentals - 2nd edition
Summary: What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching-supported by Rogawski's Calculus Second Edition-the most successful new calculus text in 25 years!
Widely adopted in its first edition, Rogawski's Calculus worked for instructors and students by balancing formal precision with a guiding conceptual focus. Rogawski e...show morengages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus.
Now Rogawski's Calculus success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience. ...show less737373 142923184
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This workbook provides high school students with activities from algebra to calculus that use Texas Instruments software TI InterActive! TI InterActive! is software for the PC that combines a word processor, a spreadsheet, a web browser and the features of both the TI-89 and TI-83 graphing calculators. This book provides detailed instructions for analysis of functions including linear, exponential, quadratic and periodic. Additionally, the functions are used to model data collected from the Internet. The activity book is available for purchase or each activity can be downloaded free in PDF format
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Summary: ELEMENTARY STATISTICS: A STEP BY STEP APPROACH is for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. The new edition features increased emphasis on the computing technologies commonly used in such coureses. New to This Edition
&q...show moreuot;Technology Step by Step" sections show how to solve basic problems using Minitab software, the TI-83 graphing calculator, or Excel.
More examples and exercises based on actual data.
Features
Statistics Today problems open every chapter. These real-life problems, accompanied by a photo or graphic and sometimes a news item, show students the relevance of the chapter's topic. The answer is provided at chapter end.
Procedure Tables embody the book's step by step approach. These boxes summarize methods for solving various types of common problems. Worked examples include EVERY step.
Critical Thinking Challenges at the end of each chapter extend chapter concepts into new areas, inviting students to think about and apply what they have learned.
Allan G. Bluman is Professor of Mathematics at Community College of Allegheny County, near Pittsburgh. For the McKeesport and New Kensington Campuses of Pennsylvania State University, he has taught teacher-certification and graduate education statistics courses. Prior to his college teaching, he taught mathematics at a junior high school.
Professor Bluman received his B.S. from California State College in California, Penn.; his M.Ed. from the University of Pittsburgh; and, in 1971, his Ed.D., also from the University of Pittsburgh. His major field of study was mathematics education.
In addition to Elementary Statistics: A Step by Step Approach, Third Edition, and Elementary Statistics: A Brief Version, the author has published several professional articles and the Modern Math Fun Book (Cuisenaire Publishing Company). He has spoken and presided at national and local mathematics conferences and has served as newsletter editor for the Pennsylvania State Mathematics Association of Two-Year Colleges. He is a member of the American Statistical Association, the National Council of Teachers of Mathematics, and the Mathematics Council of Western Pennsylvania.
Al Bluman is married and has two children. His hobbies include writing, bicycling, and swimming.Good This book appears to be in good condition. All pages appear to be readable and free from highlighting and writing. The exterior cover does have signs of use, surface scratches, worn corners, et...show morec. Overall this book is in good condition. Hardcover Used-Good. ...show less
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Search Results
The Math Made Nice and Easy series simplifies the learning and use of math and lets you see that math is actually interesting and fun. This series is for people who have found math scary, but nevertheless need some understanding of math without having to deal with the complexities found in mostNeed help with Microbiology? Want a quick review or refresher for class? This is the book for you! REA's Microbiology Super Review gives you everything you need to know! This Super Review can be used as a supplement to your high school or college textbook, or as a handy guide for anyone who…
Revised second edition aligned for the 2008-2009 testing cycle, with a full index. REA''s MCAS Grade 10 Mathematics provides all the instruction and practice students need to excel on this high-stakes exam. The book contains all test components that students will enounter on the official exam:
Specifically designed to meet the needs of high school students, REA's High School Algebra Tutor presents hundreds of solved problems with step-by-step and detailed solutions. Almost any imaginable problem that might be assigned for homework or given on an exam is covered. Starting withThe material in this book was prepared for electrical training courses. It is a practical manual that enables even the beginner to grasp the various topics quickly and thoroughly. The book is one of a kind in that it teaches the concepts of basic electricity in a way that''s clear, to-the-point,Specifically designed to meet the needs of high school students, REA's High School Chemistry Tutor presents hundreds of solved problems with step-by-step and detailed solutions. Almost any imaginable problem that might be assigned for homework or given on an exam is covered. Included are
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״Have you forgotten most of your algebra? Algebra Touch will refresh your skills using touch-based techniques built from the...
