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https://en.wikipedia.org/wiki/Eva%20Vedel%20Jensen	Eva Bjørn Vedel Jensen (born 14 June 1951) is a Danish mathematician and statistician known for her work in spatial statistics, stereology, stochastic geometry, and medical imaging. She is a professor emeritus in the Department of Mathematical Sciences at Aarhus University. Education and career After earning a master's degree at Aarhus University in 1976, she became a faculty member at the university in 1979. She completed a doctorate at Aarhus in 1987, and became full professor there in 2003. Recognition Vedel Jensen has been an Elected Member of the International Statistical Institute since 1992, and is also a member of the Royal Danish Academy of Sciences and Letters. She won the Villum Kann Rasmussen Annual Award for Technical and Scientific Research of the Villum Foundation in 2009. She was named a knight of the Order of the Dannebrog in 2010. The University of Bern gave her an honorary doctorate in 2013. Selected publications Vedel Jensen is the author of books including: Local Stereology (World Scientific, 1998) Stereology for Statisticians (with Adrian Baddeley, Chapman & Hall/CRC, 2005) She has also written several highly cited papers with Hans Jørgen G. Gundersen including: References External links Living people Danish mathematicians Danish statisticians Danish women mathematicians Women statisticians Aarhus University alumni Academic staff of Aarhus University Elected Members of the International Statistical Institute Knights of the Order of the Dannebrog Members of the Royal Danish Academy of Sciences and Letters 1951 births Spatial statisticians
https://en.wikipedia.org/wiki/List%20of%20Inter%20Miami%20CF%20records%20and%20statistics	Inter Miami CF is an American professional football team based in Miami, that competes in Major League Soccer. This is a list of club records for Miami, which dates from their inaugural season in 2020 to present. Player records Key MLS = Major League Soccer PO = MLS Cup Playoffs OC = U.S. Open Cup LC = Leagues Cup CCC = CONCACAF Champions Cup Current players on the Miami roster are shown in bold. Most appearances Top goalscorers Top assisters Most clean sheets Coaching records Honors See also List of Inter Miami CF players List of Inter Miami CF seasons References Inter Miami CF Miami-related lists American soccer clubs records and statistics Inter Miami CF records and statistics
https://en.wikipedia.org/wiki/Argentina%20national%20football%20team%20results%20%281902%E2%80%931919%29	This page details the match results and statistics of the Argentina national football team from 1902 to 1919. Key Key to matches Att.=Match attendance (H)=Home ground (A)=Away ground (N)=Neutral ground Key to record by opponent Pld=Games played W=Games won D=Games drawn L=Games lost GF=Goals for GA=Goals against Results Argentina's score is shown first in each case. Notes Record by opponent References Argentina national football team results
https://en.wikipedia.org/wiki/Ayse%20Bilgin	Ayşe Ayşin Bombaci Bilgin is an Australian statistician and statistics educator. She is an associate professor of mathematics and statistics at Macquarie University and the president (2021-2023) of the International Association for Statistical Education. Bilgin’s research explores applications of statistics in health sciences and learning and teaching in statistics. Education Bilgin earned a master's degree in statistics from the University of Newcastle (Australia) in 1997, and completed her PhD in 2004 in the University of Newcastle School of Medical Practice and Population Health. Bilgin also has a Bachelor’s degree in engineering, an MBA, a post graduate diploma in Higher Education (Learning and teaching) and a master’s degree in Higher Education (Leadership and management). Recognition Bilgin became an Elected Member of the International Statistical Institute in 2015. She was president of the International Association for Statistical Education for the 2021-20231 term and past president 2023-2025. Bilgin is the recipient of several learning and teaching awards for her outstanding contributions to student learning such as an Australian Learning and Teaching Council Citation for ‘Outstanding Contributions to Student Learning’, a Macquarie University VC Citation, ATEM Award Community Engagement (Highly Commended); Higher Education Award for Employability; joint-recipient of Australian Awards for University Teaching (AAUT).She was awarded “Excellence in research: Five Future-shaping Priorities (Healthy People)” by Macquarie University and she was a member of research team which were the finalist of the Eureka Prize in 2017. References External links Year of birth missing (living people) Living people Australian statisticians Women statisticians Statistics educators University of Newcastle (Australia) alumni Academic staff of Macquarie University Elected Members of the International Statistical Institute
https://en.wikipedia.org/wiki/Bmon	bmon is a free and open-source monitoring and debugging tool to monitor bandwidth and capture and display networking-related statistics. It features various output methods including an interactive curses user interface and programmable text output for scripting. bmon allows the user to see: Network bandwidth real-time visualization Total amount of transmitted data CRC errors Collisions ICMPv6 traffic packets References Linux software
https://en.wikipedia.org/wiki/Qing%20Nie	Qing Nie is a mathematician and systems biology researcher. He is a Chancellor's Professor of Mathematics, Developmental and Cell Biology, and Biomedical Engineering at University of California, Irvine. He is also the director of the Center for Mathematical and Computational Biology and the NSF-Simons Center for Multiscale Cell Fate Research at the University. Nie has published over 170 research papers in the areas of developmental biology, stem cells, computational single-cell genomics, multiscale modeling, deep learning, fluid mechanics & materials, and scientific computing. He has applied systems biology and data-driven methods to study complex biological systems, focusing on single-cell analysis, regeneration, development, and their applications to diseases. Education Nie studied Computational Mathematics at Wuhan University and received his bachelor's degree in 1988. He then moved to the U.S. and completed his Doctoral degree in Mathematics from Ohio State University in 1995. He completed his Postdoctoral Fellowship from University of Minnesota and The LE Dickson Instructorship at University of Chicago in 1997 and 1999, respectively. Career Nie joined University of California in 1999 as an assistant professor of mathematics. He was promoted to associate professor in 2002 and became a professor of mathematics in 2005. He was a founding faculty member of the Department of Biomedical Engineering. At University of California, Nie was appointed as director of the Center for Mathematical and Computational Biology in 2005, and director for the Mathematical and Computational Biology PhD Gateway Program (2014-2019). He has been an associate director of the Center for Complex Biological Systems since 2007. Nie is the director of the NSF-Simons Center for Multiscale Cell Fate Research since 2018. As of 2020, Nie has trained 17 PhD students with degrees in Mathematics, Biomedical Engineering, and Mathematical, Computational, Systems Biology. Nie has been co-director of NIH T32 predoctoral training grants on Mathematical, Computational, and Systems Biology since 2007. Research Nie has conducted research on computational fluids mechanics, material sciences and scientific computing during his PhD and postdoctoral fellows training and his early faculty career. His research focus shifted mainly computational systems biology since his tenure in 2002. He has applied systems biology and data-driven methods to study complex systems in developmental and cell biology, focusing on single-cell analysis and multiscale modeling of stem cells, regeneration, and development, and their connections with cancers and other diseases. Most of Nie's research has been funded by NSF, NIH and private foundation grants. Awards and honors 2005—2008 - Chancellor's Fellow, University of California 2013 - Fellow, American Association for the Advancement of Science 2014 - Fellow, American Physical Society SIAM Fellow in the 2021 class of fellows, "for research and mentoring cont
https://en.wikipedia.org/wiki/Masaya%20Shibayama	is a Japanese footballer currently playing as a midfielder for Omiya Ardija. Career statistics Club . Notes References External links 2002 births Living people Japanese men's footballers Men's association football midfielders J2 League players Omiya Ardija players
https://en.wikipedia.org/wiki/Kaiga%20Murakoshi	is a Japanese footballer currently playing as a midfielder for ReinMeer Aomori, on loan from Matsumoto Yamaga. Career statistics Club . Notes References External links 2001 births Living people Japanese men's footballers Men's association football midfielders J2 League players J3 League players Matsumoto Yamaga FC players ReinMeer Aomori players
https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Thailand	This article presents statistics covering the COVID-19 pandemic in Thailand. Maps Graphs Overview New confirmed cases per day in Thailand New confirmed deaths per day in Thailand References Statistics Thailand
https://en.wikipedia.org/wiki/Parco%20del%20Roccolo	{ "type": "FeatureCollection", "features": [ { "type": "Feature", "properties": {}, "geometry": { "type": "Point", "coordinates": [ 8.914031982421877, 45.546995468561725 ] } } ] } The Parco del Roccolo is a local park of interest to more than one municipality and it is located between the rivers Olona and Ticino in the northern part of the Po Valley, in a north-western area in the province of Milan, on the southern edge of the Altomilanese. The park includes wooded and agricultural areas in the municipalities of Arluno, Busto Garolfo, Canegrate, Casorezzo (where the park headquarters are located), Nerviano (since 1997) and Parabiago, with a surface of 1595 hectares (about 16 km²). The park takes its name from a technique once used in bird trapping, now considered illegal, the Roccolo: an oval clearing in which stood a three-storey tower camouflaged among the vegetation. It was established in 1991 for the safeguard of the natural elements of the area and for the enhancement of agriculture, which involves about 80% of the surface of the park, with the cultivation of corn, wheat, oats, barley, soybeans and fodder. Of the remaining land area, 9% is characterized by forests, while 1% by roads, quarries and the Villoresi canal with its network of secondary irrigation canals. Another characteristic of the park is the presence of numerous farmhouses scattered throughout its territory, witnesses to the historical agricultural past of the area. Recognized in 1994 as an agricultural park of supra-municipal interest by the Lombardy Region, it is currently being extended to the WWF Oasis of the Vanzago woods. History The Roccolo Park was born from the debris transported by the Olona and Ticino rivers from the alpine valleys. 15,000 years ago during the last phase of the glaciation, the temperature rose creating a colony of birch and conifer forests. The postglacial period is distinguished by the presence of broadleaf trees interrupted by streams. Later, our ancestors began to modify the landscape thanks to agro-pastoral activity in the Po Valley. Habitat Agricoltural fields As already mentioned, the cultivated areas constitute the majority of the park's territory. Among the elements that make up the flora of this type of environment, in addition to the cultivated species, you can find cornflower, chamomile and poppy. As for the animal species present, there are foxes, hares, pheasants, hedgehogs, thrushes, larks and voles. Wooded areas The second living element of the Roccolo is the bush. The wooded flora is represented by plants existing in the area for the most part only since the 19th century: ailanthus, robinia, late cherry and red oak. Only in the Woods of Arluno and Brughierezza (between Casorezzo and Busto Garolfo), you can still admire plants native to the Po Valley such as oak, lily of the valley, Solomon's seal and periwinkle. These areas are the natural
https://en.wikipedia.org/wiki/Michael%20%28footballer%2C%20born%201999%29	Michael Rangel dos Santos de Almeida (born 27 May 1999), commonly known as Michael, is a Brazilian footballer who currently plays as a defender for Bnei Yehuda. Career statistics Club Notes References External links 1999 births Living people Brazilian men's footballers Brazil men's under-20 international footballers Men's association football defenders Israeli Premier League players CR Flamengo footballers Bnei Yehuda Tel Aviv F.C. players Brazilian expatriate men's footballers Brazilian expatriate sportspeople in Israel Expatriate men's footballers in Israel Footballers from Rio de Janeiro (city)
https://en.wikipedia.org/wiki/Marcelinho%20%28footballer%2C%20born%202002%29	Marcelo José de Lima Filho (born 11 December 2002), commonly known as Marcelinho, is a Brazilian footballer who currently plays as a forward for Cruzeiro. Career statistics Club Notes References 2002 births Living people Brazilian men's footballers Men's association football forwards Campeonato Brasileiro Série A players Atlético Clube Goianiense players Sociedade Esportiva Palmeiras players
https://en.wikipedia.org/wiki/Jiuzhang	Jiuzhang may refer to: Jiuzhang suanshu, or The Nine Chapters on the Mathematical Art, Chinese mathematics book, composed from the 10th–2nd century BCE Shu shu Jiuzhang, or Mathematical Treatise in Nine Sections, 13th century Chinese mathematical text by Qin Jiushao Jiu Zhang, collection of poems attributed to Qu Yuan Nine Chapter Law, or Jiuzhang Lü, law of the Han dynasty Jiuzhang (quantum computer), a model quantum computer developed by University of Science and Technology of China See also Zhao Jiuzhang
https://en.wikipedia.org/wiki/Park%20Sang-hyeok	Park Sang-hyeok (; born 20 April 1998) is a South Korean footballer currently playing as a midfielder for Suwon Bluewings. Career statistics Club Notes References 1998 births Living people South Korean men's footballers Korea University alumni Men's association football midfielders K League 1 players Suwon Samsung Bluewings players Footballers from Seoul
https://en.wikipedia.org/wiki/List%20of%20Columbus%20Crew%20records%20and%20statistics	The Columbus Crew is an American professional soccer team based in Columbus, Ohio, that competes in Major League Soccer (MLS). This is a list of club records for Columbus, which dates from their inaugural season in 1996 to present. Honors Individual Club Awards MLS Fair Play Award (6): 1997, 1999, 2004, 2007, 2016, 2021 Player records Appearances Bold denotes players still playing for the club. † Includes MLS is Back Tournament knockout round. Goals Bold denotes players still playing for the club. † Includes MLS is Back Tournament knockout round. Assists Bold denotes players still playing for the club. Shutouts Bold denotes players still playing for the club. Coaching records Trophies International results By competition By club (Includes: CONCACAF Giants Cup, CONCACAF Champions Cup, Campeones Cup, and Leagues Cup) By nation (Includes: CONCACAF Giants Cup, CONCACAF Champions Cup, Campeones Cup, and Leagues Cup) By season Transfers As per MLS rules and regulations; some transfer fees have been undisclosed and are not included in the tables below. Highest transfer fees paid Highest transfer fees received References Columbus Crew Columbus Crew records and statistics Columbus Crew