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״Have you forgotten most of your algebra? Algebra Touch will refresh your skills using touch-based techniques built from the ground up for your iPhone/iPad/iPod Touch. Say you have x + 3 = 5. You can drag the 3 to the other side of the equation. Enjoy the wonderful conceptual leaps of algebra, without getting bogged down by the tedium of traditional methods. Drag to rearrange, tap to simplify, and draw lines to eliminate identical terms. Easily switch between lessons and randomly-generated practice problems. Create your own sets of problems to work through in the equation editor, and have them appear on all of your devices with iCloud. (there is a version of this app for OSX as well!) Current material covers: Simplification, Like Terms, Commutativity, Order of Operations, Factorization, Prime Numbers, Elimination, Isolation, Variables, Basic Equations, Distribution, Factoring Out, Substitution.״This app costs $1.99
An individual's ability to recall basic math concepts is essential for him/her to grasp higher-oder concepts. Students who...
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An individual's ability to recall basic math concepts is essential for him/her to grasp higher-oder concepts. Students who can recall facts effortlessly devote more of their mental energy to learning advanced skills and perform better in math. This lesson plan provides several strategies to ensure mastery.
This module (eCouse) is designed to standalone as an instructional tool to cover the topic of Linear Equations from point and...
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This module (eCouse) is designed to standalone as an instructional tool to cover the topic of Linear Equations from point and slope equations. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.
This module (eCouse) is designed to stand alone as an instructional tool to cover the topic of Linear Equations II from point...
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This module (eCouse) is designed to stand alone as an instructional tool to cover the topic of Linear Equations II from point and slope equations. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expresions using...
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This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expresions using properties of real numbers and rules of exponentiation. Learners would benefit by reviewing modules in sequence for the related course in Beginning Algebra.
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expressions....
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This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of Variable Expressions. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.
This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of factoring polynomials....
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This module (eCourse) is designed to stand alone as an instructional tool to cover the topic of factoring polynomials. Learners would benefit by reviewing modules in sequence for the course Beginning Algebra.
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Featured Research
from universities, journals, and other organizations
The aftermath of calculator use in college classrooms
Date:
November 12, 2012
Source:
University of Pittsburgh
Summary:
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, experts say. They have proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students.
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Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center. King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
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"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves -- a mathematical function that describes a smooth repetitive oscillation -- and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes -- especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics.
University of Pittsburgh. "The aftermath of calculator use in college classrooms." ScienceDaily. ScienceDaily, 12 November 2012. <
University of Pittsburgh. (2012, November 12). The aftermath of calculator use in college classrooms. ScienceDaily. Retrieved January 24, 2015 from
University of Pittsburgh. "The aftermath of calculator use in college classrooms
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TheGraphs and Modelsseries by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students ''see the math'' through its focus on visualization and technology. These texts continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications.
With theFifth Edition, visualization is taken to...show more a new level with technology. The authors also integratesmartphone apps, encouraging readers to visualize the math. In addition, ongoing review has been added with newMid-Chapter Mixed Reviewexercise sets and newStudy Guide summariesto help students prepare for tests. ...show less
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Keep your tenth grader involved and excited about geometry to the very end with the Lifepac Geometry Unit 10 Worktext! This colorful, interesting worktext serves as a comprehensive review of the entire year. Topics reviewed include proofs, angles, area and volume, polygons, circles, and more. Tests are included. Format: Paperback. Grade Level: 10th Grade.
Want to teach your teen how to find area and volume? Not sure how to explain formulas clearly? Just get the Lifepac 10th Geometry Unit 8 Worktext! This slim, consumable worktext is packed with step-by-step lessons that cover how to find area of polygons, circles, and the surface area and volume of solid shapes! Tests are included. Format: Paperback. Grade Level: 10th Grade.
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two general approaches to computation: using computation as a numerical tool to approximate answers or using a computer algebra system to provide exact mathematical answers by symbolic manipulation. This book explores the second of these approaches, using the computer algebra system Mathematica. … Though this work does teach students how to use Mathematica, it does so with the goal of providing new insights into basic mathematics, which can then be applied to more advanced mathematics. … Summing Up: Recommended. Lower- and upper-division undergraduates." (D. Z. Spicer, Choice, Vol. 50 (7), March, 2013)
"Three main chapters form the core of the book. In the first chapter, the authors talk about using a computer algebra system like Mathematica for problems in number theory … . Chapters 2 and 3 are devoted to calculus and linear algebra, respectively. … The mathematical content of the chapters is … elementary and written in a style easily understandable by nonspecialists. … a very good introduction for beginners to this interesting and important topic." (Kai Diethelm, ACM Computing Reviews, March, 2013)
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This applet is part of a larger collection of lessons on graph theory. The focus of this particular applet is on Spanning...
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This applet is part of a larger collection of lessons on graph theory. The focus of this particular applet is on Spanning Trees. The user will explore depth first and breadth first methods of developing spanning trees from a connected graph.
Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math...
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Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math (basic arithmetic and math to calculus), statistics, biology, physics, chemistry, finance, and other topics. The topics cover K-12 levels and higher education. The simple and clear presented information enables learners to see and review the topics and how to solve the problems at their pace with as much practice as they wish. In particular there are over a thousand videos just for mathematics. The site also contains a handful of interactive mathematics learning objects that are of the drill and practice typedemonstrates real-world applications of math to all those students who say, "How will I ever use this?" You don't get much...
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demonstrates real-world applications of math to all those students who say, "How will I ever use this?" You don't get much more real world than solving the problems of dividing estates fairly, apportioning legislative seats, or cutting a cake in even pieces. Each activity includes printable worksheet materials as you incorporate this standards-based subject--discrete mathematics--in your math classes (grade 9 and up).
This extensive site is primarily intended as an online supplement to the text Finite Mathematics by Stefan Waner and Steven...
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This extensive site is primarily intended as an online supplement to the text Finite Mathematics by Stefan Waner and Steven R. Costenoble. However, as the authors explain on their home page, this material is pertinent and freely available to anyone studying in this subject area. Of particular interest will be the online tutorials, interactive quizzes and exercises, and various Java, Javascript, and Excel spreadsheet utilities. The following chapter headings indicate the topics covered: Linear Functions and Models, Systems of Linear Equations and Matrices, Matrix Algebra, Linear Programming, Mathematics of Finance, Sets and Counting, Probability, Statistics, Markov Systems, Game Theory. There is also a review of Algebra.
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in a very pedagogical style and seems to be the mirror of the original ideas of its author in the area of mathematical physics. … The typography is excellent and the figures are beautiful. … Graduate and advanced undergraduate students in physics and even in mathematics will find in this book an understanding of the contribution of Clifford algebras to the field of differential geometry as well as motivation to continue their study." (Pierre Anglès, Mathematical Reviews, March, 2014)
"The book under review is perfectly organized textbook for undergraduate students in mathematics and physics due to the large experience of the author. … The author provides quite interesting historical analysis … . This book is a natural continuation of the previous book of the author … ." (Milen Hristov, JGSP Journal of Geometry and Symmetry in Physics, Vol. 33, 2014)
"The author develops the differential geometry of curves and surfaces by using Clifford's geometric algebra. … The book is enriched with several very interesting and extensive historical and biographical presentations. … it can serve as an accompanying source for someone who studies differential geometry, or for someone who wants to look at known facts from a different viewpoint. Also, it is ideal for studying geometry through historical development, and thus this book could also be useful for reading courses on certain aspects of geometry." (A. Arvanitoyeorgos, Zentralblatt MATH, Vol. 1232, 2012)
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This site offers several tutorials on algebra, trigonometry, calculus, differentail equations, complex variables, matrix...
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This site offers several tutorials on algebra, trigonometry, calculus, differentail equations, complex variables, matrix algebra, and tables. Cyber Exam which contains quizzes and tests, and Cyber Board which answers FAQs and more are included.
This book is a guide through a playlist of Calculus instructional videos. The format, level of details and rigor, and...
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This book is a guide through a playlist of Calculus instructional videos. The format, level of details and rigor, and progression of topics are consistent with a semester long college level second Calculus course, or equivalently, together with the first workbook, an AP Calculus BC course. The book further provides simple summary of videos, written definitions and statements, worked out examples--even though fully step-by-step solutions are to be found in the videos-- and an index. The playlist and the book are divided into 16 thematic learning modules. Exercises, some with and some without solutions, and sample tests with solutions are provided in a separate companion manual. The book can be used for self study, or as a textbook for a Calculus course following the "flipped classroom" model
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This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
I'm a first-year math teacher in high school and I use this book very often. It's a great way to summarize the material for a review in general and before a test. It's an essential tool for a quick reference because it puts all the rules on a subject together on one page. For example, a page "Common Forms of Linear Equations" lists 6 equations: Standard form, Slope-Intercept form, Point-Slope form along with equations for Vertical Line, Horizontal Line and Slope-Intercept form passing through origin. When we did the unit on linear functions, this was a great way to put all that we have learned together and have a flash card for easy reference.
This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
I wasn't sure exactly how I would use this book since it is my first year teaching. The resources compiled in this book are so simple that any student can follow along. There are teacher only lists that deal with things like struggling students, students who hate math, student who just like to be a pain in the butt, etc. The back of the book also contains some cool hands on projects that can be used. Geometry nets, tangram cutouts, blank checks for a financial unit, graph paper that you can copy or scan to use in the classroom. The book goes from pre-algebra to calculus. Besides all the problems, definitions, and explanations, the book has specific strategies to help students with all types of learning styles get a grasp of the material. Testing strategies are also in one of the "lists". Don't let the word list fool you this book is soooo much more!!! Buy it you won't be disappointed.
This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
I use my copy of The Math Teacher's Book of Lists frequently. It's full of great reproduceable templates, and info pages such as lists of primes, perect numbers, square numbers, triangular numbers, etc. It's also a great reference to refresh your own memory on topics that have gotten rusty. I purchase a copy for each new math teacher I mentor. It makes a great gift. Every year I get my copy of The Math Teacher's Book of Lists off the shelf and page through it. Each time I do this, I find several pages that I can use to make my job easier or to explain a concept more clearly to the kids.