https://en.wikipedia.org/wiki/Nashrul%20Amin	Nashrul Amin (born 17 June 1997) is a Singaporean footballer who plays as a Winger for Tanjong Pagar United FC in the Singapore Premier League. Career statistics Club Notes References Living people 1997 births Singaporean men's footballers Men's association football midfielders Tanjong Pagar United FC players Singapore Premier League players
https://en.wikipedia.org/wiki/Argentina%20national%20football%20team%20results%20%281920%E2%80%931939%29	This page details the match results and statistics of the Argentina national football team from 1920 to 1939. Key Key to matches Att.=Match attendance (H)=Home ground (A)=Away ground (N)=Neutral ground Key to record by opponent Pld=Games played W=Games won D=Games drawn L=Games lost GF=Goals for GA=Goals against Results Argentina's score is shown first in each case. Notes Record by opponent References Argentina national football team results
https://en.wikipedia.org/wiki/Point%20Processes	Point Processes is a book on the mathematics of point processes, randomly located sets of points on the real line or in other geometric spaces. It was written by David Cox and Valerie Isham, and published in 1980 by Chapman & Hall in their Monographs on Applied Probability and Statistics book series. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Topics Although Point Processes covers some of the general theory of point processes, that is not its main focus, and it avoids any discussion of statistical inference involving these processes. Instead, its aim is to present the properties and descriptions of several specific processes arising in applications of this theory, which had not been previously collected in texts in this area. Three of its six chapters concern more general material, while the final three are more specific. The first chapter includes introductory material on standard processes: Poisson point processes, renewal processes, self-exciting processes, and doubly stochastic processes. The second chapter provides some general theory including stationarity, orderliness (meaning that the probability of multiple arrivals in short intervals is sublinear in the interval length), Palm distributions, Fourier analysis, and probability-generating functions. Chapter four (the third of the more general chapters) concerns point process operations, methods of modifying or combining point processes to generate other processes. Chapter three, the first of the three chapters on more specific models, is titled "Special models". The special models that it covers include non-stationary Poisson processes, compound Poisson processes, and the Moran process, along with additional treatment of doubly stochastic processes and renewal processes. Until this point, the book focuses on point processes on the real line (possibly also with a time dimension), but the two final chapters concern multivariate processes and on point processes for higher dimensional spaces, including spatio-temporal processes and Gibbs point processes. Audience and reception The book is primarily a reference for researchers. It could also be used to provide additional examples for a course on stochastic processes, or as the basis for an advanced seminar. Although it uses relatively little advanced mathematics, readers are expected to understand advanced calculus and have some familiarity with probability theory and Markov chains. Writing some ten years after its original publication, reviewer Fergus Daly of The Open University writes that his copy has been well used, and that it "still is a very good book: lucid, relevant and still not matched in its approach by any other text". References Mathematics books 1980 non-fiction books Point processes
https://en.wikipedia.org/wiki/The%20Geometry%20of%20Numbers	The Geometry of Numbers is a book on the geometry of numbers, an area of mathematics in which the geometry of lattices, repeating sets of points in the plane or higher dimensions, is used to derive results in number theory. It was written by Carl D. Olds, Anneli Cahn Lax, and Giuliana Davidoff, and published by the Mathematical Association of America in 2000 as volume 41 of their Anneli Lax New Mathematical Library book series. Authorship and publication history The Geometry of Numbers is based on a book manuscript that Carl D. Olds, a New Zealand-born mathematician working in California at San Jose State University, was still writing when he died in 1979. Anneli Cahn Lax, the editor of the New Mathematical Library of the Mathematical Association of America, took up the task of editing it, but it remained unfinished when she died in 1999. Finally, Giuliana Davidoff took over the project, and saw it through to publication in 2000. Topics The Geometry of Numbers is relatively short, and is divided into two parts. The first part applies number theory to the geometry of lattices, and the second applies results on lattices to number theory. Topics in the first part include the relation between the maximum distance between parallel lines that are not separated by any point of a lattice and the slope of the lines, Pick's theorem relating the area of a lattice polygon to the number of lattice points it contains, and the Gauss circle problem of counting lattice points in a circle centered at the origin of the plane. The second part begins with Minkowski's theorem, that centrally symmetric convex sets of large enough area (or volume in higher dimensions) necessarily contain a nonzero lattice point. It applies this to Diophantine approximation, the problem of accurately approximating one or more irrational numbers by rational numbers. After another chapter on the linear transformations of lattices, the book studies the problem of finding the smallest nonzero values of quadratic forms, and Lagrange's four-square theorem, the theorem that every non-negative integer can be represented as a sum of four squares of integers. The final two chapters concern Blichfeldt's theorem, that bounded planar regions with area can be translated to cover at least lattice points, and additional results in Diophantine approximation. The chapters on Minkowski's theorem and Blichfeldt's theorem, particularly, have been called the "foundation stones" of the book by reviewer Philip J. Davis. An appendix by Peter Lax concerns the Gaussian integers. A second appendix concerns lattice-based methods for packing problems including circle packing and, in higher dimensions, sphere packing. The book closes with biographies of Hermann Minkowski and Hans Frederick Blichfeldt. Audience and reception The Geometry of Numbers is intended for secondary-school and undergraduate mathematics students, although it may be too advanced for the secondary-school students; it contains exercises maki
https://en.wikipedia.org/wiki/Anne-Sophie%20Kaloghiros	Anne-Sophie Kaloghiros is a mathematics researcher in algebraic geometry and senior lecturer in Mathematics at Brunel University London. Kaloghiros was awarded the London Mathematical Society (LMS) Emmy Noether Fellowship in 2020. Professional career Kaloghiros earned her BA in pure mathematics (honours) from the Université d’Orsay, Paris XI in 2001, a Degree of the Ecole Centrale Paris in 2003, and a Certificate of Advanced Studies in Mathematics, Part III (Distinction) at Queens’ College, University of Cambridge in 2003 as well. Kaloghiros earned her PhD in Algebraic Geometry from University of Cambridge in 2007. Her dissertation, The Topology of Terminal Quartic 3-Folds, was supervised by Alessio Corti. She was a junior research fellow, Trinity Hall, University of Cambridge 2007-2011, a postdoctoral fellow, University of Cambridge in 2011, and research associate, Imperial College London 2012-2014. She has held visiting and postdoctoral positions at the Mathematical Sciences Research Institute (MSRI, Berkeley) in 2009 and 2019, at the Research Institute for Mathematical Sciences (RIMS, Kyoto University) 2009-2010, University of Illinois at Chicago in 2011, and the Hausdorff Research Institute for Mathematics (HIM, Bonn, Germany) in 2014. She is currently a senior lecturer in Maths/Op at Brunel University London. She is an expert on algebraic geometry and birational geometry. She serves on the London Mathematical Society Mentoring African Research in Mathematics (MARM) board. Awards and honors Kaloghiros received the Brunel Athena Swan Award for 2017-2018. In 2020, she was awarded the London Mathematical Society (LMS) Emmy Noether Fellowship. Her research has been funded by the Heilbronn Institute for Mathematical Research, the Engineering and Physical Sciences Research Council (EPSRCP), the London Mathematical Society, Edinburgh Mathematical Society, and Glasgow Mathematical Journal Trust. References External links Home page 21st-century French mathematicians Living people Alumni of the University of Cambridge Date of birth missing (living people) Nationality missing Year of birth missing (living people)
https://en.wikipedia.org/wiki/Corestriction	In mathematics, a corestriction of a function is a notion analogous to the notion of a restriction of a function. The duality prefix co- here denotes that while the restriction changes the domain to a subset, the corestriction changes the codomain to a subset. However, the notions are not categorically dual. Given any subset we can consider the corresponding inclusion of sets as a function. Then for any function , the restriction of a function onto can be defined as the composition . Analogously, for an inclusion the corestriction of onto is the unique function such that there is a decomposition . The corestriction exists if and only if contains the image of . In particular, the corestriction onto the image always exists and it is sometimes simply called the corestriction of . More generally, one can consider corestriction of a morphism in general categories with images. The term is well known in category theory, while rarely used in print. Andreotti introduces the above notion under the name coastriction, while the name corestriction reserves to the notion categorically dual to the notion of a restriction. Namely, if is a surjection of sets (that is a quotient map) then Andreotti considers the composition , which surely always exists. References Set theory Functions and mappings Category theory Hopf algebras Abelian group theory Mathematics articles needing expert attention
https://en.wikipedia.org/wiki/Vitaly%20Khonik	Khonik Vitaly Alexandrovich (Russian: Хоник Виталий Александрович; born 17 December 1955) is a Russian physicist, doctor of physics and mathematics, professor, head of a laboratory researching the physics of non-crystalline materials, and head of the Department of General Physics at Voronezh State Pedagogical University (VSPU). He was born in Kemerovo, USSR. His laboratory collaborates with the Institute of Solid State Physics of the Russian Academy of Sciences, the Institute of Physics of the Slovak Academy of Sciences, the Institut für Materialphysik in Germany and the School of Mechanics and Civil Architecture of Northwestern Polytechical University in China. Education, academic degrees and titles 1994 - Professor 1992 - Doctor of Science (physics & mathematics), focusing on solid state physics 1991 - Senior researcher in solid state physics 1983 - Candidate for a doctoral degree in solid state physics 1978 - Graduated from Voronezh Polytechnic Institute (VPI), majoring in solid state physics Employment history 2010 to present - Head of the Department of General Physics at VSPU 1992 to 2010 - Professor at VSPU 1992 - Associate professor at VSPU 1991-1992 - Associate professor at VPI 1985-1991 - Senior researcher at VPI 1984-1985 - Junior researcher at VPI 1981-1983 - Doctoral student at VPI 1978-1981 - Engineer and physicist at VPI Academic awards Awarded the title "Soros Professor" in 1997, 1998 and 1999. Honored Worker in Higher Professional Education (2011). International experience July 2019 - Visiting professor at Northwestern Polytechical University, Xi'an, China July 2018 - Visiting professor at Northwestern Polytechical University, Xi'an, China October 2016 - Visiting professor at the Institute of Physics, Chinese Academy of Sciences, Beijing, China August 2012 - Visiting professor at the department of physics, University of Illinois at Urbana-Champaign, USA May 2009 - Guest professor at the school of materials science, Harbin Institute of Technology, China April 2007 – Guest professor at Roskilde University, Denmark January 2007 to February 2007 – Visiting scholar at the physics department, University of Illinois at Urbana-Champaign, USA January 2006 to March 2006 – Scholar of the Japanese Society for the Promotion of Science (JSPS) at the graduate school of natural science and technology of Kanazawa University, Japan January 2005 to February 2005 – Visiting scholar at the physics department, University of Illinois at Urbana-Champaign, USA April 2003 to August 2003 – Visiting scholar at the physics department, University of Illinois at Urbana-Champaign, USA October 2002 to December 2002 – Scholar of the German Service for Academic Exchanges (DAAD), Technical University Carolo-Wilhelmina, Braunschweig, Germany May 1999 to April 2000 – Associate professor of the mechanical system engineering department, Kanazawa University, Kanazawa, Japan Visiting professor at the Institute of Experimental Phys
https://en.wikipedia.org/wiki/Biorthogonal%20nearly%20coiflet%20basis	In applied mathematics, biorthogonal nearly coiflet bases are wavelet bases proposed by Lowell L. Winger. The wavelet is based on biorthogonal coiflet wavelet bases, but sacrifices its regularity to increase the filter's bandwidth, which might lead to better image compression performance. Motivation Nowadays, a large amount of information is stored, processed, and delivered, so the method of data compressing — especially for images — becomes more significant. Since wavelet transforms can deal with signals in both space and frequency domains, they compensate for the deficiency of Fourier transforms and emerged as a potential technique for image processing. Traditional wavelet filter design prefers filters with high regularity and smoothness to perform image compression. Coiflets are such a kind of filter which emphasizes the vanishing moments of both the wavelet and scaling function, and can be achieved by maximizing the total number of vanishing moments and distributing them between the analysis and synthesis low pass filters. The property of vanishing moments enables the wavelet series of the signal to be a sparse presentation, which is the reason why wavelets can be applied for image compression. Besides orthogonal filter banks, biorthogonal wavelets with maximized vanishing moments have also been proposed. However, regularity and smoothness are not sufficient for excellent image compression. Common filter banks prefer filters with high regularity, flat passbands and stopbands, and a narrow transition zone, while Pixstream Incorporated proposed filters with wider passband by sacrificing their regularity and passband flatness. Theory The biorthogonal wavelet base contains two wavelet functions, and its couple wavelet , while relates to the lowpass analysis filter and the high pass analysis filter . Similarly, relates to the lowpass synthesis filter and the high pass synthesis filter . For biorthogonal wavelet base, and are orthogonal; Likewise, and are orthogonal, too. In order to construct a biorthogonal nearly coiflet base, the Pixstream Incorporated begins with the (max flat) biorthogonal coiflet base. Decomposing and reconstructing low-pass filters expressed by Bernstein polynomials ensures that the coefficients of filters are symmetric, which benefits the image processing: If the phase of real-valued function is symmetry, than the function has generalized linear phase, and since the human eyes are sensitive to symmetrical error, wavelet base with linear phase is better for image processing application. Recall that the Bernstein polynomials are defined as below: which can be considered as a polynomial f(x) over the interval . Besides, the Bernstein form of a general polynomial is expressed by where d(i) are the Bernstein coefficients. Note that the number of zeros in Bernstein coefficients determines the vanishing moments of wavelet functions. By sacrificing a zero of the Bernstein-basis filter at (which sacrifices i