This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
I teach pre-algebra to students who are far below level. My kids have made good gains year after year with hands-on methods and with study guides I have made for them throughout the year. I have created so many materials which are like "cheat" sheets of quick reference guides for topics. My students use their reference sheets or study guides and eventually do not need to refer to the study guides. As you can imagine, making study guides with essential information is very time consuming.
For example, there is a page in the book just for triangle terms with a visual and explanations for triangle, side, vertex, area, angle bisector.... another page has the common forms of linear equations--standard, vertical line, horizontal line, slope-intercept, etc.
My two daughters who are in high school were already glancing through the book because of the reference pages for Calculus. This book is a wonderful reference for intermediate grades (4-6) all the way through Calculus. I wish I had found this book years ago. It would have saved me a lot of time!
This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
This book is amazing. I thought I might find a dozen or so lists to use in my 8th grade math classes, but more that half of the lists are appropriate. It is a great resource for any 5-12 grade teacher.
This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
This is an amazing book for math teachers. It is divided up by subject (i.e. Algebra, Calculus), and then lists formulas or equations for them. It's not a work book, so don't think that that is what you're getting. Instead, it is a resource book that you can use to share with students or to brush up on your knowledge of math.
I highly recommend this if you're a math teacher or want a good reference book for math.
This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
First we went to Barnes n Noble and it was very expensive so we checked in Amazon. Like always I find almost everything here. The book is really good for reference and really easy to understand. I would recommend this item..
This review is from: The Math Teacher's Book Of Lists: Grades 5-12, 2nd Edition (Paperback)
I have been using this book to reference any area of math you could possibly want to learn more about. I have currently used it while tutoring a 7th grade student and the book provides excellent examples and explanations of various algebra related topics. The book includes any area of math you with to reference. The only drawback is that there is no index, so you have to search for topics in the table of contents.
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Trade in Edexcel GCSE Mathematics Higher Course (Exceptional Preparation for Edexcel GCSE) for an Amazon Gift Card of up to £0.25, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more
Most Helpful Customer Reviews
This book, while very good, tends to have flaws in its exercises. I have found that since using the book, in the answers there are 'There is no real answer to this question, it could be anything'. But the layout of the book is flawless. The book doesn't require a teacher, and teachers have found themselves just reading from the book when explaining topics. There are some typos in it, for example on one page the questions go 1, 2, 3, 4, 5, 6, 7, 6... but this is the worst it gets (which is very good considering it has been done very hastely due to the change in the GCSE exam). There is one major flaw with the book. This is that the answers are in the back. On questions where no working is needed, the pupils just copy the answers from the back and graphs are practically traced. There should be a separate teachers edition and pupils should not have access to the answers. The book could do with some more help towards the coursework. I had to use an OCR book (for the Edexcel course) to help pupils understand what the coursework required. Overall, a good book with flaws. BUT certainly the BEST BOOK on the market today.
I have been working from this book in the classroom. Initially I paid little attention to explanations and found the exercised daunting, as some are far too long. After reviewing and learning new modules from the book, I found the explanations invaluable. This book, made by Edexcel for Edexcel, covers the entire Edexcel GCSE Mathematics Higher course (to A*). If you have a poor mathematics teacher I advise that you make good use of this book, ideally at home. I strongly disagree with those views above ? ironically of a teacher ? regarding the included answers. His views are exactly the reason why people don?t want to learn; they feel they are forced, controlled and scrutinized. The answers allow those willing to learn to quickly check up on answers and as a result act as they see fit (e.g. seek advise, review explanations).
This book covers GCSE Level Mathematical topics well. An excellent buy, well worth the money spent. If you are doing GCSE Maths, this book will help you well with your studies. It also covers Algebraic Fractions and Quadratic Inequalities.
I already knew what I was getting with this textbook as it was the very one I used at high school myself - I'm planning to teach myself some maths and physics, so wanted to revise without paying what seems like loads for a current textbook. It isn't up to date with the post-2006 exams, but that's fine by me. I took my GCSEs in 2007 but my teachers didn't want to change textbook, so we kept these, and I think they're pretty good for the kinds of things I need it for! Nowadays we can Google something if we don't understand it, and that's what I do anyway, so this book is great for explaining the basic concepts and giving me loads of practice questions. Admittedly, it is obviously meant for students who have teachers to explain things, but my maths is just a little rusty - it is still there knocking around in my head, so the reminder and the practice is all I need. Great and very cheap! Hooray!
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Algebraic Geometry over the Complex Numbers is a strong addition to existing introductory literature on algebraic geometry. The author's treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields.
- Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples.
"Algebraic Geometry over the Complex Numbers" is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory.
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Mathematical Reasoning for Elementary School Teachers (6th Edition)
9780321693129
ISBN:
0321693124
Edition: 6 Pub Date: 2011 Publisher: Addison Wesley
Summary: Calvin T. Long is the author of Mathematical Reasoning for Elementary School Teachers (6th Edition), published 2011 under ISBN 9780321693129 and 0321693124. Three hundred fifty two Mathematical Reasoning for Elementary School Teachers (6th Edition) textbooks are available for sale on ValoreBooks.com, one hundred forty one used from the cheapest price of $1.80, or buy new starting at $34
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Find a San Marino Algebra 1Word processors are such an important tool for the modern world as few formal documents are fully handwritten. Word is useful in high school, college, and especially at work. Learning the full extents of a word processor will expand the opportunities for a studentThe basic knowledge of physics is, however, open to everyone with a little effort. We can study meteorites falling from the sky, starlight in its course, and the power of the Sun, all with some simple principles. As much as possible I try to make the principles of physics, chemistry, and math seem plausible, reasonable, and, in the end, the only thing that they could possibly be.
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helpful examples and exercises that provide motivation for the reader
Presents the Laplace transform early in the text and uses it to motivate and develop solution methods for differential equations
Takes a streamlined approach to linear systems of differential equations
Protected instructor solution manual is available on springer.com
Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations.
Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.
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Exercises in results and notions for a student in mathematics requires solving ex ercises. The exercises are also meant to test the reader's understanding of the text material, and to enhance the skill in doing calculations. This book is written with these three things in mind. It is a collection of more than 450 exercises in Functional Analysis, meant to help a student understand much better the basic facts which are usually presented in an introductory course in Functional Analysis. Another goal of this book is to help the reader to understand the richness of ideas and techniques which Functional Analysis offers, by providing various exercises, from different topics, from simple ones to, perhaps, more difficult ones. We also hope that some of the exercises herein can be of some help to the teacher of Functional Analysis as seminar tools, and to anyone who is interested in seeing some applications of Functional Analysis. To what extent we have managed to achieve these goals is for the reader to decide.
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From Real to Complex course in real and complex analysis that links analysis and topology
Approaches complex analysis through real analysis, with an overarching theme being the search for a primitive
Emphasises various forms of homotopy, together with the winding number and its properties
The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology.
Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon.
Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.
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7.2 Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body
This three-part example illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. This example is adapted from High School Mathematics at Work, a publication from the National Research Council (1998, p. 80). These activities allow high school students to study modeling in greater depth, as described in the Algebra Standard.
Through multiple representations of a common concept, better insight into, and a deeper understanding of, the problem situation can be achieved.
The following links to an updated version of the e-example
Using Graphs,
Equations, and Tables to Investigate Iteration and Recursion (7.2)
In this e-example, students are able to iterate up to 100
times after defining their own initial value and recursive function.
The e-example below contains the original applet which conforms more closely to the pointers in the book.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Explores mathematical concepts using examples from science. Offers participants an opportunity to enhance the mathematical skills needed to teach science and mathematics more effectively. Emphasizes practices common to the Common Core State Standards (CCSS) for Mathematics and the 2013 Next Generation of Science Standards (NGSS). Each class covers critical concepts in mathematics applied to hands-on activities and laboratory exercises. Topics include ratios and proportions, algebraic equations (linear and quadratic), systems of linear equations, functions (linear and quadratic), graphical representation, and fundamentals of statistical analysis, plane geometry, trigonometry and vector analysis.
Recently re-designed to respond to the specific call in the CCSS-Math and Massachusetts curriculum framework for students to use math flexibly in a wide range of applications, for math teachers to provide opportunities to apply math in context, and for teachers in content areas outside of math, particularly science, to ensure that students are using math to make meaning of and access content. Will also address technical writing, formative assessment, and short- or long-term research projects. Required for Northeastern University's Master of Education degree, Learning and Instruction concentration, science focus and a recommended prerequisite for some other CCC classes (i.e., Physics I and II; Pre-engineering Design; Integrating the Sciences through Energy).
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...
More About
This Book
applications and the real world. Nearly 50 math concepts are presented with multiple examples of how each is applied in everyday environments, such as the workplace, nature, science, sports, and even parking. From logarithms to matrices to complex numbers, concepts are discussed for a variety of mathematics courses, including:
• algebra
• geometry
• trigonometry
• analysis
• probability
• statistics
• calculus
In one entry, for example, the authors show how angles are used in determining the spaces of a parking lot. When describing exponential growth, the authors demonstrate how interest on a loan or credit card increases over time. The concept of equations is described in a variety of ways, including how business managers estimate how many hours it takes a certain number of employees to complete a task, as well as how a to compute a quarterback's passing rating. Websites listed at the end of each entry provide additional examples of everyday math for both students and teachers.