https://en.wikipedia.org/wiki/Blichfeldt%27s%20theorem	Blichfeldt's theorem is a mathematical theorem in the geometry of numbers, stating that whenever a bounded set in the Euclidean plane has area , it can be translated so that it includes at least points of the integer lattice. Equivalently, every bounded set of area contains a set of points whose coordinates all differ by integers. This theorem can be generalized to other lattices and to higher dimensions, and can be interpreted as a continuous version of the pigeonhole principle. It is named after Danish-American mathematician Hans Frederick Blichfeldt, who published it in 1914. Some sources call it Blichfeldt's principle or Blichfeldt's lemma. Statement and proof The theorem can be stated most simply for points in the Euclidean plane, and for the integer lattice in the plane. For this version of the theorem, let be any measurable set, let denote its area, and round this number up to the next integer value, . Then Blichfeldt's theorem states that can be translated so that its translated copy contains at least points with integer coordinates. The basic idea of the proof is to cut into pieces according to the squares of the integer lattice, and to translate each of those pieces by an integer amount so that it lies within the unit square having the origin as its lower right corner. This translation may cause some pieces of the unit square to be covered more than once, but if the combined area of the translated pieces is counted with multiplicity it remains unchanged, equal to . On the other hand, if the whole unit square were covered with multiplicity its area would be , less than . Therefore, some point of the unit square must be covered with multiplicity at least . A translation that takes to the origin will also take all of the points of that covered to integer points, which is what was required. More generally, the theorem applies to -dimensional sets , with -dimensional volume , and to an arbitrary -dimensional lattice (a set of points in -dimensional space that do not all lie in any lower dimensional subspace, are separated from each other by some minimum distance, and can be combined by adding or subtracting their coordinates to produce other points in the same set). Just as the integer lattice divides the plane into squares, an arbitrary lattice divides its space into fundamental regions (called parallelotopes) with the property that any one of these regions can be translated onto any other of them by adding the coordinates of a unique lattice point. If is the -dimensional volume of one of parallelotopes, then Blichfeldt's theorem states that can be translated to include at least points of . The proof is as before: cut up by parallelotopes, translate the pieces by translation vectors in onto a single parallelotope without changing the total volume (counted with multiplicity), observe that there must be a point of multiplicity at least , and use a translation that takes to the origin. Instead of asking for a transla
https://en.wikipedia.org/wiki/Kirsten%20Flipkens%20career%20statistics	This is a list of the main career statistics of professional Belgian tennis player Kirsten Flipkens. Performance timelines Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records. Singles Doubles Mixed doubles Significant finals Grand Slam tournaments Mixed doubles: 1 (runner-up) WTA career finals Singles: 4 (1 title, 3 runner-ups) Doubles: 15 (7 titles, 8 runner–ups) WTA 125 finals Singles: 1 (title) ITF Circuit finals Singles: 25 (13 titles, 12 runner–ups) Doubles: 2 (2 titles) WTA Tour career earnings As of 29 August 2022 {\|cellpadding=3 cellspacing=0 border=1 style=border:#aaa;solid:1px;border-collapse:collapse;text-align:center; \|-style=background:#eee;font-weight:bold \|width="90"\|Year \|width="100"\|Grand Slam <br/ >titles'\|width="100"\|WTA <br/ >titles \|width="100"\|Total <br/ >titles \|width="120"\|Earnings ($) \|width="100"\|Money list rank \|- \|2009 \|0 \|0 \|0 \| align="right" \|185,953 \| 97 \|- \|2010 \|0 \|0 \|0 \| align="right" \|202,216 \| 91 \|- \|2011 \|0 \|0 \|0 \| align="right" \|n/a \| n/a \|- \|2012 \|0 \|1 \|1 \| align="right" \|n/a \| n/a \|- \|2013 \|0 \|0 \|0 \| align="right" \|1,144,247 \| 20 \|- \|2014 \|0 \|0 \|0 \| align="right" \|553,201 \|48 \|- \|2015 \|0 \|0 \|0 \| align="right" \|307,927 \|105 \|- \|2016 \|0 \|1 \|1 \| align="right" \|392,045 \|86 \|- \|2017 \|0 \|1 \|1 \| align="right" \|515,984 \|69 \|- \|2018 \|0 \|2 \|2 \| align="right" \|643,250 \|59 \|- \|2019 \|0 \|1 \|1 \| style="text-align:right" \|702,391 \|58 \|- \|2020 \|0 \|0 \|0 \| align="right" \|325,900 \|71 \|- \|2021 \|0 \|0 \|0 \| style="text-align:right" \|147,651 \|198 \|- \|2022 \|0 \|0 \|0 \| style="text-align:right" \|401,437 \|86 \|- style="font-weight:bold;" \|Career \|0 \|6 \|6 \| align="right" \|6,036,281 \| 107 \|} Head-to-head Record against top 10 playersFlipkens's record against players who have been ranked in the top 10. Active players are in boldface.'' Top 10 wins Notes References Flipkens, Kirsten
https://en.wikipedia.org/wiki/Maria%20Sakkari%20career%20statistics	This is a list of the main career statistics of professional Greek tennis player Maria Sakkari. Sakkari has won one singles title on the WTA Tour at the Morocco Open in 2019. She also has two WTA 1000 finals, both achieved in 2022; the Indian Wells Open and Guadalajara Open. In 2021, she reached her first Grand Slam semifinal at the French Open. In the same year later, she reached semifinals of the US Open as well. Sakkari finished season of 2021 playing at the year-end WTA Finals, becoming the first Greek female player to accomplish that. After passing group stage, she lost to Anett Kontaveit in the semifinals. In September 2021, right after reaching US Open semifinals, Sakkari made her debut into the top 10, becoming the first Greek female player to achieve that milestone. One year later, in March 2022, she achieved a career-high singles ranking of world No. 3, in March 2022. Performance timelines P = postponed Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records. Singles Current through the 2023 US Open. Doubles Current after the 2023 United Cup against Belgium. WTA 1000 finals Singles: 3 (1 title, 2 runner-ups) WTA Tour career finals Sakkari debuted on the WTA Tour in 2015 at the US Open as a qualifier. Since then, she has won one singles title and reached an additional seven singles finals. Singles: 9 (2 titles, 7 runner-ups) ITF Circuit finals Sakkari debuted on the ITF Women's World Tennis Tour in 2010 at Mytilene in her homeland Greece. In singles, she has been in 17 finals and won seven of them, while in doubles she has been in nine finals and won five of them. Her biggest title on the ITF Circuit was the $75k Dubai Tennis Challenge in the doubles draw in November 2015. Singles: 17 (7 titles, 10 runner–ups) Doubles: 9 (5 titles, 4 runner–ups) WTA Tour career earnings Correct through the 2022 Emilia-Romagna Open Career Grand Slam statistics Seedings The tournaments won by Sakkari are in boldface, and advanced into finals by Sakkari are in italics. Best Grand Slam results details Grand Slam winners are in boldface, and runner–ups in italics. Head-to-head records Record against top 10 players She has a record against players who were, at the time the match was played, ranked in the top 10. Double bagel matches (6–0, 6–0) Notes References Sakkari, Maria