Editorial Reviews
From The Critics
Mathematics educators Glazer (U. of Georgia) and McConnell (North Park U.) describe practical uses of some common mathematical concepts and techniques. The arrangement is by concept, so the reference would probably be most useful to high school teachers and librarians, rather than students seeking techniques for particular problems. The techniques themselves are not explained. Annotation c. Book News, Inc., Portland, OR
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Meet the Author
EVAN M. GLAZER is a Ph.D. candidate at the University of Georgia in the Department of Instructional Technology, and a former mathematics teacher at Glenbrook South High School in Glenview, IL. Previous publications include Using Internet Primary Sources to Teach Critical Thinking Skills in Mathematics (Greenwood
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
| 677.169 | 1 |
Math For Nurses - 8th edition
Summary: Compact and easy-to-use, Math for Nurses is a pocket-sized guide/reference to dosage calculation and drug administration. It includes a review of basic math skills, measurement systems, and drug calculations/preparations. Math for Nurses helps students to calculate dosages accurately and improve the accuracy of drug delivery. The author uses a step-by-step approach with frequent examples to illustrate problem-solving and practical applications. Readers will find it great for use in the clinical ...show moresetting or as a study aid. Practice problems throughout the text and end-of-chapter and end-of-unit review questions will aid students' application and recall of material. A handy pull-out card contains basic equivalents, conversion factors, and math formulas32 +$3.99 s/h
VeryGood
BookCellar-NH Nashua, NH
1609136802
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Polyhedral and Algebraic Methods in Computationallies the theory to computer graphics, curve reconstruction and robotics
Establishes interconnections with other disciplines such as algebraic geometry, optimization and numerical mathematics
Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry.
The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations.
The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics.
Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established.
Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.
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Browse related Subjects
The Bittinger Concepts and Applications Program delivers proven pedagogy, guiding students from skills-based math to the concepts-oriented math required for college courses.The Bittinger Concepts and Applications Program delivers proven pedagogy, guiding students from skills-based math to the concepts-oriented math required for college courses
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This is a collection of activities for use in precalculus and single variable calculus. It is prefaced by a brief summary of...
see more
This is a collection of activities for use in precalculus and single variable calculus. It is prefaced by a brief summary of what I know about group learning and how I use the activities. Many activities are quick combinations of discovery and practice. The statistics gets a bit lengthy, but I thought I'd include it anyway. As far as I recall, my text is only mentioned once and this posting should not be considered a commercial. Use the activities any way you want.
This is an activity that provides the student with the graph of the derivative of a function and asks the student to use the...
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This is an activity that provides the student with the graph of the derivative of a function and asks the student to use the mouse to sketch the graph of the original function that passes through the origin
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This is a free online textbook offered by BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is...
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This is a free online textbook offered by free online textbook 'is suitable for both students and a general audience interested in learning what pure mathematics...
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This free online textbook 'is is a free textbook from BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is suitable for...
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This is a free textbook fromAccording to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is...
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According to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.Although this book may be more meaningful to the student who has had some calculus, there is no prerequisite other than a measure of mathematical maturity. The text is an expansion and refinement of the author's lecture notes developed over ten years of teaching proof courses at Virginia Commonwealth University. The text is catered to the program at VCU to an extent, but the author kept the larger audience of undergraduate mathematics students in mind.
'This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all...
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'This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems.''The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals.Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.'
This is a free, online wikibook, so the content is continually being updated and refined. According to the authors, "This...
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This is a free, online wikibook, so the content is continually being updated and refined. According to the authors, "This wikibook aims to be a quality calculus textbook through which users may master the discipline. Standard topics such as limits, differentiation and integration are covered as well as several others.״
The emphasis in this free, online textbook is on problems - calculations and story problems. "The more problems you do, the...
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The emphasis in this free, online textbook is on problems - calculations and story problems. "The more problems you do, the better you will be at doing them, as patterns will start to emerge in both the problems and in successful approaches to them.״
'This is a four unit module. The first two units cover the basic concepts of the differential and integral calcualus of...