https://en.wikipedia.org/wiki/Lesia%20Tsurenko%20career%20statistics	This is a list of the main career statistics of professional Ukrainian tennis player Lesia Tsurenko. Performance timelines Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records. Singles Current after the 2023 US Open. Doubles WTA Tour finals Singles: 6 (4 titles, 2 runner-ups) ITF finals Singles: 13 (6 titles, 7 runner–ups) Doubles: 16 (8 titles, 8 runner–ups) Best Grand Slam tournament results details Grand Slam winners are in boldface, and runner–ups are in italics. Record against other players Record against top 10 players Active players are in boldface. Top-10 wins Notes References Tsurenko, Lesia
https://en.wikipedia.org/wiki/Kate%C5%99ina%20Siniakov%C3%A1%20career%20statistics	This is a list of the main career statistics of professional Czech tennis player Kateřina Siniaková. To date, Siniaková has won five singles and twenty-three doubles titles on the WTA Tour, including seven Grand Slam titles: Australian Open (2022, 2023), French Open (2018, 2021), Wimbledon Championships (2018, 2022) and US Open (2022). All these big achievements she made alongside countrymate Barbora Krejčíková. By winning the 2022 US Open, she collected all grand slams ("Career Grand Slam"). In the same time, she achieved "Career Golden Slam" and "Career Super Slam", thanks to previously winning gold at the 2020 Summer Tokyo Olympics and 2021 WTA Finals. Achieving all of this alongside Krejčíková, they became the second women's pair (and the third and fourth women overall, after Gigi Fernández and Pam Shriver) to complete this goal. Beside Grand Slam success, in doubles she also won the WTA Finals in 2021, two WTA 1000 titles (one Mandatory - the Madrid Open in 2021 and one non-Mandatory - the Canadian Open in 2019. Despite having less success in singles, she still left her mark. Her most significant results are two quarterfinals at the China Open and Wuhan Open in 2018. At Grand Slam tournaments, she reached the round of 16 at the 2019 French Open, where she also defeated world No. 1, Naomi Osaka, to make her biggest win so far. She also became the No. 1 doubles player on 22 October 2018, while she achieved a career-high singles ranking of world No. 31 on the same day. Performance timelines Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup and Olympic Games are included in win–loss records. Singles Current through the 2023 Jiangxi Open. Doubles Current after the 2023 China Open. Mixed doubles Grand Slam finals Doubles: 9 (7 titles, 2 runner-ups) Other significant finals Olympic finals Doubles: 1 (gold medal) WTA Finals finals Doubles: 3 (1 title, 2 runner-ups) WTA 1000 finals Doubles: 6 (3 titles, 3 runner-ups) WTA Tour finals Singles: 10 (5 titles, 5 runner-ups) Doubles: 39 (23 titles, 16 runner-ups) WTA Challenger finals Doubles: 1 (title) ITF Circuit finals Singles: 9 (8 titles, 1 runner–up) Doubles: 7 (4 titles, 3 runner–ups) Junior Grand Slam finals Girls' singles: 1 (runner–up) Girls' doubles: 3 (3 titles) WTA Tour career earnings Current through the 2023 Canadian Open. {\|cellpadding=3 cellspacing=0 border=1 style=border:#aaa;solid:1px;border-collapse:collapse;text-align:center; \|-style=background:#eee;font-weight:bold \|width="90"\|Year \|width="100"\|Grand Slam <br/ >titles\|width="100"\|WTA <br/ >titles \|width="100"\|Total <br/ >titles \|width="120"\|Earnings ($) \|width="100"\|Money list rank \|- \|2014 \|0 \|1 \|1 \| align="right" \|145,519 \|148 \|- \|2015 \|0 \|1 \|1 \| align="right" \|358,870 \|86 \|- \|2016 \|0 \|0 \|0 \| align="right" \|611,431 \|55 \|- \|2017 \|0 \|2 \|2 \| align="right" \|1,072,694 \|35 \|- \|2018 \|2 \|0 \|2 \| align="right" \|2,063,611 \| 18 \|- \|2019 \|0 \|3 \|3 \| align="right" \|1,350,132 \|29 \|- \|2020
https://en.wikipedia.org/wiki/Karol%C3%ADna%20Muchov%C3%A1%20career%20statistics	This is a list of the main career statistics of professional Czech tennis player Karolína Muchová. Despite only winning one WTA Tour level tournament, she is recognized due to her successful Grand Slam performances. Her biggest one was at the 2023 French Open, where she was advanced to the final but lost to world No. 1 Iga Świątek. At the 2021 Australian Open, she shocked world No. 1 Ashleigh Barty to reach semifinals. Two years later, she came to the another Grand Slam semifinals but this time at the US Open. Along with that, she has two back-to-back quarterfinals at Wimbledon Championships (2019 and 2021). In the late August 2023, she made her debut into the top 10 on the WTA Rankings after reaching final of the WTA 1000 Cincinnati Open. Performance timelines Only main-draw results in WTA Tour, Grand Slam, Fed Cup/Billie Jean King Cup, Hopman Cup, United Cup and Olympic Games are included in win–loss records. Singles Current after the 2023 US Open. Doubles Current after the 2023 US Open. Significant finals Grand Slam finals Singles: 1 (1 runner-up) WTA 1000 finals Singles: 1 (runner-up) WTA Tour finals Singles: 4 (1 title, 3 runners-up) Note: Tournaments sourced from official WTA archives ITF Circuit finals Singles: 10 (2 titles, 8 runner–ups) Doubles: 3 (1 title, 2 runner–ups) Note: Tournaments sourced from official ITF archives Billie Jean King Cup participation Singles: 3 (2–1) Doubles: 2 (1–1) WTA Tour career earnings Current after the 2023 US Open. {\|cellpadding=3 cellspacing=0 border=1 style=border:#aaa;solid:1px;border-collapse:collapse;text-align:center; \|-style=background:#eee;font-weight:bold \|width="90"\|Year \|width="100"\|Grand Slam <br/ > singles titles\|width="100"\|WTA <br/ > singles titles \|width="100"\|Total <br/ > singles titles \|width="120"\|Earnings ($) \|width="100"\|Money list rank \|- \|2014 \|0 \|0 \|0 \|align=right\|3,700 \|800 \|- \|2015 \|0 \|0 \|0 \| align="right" \|7,470 \|596 \|- \|2016 \|0 \|0 \|0 \| align="right" \|26,507 \|326 \|- \|2017 \|0 \|0 \|0 \| align="right" \|19,788 \|407 \|- \|2018 \|0 \|0 \|0 \| align="right" \|197,041 \| 161 \|- \|2019 \|0 \|1 \|1 \| align="right" \|1,155,524 \|36 \|- \|2020 \|0 \|0 \|0 \| align="right" \|493,478 \|42 \|- \|2021 \|0 \|0 \|0 \| align="right" \|1,351,039 \|21 \|- \|2022 \|0 \|0 \|0 \|align=right\|443,949 \|112 \|- \|2023 \|0 \|0 \|0 \|align=right\|2,804,438 \|bgcolor=eee8aa\|7 \|- style="font-weight:bold" \|Career \|0 \|1 \|1 \|align=right\|6,509,545 \|107 \|} Career Grand Slam statistics Grand Slam seedings The tournaments won by Muchová are in boldface, and advanced into finals by Muchová are in italics. Best Grand Slam results details Grand Slam winners are in boldface', and runner–ups are in italics.'' Record against other players No. 1 wins Record against top 10 players She has a 11–15 () record against players who were, at the time the match was played, ranked in the top 10. Notes References Muchová, Karolína