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'This is a four unit module. The first two units cover the basic concepts of the differential and integral calcualus of functions of a single variable. The third unit is devoted to sequences of real numbers and infinite series of both real numbers and of some special functions. The fourth unit is on the differential and integral calculus of functions of several variables.Starting with the definitions of the basic concepts of limit and continuity of functions of a single variable the module proceeds to introduce the notions of differentiation and integration, covering both methods and applications.Definitions of convergence for sequences and infinite series are given. Tests for convergence of infinite series are presented, including the concepts of interval and radius of convergence of a power series.Partial derivatives of functions of several variables are introduced and used in formulating Taylor's theorem and finding relative extreme values
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KEY BENEFIT:
Basic College Mathematics (11th Edition): Search Results
Book Description:Pearson, 2009. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: KEY BENEFIT : KEY TOPICS : Whole Numbers; Fraction Notation: Multiplication and Division; Fraction Notation and Mixed Numerals; Decimal Notation; Ratio and Proportion; Percent Notation; Data, Graphs, and Statistics; Measurement; Geometry; Real Numbers; Algebra: Solving Equations and Problems MARKET : For all readers interested in basic college mathematics. Bookseller Inventory # ABE_book_new_0321599195 9780321599193
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More About
This Textbook
Overview
Improve your algebra and problem-solving skills with A COMPANION TO CALCULUS! Every chapter in this companion provides the conceptual background and any specific algebra techniques you need to understand and solve calculus problems related to that topic. Verbal descriptions, diagrams, graphs, pictures, symbolic formulas, and numerical data are all used to reinforce communicating and understanding in different modes.
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Meet the Author
Dennis Ebersole is Professor of Mathematics and Computer Science at Northampton Community College where he has taught since 1971. His interests include improving mathematics education in grades K-12. Since 1989 he has administered several grant-funded programs for teachers of mathematics to strengthen their mathematical and pedagogical knowledge and skills. In addition to A COMPANION TO CALCULUS, he has authored or coauthored five other mathematics texts. He is a contributing writer for the revision of "Mathematics Standards Before Calculus" in BEYOND CROSSROADS, published by the American Mathematics Association of Two Year Colleges.
Doris Schattschneider holds a Ph.D. in mathematics from Yale University and taught mathematics at Moravian College for 34 years. She is the author of more than 40 articles, and author or editor of several books. She was Director for two FIPSE-funded projects that developed A COMPANION TO CALCULUS and mentored several campuses in developing a course integrating precalculus review with a first course in calculus. She has been active in the Mathematical Association of America (MAA) at all levels, and was editor of MATHEMATICS MAGAZINE 1981-1985. In 1993 she received the national MAA Award for Distinguished Teaching of College or University Mathematics.
Alicia Sevilla has a Ph.D. in mathematics from Cornell University and is Professor of Mathematics at Moravian College, where she has taught for over 20 years. She participated in the two FIPSE projects that produced the COMPANION TO CALCULUS and mentored other institutions to adopt the integrated approach. She recently served as Chair of the Department of Mathematics and Computer Science, and was co-director of a National Science Foundation grant to develop and implement a quantitative reasoning course. She is an active member of the Mathematical Association of America, and serves as Coordinator of Student Chapters for the Eastern Pennsylvania and Delaware Section.
Kay Somers earned a Ph.D. in mathematics from Rensselaer Polytechnic Institute. She has worked in industry as a statistics and operations research analyst and is Professor of Mathematics at Moravian College where she has taught for 23 years. She recently served as Director of General Education at Moravian and was co-director for several federal grants. The most recent of these was a National Science Foundation grant to develop and implement a quantitative reasoning course. She is active in the Mathematical Association of America and serves on the MAA Classroom Resources Editorial Board. She received the Lindback Foundation Award for Excellence in Teaching at Moravian College in 1990
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).Pc Calculator is a clever note and formula editor combined with an advanced and strong scientific calculator. Being an editor it is extremely user-friendly allowing all possible typing and other errors to be easily corrected and fast recalculated
| 677.169 | 1 |
ents the notion of experimental mathematics to include pre-college curriculum
Introduces a pedagogy of computer experimentation with mathematical models depending on parameters
Provides teacher candidates with research-like experience in mathematics and its pedagogy
Presents modeling activities in both technology-enabled and technology-immune approach
Presents original examples of experimental mathematics pedagogy
This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, this book addresses a call for the preparation of teachers capable of utilizing modern technology tools for the modeling-based teaching of mathematics with a focus on methods conducive to the improvement of the whole STEM education at the secondary level. By the same token, using the book's pedagogy and its mathematical content in a pre-college classroom can assist teachers in introducing students to the ideas that develop the foundation of engineering profession.
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Tuesday, February 10Wednesday, February 11Monday, February 16, 7-9pm, Spinelli Center. Basics of Lines. Graph a line from an equation in point-slope form, slope-intercept form, or standard form. Obtain the equation of a line from a graph. Change from one equation form to another equation form. Solve a set of linear equations (intersecting lines).
Tuesday, February 24, 7-9pm, Spinelli Center: Supervised pre-calculus practice problems. If you attended the review presentations on exponents & logarithms, lines, and/or trigonometry and would like more practice, a tutor will have handouts and will be available for questions.