https://en.wikipedia.org/wiki/Knots%20Unravelled	Knots Unravelled: From String to Mathematics is a book on the mathematics of knots, intended for schoolchildren and other non-mathematicians. It was written by mathematician Meike Akveld and mathematics publisher Andrew Jobbings, and published in 2011 by Arbelos, Jobbings's firm. Topics The main problem studied in the book is the use of knot invariants to test whether a loop is knotted or distinguish knots from each other. It has seven short chapters, separated by "interludes" providing examples including Celtic knots, knotted papercraft, neckties, ropework, torus knots, and a form of the trefoil knot that can only sit on a plane with two points in contact. Small exercises, called "tasks" and often involving practical experiments rather than mathematical calculation, are scattered throughout the book, with answers at the end. The first chapter is introductory, and the second describes knot diagrams and the Reidemeister moves that change one diagram to another without changing the underlying knot. The next three chapters discuss particular knot invariants. These begin with the crossing number of a knot, the minimum number of crossings in its diagrams. Chapter four discusses another invariant, the unknotting number, the minimum number of local changes to a diagram that can unknot a given knot, while also discussing chirality (the phenomenon of a knot being different from its mirror image) and composite knots. Chapter five covers tricolorability, an invariant defined by coloring the arcs of a diagram according to certain rules. Chapter six generalizes the problem from knots to links, systems of more than two loops that cannot be separated from each other. The final chapter, necessarily more mathematical than the others, is on the Jones polynomial. Other material in the book includes historical asides, pointers to research topics, many illustrations, and an appendix with a table of small knots. Audience and reception This book is unusual among books on knot theory, an advanced mathematical subject, in being written for laypeople and schoolchildren, with no equations and little calculation. Knot theorist Scott Taylor describes it as "filled with delightful mathematical ideas", an ideal way to attract bored students to mathematics, and Jeff Johannes describes it as "my new favourite for introducing knot theory to non-mathematicians". However, reviewer Roger Fenn suggests that, for use in secondary-school mathematics classes, the section giving solutions to the tasks needs expansion. References Popular mathematics books 2011 non-fiction books Knot theory
https://en.wikipedia.org/wiki/Jennifer%20Brady%20career%20statistics	This is a list of the main career statistics of professional American tennis player Jennifer Brady. Performance timelines Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records. Singles Current through the 2023 US Open. Doubles Significant finals Grand Slam tournaments Singles: 1 (runner-up) WTA career finals Singles: 2 (1 title, 1 runner-up) Doubles: 1 (1 title) WTA 125 tournament finals Singles: 1 (runner-up) Doubles: 1 (runner-up) ITF Circuit finals Singles: 6 (4 titles, 2 runner–ups) Doubles: 5 (5 titles) WTA Tour career earnings As of 1 November 2021 Career Grand Slam statistics Grand Slam seedings The tournaments won by Brady are in boldface, and advanced into finals by Brady are in italics. Head-to-head-records Record against top 10 players Brady's record against players who have been ranked in the top 10. Active players are in boldface. No. 1 wins Top 10 wins Notes References Brady, Jennifer
https://en.wikipedia.org/wiki/1971%E2%80%9372%20Rochdale%20A.F.C.%20season	The 1971–72 season saw Rochdale compete for their 3rd consecutive season in the Football League Third Division. Statistics \|} Final League Table Competitions Football League Third Division F.A. Cup League Cup Lancashire Cup Rose Bowl References Rochdale A.F.C. seasons Rochdale
https://en.wikipedia.org/wiki/Meike%20Akveld	Meike Maria Elisabeth Akveld is a Swiss mathematician and textbook author, whose professional interests include knot theory, symplectic geometry, and mathematics education. She is a tenured senior scientist and lecturer in the mathematics and teacher education group in the Department of Mathematics at ETH Zurich. She is also the organizer of the Mathematical Kangaroo competitions in Switzerland, and president of the Association Kangourou sans Frontières, a French-based international society devoted to the popularization of mathematics. Education Akveld earned a bachelor's degree from the University of Warwick and took Part III of the Mathematical Tripos at the University of Cambridge. She completed her Ph.D. at ETH Zurich in 2000, with the dissertation Hofer geometry for Lagrangian loops, a Legendrian knot and a travelling wave jointly supervised by Dietmar Salamon and Leonid Polterovich. Books Akveld's mathematics books include: Canonical metrics in Kähler geometry (by Tian Gang, based on notes taken by Akveld, Birkhäuser, 2000) Knoten in der Mathematik: Ein Spiel mit Schnüren, Bildern und Formeln (Knots in mathematics: A game with strings, pictures and formulas, in German, Orell Füssli, 2007) Hofer geometry for Lagrangian loops: And a Legendrian Knot and a travelling wave (VDM Verlag, 2008) Integrieren - do it yourself (in German, with Ursula Eisler and Daniel Zogg, Orell Füssli, 2010) Knots Unravelled: From String to Mathematics (with Andrew Jobbings, Arbelos, 2011) Analysis I and Analysis II (in German, with René Sperb, VDF Hochschulverlag, 2012 and 2015) Knopen in de wiskunde (Knots in mathematics, in Dutch, with Ab van der Roest, Epsilon Uitgaven, 2015) Mathe mit dem Känguru 5: Die schönsten Aufgaben von 2015 bis 2019 (Math with the kangaroo 5: The most beautiful problems from 2015 to 2019, in German, with Alexander Unger, Monika Noack, and , Hanser Verlag, 2019) References External links Home page Year of birth missing (living people) Living people Swiss mathematicians Swiss women mathematicians Alumni of the University of Warwick Alumni of the University of Cambridge ETH Zurich alumni Academic staff of ETH Zurich Mathematics educators Topologists
https://en.wikipedia.org/wiki/Zsolt%20Venczel	Zsolt Venczel (born 25 November 2002) is a Hungarian professional footballer who plays for Kápolnásnyék. Career statistics . References 2002 births Footballers from Budapest Living people Hungarian men's footballers Men's association football defenders Budafoki MTE footballers Nemzeti Bajnokság I players
https://en.wikipedia.org/wiki/Neda%20Bokan	Neda Bokan (born 1947) is a Serbian mathematician specializing in differential geometry. Education and career Bokan joined the Mathematical Institute of the Serbian Academy of Sciences and Arts as an assistant in 1969, began working at the University of Belgrade in 1971, and completed a Ph.D. there in 1979, with a dissertation on transformation groups of almost-contact manifolds supervised by Mileva Prvanović. She eventually became full professor at the University of Belgrade, served as dean of mathematics from 1998 to 2001 and again from 2003 to 2007, and was vice rector for education from 2006 to 2012. She also worked as a full professor at the State University of Novi Pazar from 2012 to 2015. She was president of the National Entity for Accreditation and Quality Assurance in Higher Education until stepping down from that position in 2019. She is the author of ten textbooks, and in 2013 became editor-in-chief of the journal Matematički Vesnik, the journal of the Mathematical Society of Serbia. References 1947 births Living people Serbian mathematicians Women mathematicians Differential geometers University of Belgrade alumni Academic staff of the University of Belgrade
https://en.wikipedia.org/wiki/Argentina%20national%20football%20team%20results%20%281940%E2%80%931959%29	This page details the match results and statistics of the Argentina national football team from 1940 to 1959. Key Key to matches Att.=Match attendance (H)=Home ground (A)=Away ground (N)=Neutral ground Key to record by opponent Pld=Games played W=Games won D=Games drawn L=Games lost GF=Goals for GA=Goals against Results Argentina's score is shown first in each case. Notes Record by opponent References Argentina national football team results