If you would like to review topics listed below, please contact Karyn Nelson (krnelson@smith.edu) to arrange an appointment:
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Ratti and McWaters wrote this series with the primary goal of preparing students to be successful in calculus. Having taught both calculus and precalculus, the authors saw firsthand where students would struggle, where they needed help making connections, and what material they needed in order to succeed in calculus. Their experience in the classroom shows in each chapter, where they emphasize conceptual development, real-life applications, and extensive exercises to encourage a deeper understanding. Precalculus: A Unit Circle Approach, Second Edition, offers the best of both worlds: rigorous topics and a friendly, "teacherly" tone.
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Discussion
Discussion for Applied Math STAIR
Diana Nicaj
(Student)
Great algebra lesson! The examples are very helpful and the explanations. I really love the use of polls!
Technical Remarks:
Everything seemed to work properly and was easy to follow
Time spent reviewing site:
20min.
3 years ago
Stefani Makowski
(Teacher (K-12))
Information is well organized and clearly written. This presentation allows students to learn at their own pace. As students click through the pages they are asked questions to reinforce information being covered. They are instantly told if the are correct. In addition to text, there are many diagrams and examples. A lot of information is being presented at one time, so this application would work better as a review rather than an introduction.
Time spent reviewing site:
1/2 hour
3 years ago
Melissa White
(Faculty)
This is an excellent lesson. Her instructions are very easy to follow and if you are from MI, she has listed the Mi content standards.
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9780387986210 textbook introduces the mathematical concepts and methods that underlie statistics. The course is unified, in the sense that no prior knowledge of probability theory is assumed, being developed as needed. The book is committed to both a high level of mathematical seriousness and to an intimate connection with application. In its teaching style, the book is * mathematically complete * concrete * constructive * active. The text is aimed at the upper undergraduate or the beginning Masters program level. It assumes the usual two-year college mathematics sequence, including an introduction to multiple integrals, matrix algebra, and infinite
| 677.169 | 1 |
More About
This Textbook
Overview
Bradley S. Witzel and Paul J. Riccomini
Solving Equations: An Algebra Intervention
This timely new book is filled with essential research-based information that teachers and pre-service teachers alike need in order to help more students achieve mathematical standards by employing the concrete to representational to abstract (CRA) sequence of instruction with forms of algebraic equations.
Proven to help students of all levels acquire and retain knowledge of mathematical concepts better than repeated abstract instruction alone, the CRA sequence of instruction employs: the use of hands-on manipulatives, learning to draw pictures of the steps, and finally transitioning from the pictorial representations to true abstract instruction expected by most state standards. Features placement test and fluency probes to help inform instruction and improve student proficiency. The research for CRA is powerful. However, there are few models out there that guide teachers in their delivery. All practicing teachers of mathematics, especially those who teach math to students who struggle or who have a disability, will benefit greatly from the techniques, content, and research of Witzel and Riccomini's new book, a research-based, hands-on, applicable guide for mathematics educators everywhere.
Paul J. Riccomini, Ph.D., is a former high school math teacher and special education teacher. He provides numerous professional development workshops focused on improving mathematics education through the application of evidenced-based practices. Paul is the author of several research and practitioner articles describing instruction strategies to more effectively teach math.
Bradley S. Witzel, Ph.D., is an assistant professor of special education at Winthrop University in Rock Hill, South Carolina. He has experience in the classroom as an inclusive and self contained teacher of students with higher incidence disabilities as well as a classroom assistant and classroom teacher of students with low incidence disabilities. He has published research and practitioner articles in algebra education and math education for students with and without learning disabilities as well as functional assessment and motivation procedures. Additionally, he patented an algebra technique and is the author of the book, Multisensory Algebra, a hands-on resoure of pictorial algebra techniques. Dr. Witzel currently focuses on the development of special education teachers and works to provide researched-validated practices and interventions to pre-service and in-service teachers.
Related Subjects
Meet the Author
The author team of Brad Witzel, PhD, and Paul Riccomini, PhD, are professors whose research emphases are mathematics education and students with exceptional learning needs. Simple Equations is their third intervention for struggling students in mathematics with Pearson. Teachers have been using their interventions around the globe and have found wonderful and unique success. They have also written a textbook on Computations of Fractions: Math Intervention for Elementary and Middle Grades Students, which came out in 2009, and Computation of Integers: Math Intervention for Elementary and Middle Grades Students, coming out
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Precalculus Mathematics for Calculus - With CD - 5th edition
Summary: This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help stu...show moredents develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader. ...show less
Overview. Angle Measure. Trigonometry of Right Triangles. Discovery Project: Similarity. Trigonometric Functions of Angles. The Law of Sines. The Law of Cosines. Review. Test. Focus on Modeling:Surveying.36.31 +$3.99 s/h
Good
Big Planet Books Burbank, CA
2005-10-20 Hardcover Good #34, 735 in Books.
$4253.38136.75 +$3.99 s/h
Good
Nettextstore Lincoln, NE136
| 677.169 | 1 |
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