https://en.wikipedia.org/wiki/Abelian%202-group	In mathematics, an Abelian 2-group is a higher dimensional analogue of an Abelian group, in the sense of higher algebra, which were originally introduced by Alexander Grothendieck while studying abstract structures surrounding Abelian varieties and Picard groups. More concretely, they are given by groupoids which have a bifunctor which acts formally like the addition an Abelian group. Namely, the bifunctor has a notion of commutativity, associativity, and an identity structure. Although this seems like a rather lofty and abstract structure, there are several (very concrete) examples of Abelian 2-groups. In fact, some of which provide prototypes for more complex examples of higher algebraic structures, such as Abelian n-groups. Definition An Abelian 2-group is a groupoid with a bifunctor and natural transformationswhich satisfy a host of axioms ensuring these transformations behave similarly to commutativity () and associativity for an Abelian group. One of the motivating examples of such a category comes from the Picard category of line bundles on a scheme (see below). Examples Picard category For a scheme or variety , there is an Abelian 2-group whose objects are line bundles and morphisms are given by isomorphisms of line bundles. Notice over a given line bundle since the only automorphisms of a line bundle are given by a non-vanishing function on . The additive structure is given by the tensor product on the line bundles. This makes is more clear why there should be natural transformations instead of equality of functors. For example, we only have an isomorphism of line bundlesbut not direct equality. This isomorphism is independent of the line bundles chosen and are functorial hence they give the natural transformationswitching the components. The associativity similarly follows from the associativity of tensor products of line bundles. Two term chain complexes Another source for Picard categories is from two-term chain complexes of Abelian groupswhich have a canonical groupoid structure associated to them. We can write the set of objects as the abelian group and the set of arrows as the set . Then, the source morphism of an arrow is the projection mapand the target morphism isNotice this definition implies the automorphism group of any object is . Notice that if we repeat this construction for sheaves of abelian groups over a site (or topological space), we get a sheaf of Abelian 2-groups. It could be conjectured if this can be used to construct all such categories, but this is not the case. In fact, this construction must be generalized to spectra to give a precise generalization pg 88. Example of Abelian 2-group in algebraic geometry One example is the Cotangent complex for a local complete intersection scheme which is given by the two-term complexfor an embedding . There is a direct categorical interpretation of this Abelian 2-group from deformation theory using the Exalcomm category. Note that in addition to us
https://en.wikipedia.org/wiki/Koya%20Handa	is a Japanese footballer currently playing as a forward for Verspah Oita in JFL, on loan from Blaublitz Akita. Career statistics Club . Notes Honours Blaublitz Akita J3 League (1): 2020 References External links 1998 births Living people Association football people from Akita Prefecture Japanese men's footballers Men's association football forwards Sapporo University alumni J2 League players J3 League players Japan Football League players Blaublitz Akita players Verspah Oita players
https://en.wikipedia.org/wiki/Primality%20Testing%20for%20Beginners	Primality Testing for Beginners is an undergraduate-level mathematics book on primality tests, methods for testing whether a given number is a prime number, centered on the AKS primality test, the first method to solve this problem in polynomial time. It was written by Lasse Rempe-Gillen and Rebecca Waldecker, and originally published in German as Primzahltests für Einsteiger: Zahlentheorie, Algorithmik, Kryptographie (Vieweg+Teubner, 2009). It was translated into English as Primality Testing for Beginners and published in 2014 by the American Mathematical Society, as volume 70 of their Student Mathematical Library book series. A second German-language edition was publisher by Springer in 2016. Topics Primality Testing for Beginners has six chapters, divided into two parts: four chapters on background material in number theory and computational complexity theory, and three on the AKS primality test. Chapter 1 includes basic material on number theory, including the fundamental theorem of arithmetic on unique factorization into primes, the binomial theorem, the Euclidean algorithm for greatest common divisors, and the sieve of Eratosthenes for generating the sequence of prime numbers. Chapter 2 begins the study of algorithms and their complexity, including algorithms for basic computations in arithmetic, the notion of computability, polynomial-time algorithms, randomization, and nondeterministic polynomial time. In randomized algorithms, it introduces the distinction between Las Vegas algorithms that always return the correct answer after a random amount of time (such as quicksort) and Monte Carlo algorithms for which there is a small probability of getting a wrong answer (exemplified by algorithms based on the Schwartz–Zippel lemma for polynomial identity testing). Chapter 3 provides additional material in number theory, including the Chinese remainder theorem, Fermat's little theorem, and the Fermat primality test based on it. It also introduces calculation with polynomials and with modular arithmetic. The first part of the book concludes with chapter 4, on the history of prime numbers and primality testing, including the prime number theorem (in a weakened form), applications of prime numbers in cryptography, and the widely used Miller–Rabin primality test, which runs in randomized polynomial time. Chapter 5 generalizes Fermat's little theorem from numbers to polynomials, and introduces a randomized primality test based in this generalization. Chapter 6 provides the key mathematical results behind the correctness of the AKS primality test, and chapter 7 describes the test itself. Both the correctness and the polynomial running time of the algorithm are proven rigorously. Exercises are included in each chapter, and a section at the end of the book provides answers to some of them. Another appendix lists some unsolved problems from number theory. Audience and reception Although primarily for undergraduate students of mathematics, Primality Tes
https://en.wikipedia.org/wiki/2020%20Saint-Barthelemy%20Championships	The 2020 Saint Barthélemy Championships are the 17th season of the competition. Per obtained statistics, the competitions began sometime in early to mid 2020, and as of 17 November 2020, about 7 matches have been played. It is unclear how the COVID-19 pandemic affected the competition. The competitions are broken into several mini cups and tournament. The only known competition that was played during the season was the 2020 edition of the Trophée José da Silva, or the Coupe de Noël. Clubs Eight clubs participated in the season. Arawak Arawak Veterans ASPSB ASPSB Féminines ASPSB Veterans Diables Rouges Gustavia FWI Trophée José da Silva Group stage References Saint Barthélemy football competitions Saint Barthélemy Championships Ligue
https://en.wikipedia.org/wiki/Carol%20Schumacher	Carol Smith Schumacher (born 1960) is a Bolivian-born American mathematician specializing in real analysis, a mathematics educator, and a textbook author. She is a professor of mathematics at Kenyon College, and vice president of the Mathematical Association of America. Early life and education Schumacher was born in La Paz, Bolivia as the daughter of missionaries, and grew up in Bolivia speaking both English and Spanish. She majored in mathematics at Hendrix College in Conway, Arkansas, and graduated with honors in 1982. It was in freshman calculus at Hendrix that she met her husband, physicist and quantum information theorist Benjamin Schumacher. She went to the University of Texas at Austin for graduate study, and completed her Ph.D. in 1989 with a dissertation on the theory of Banach spaces, jointly supervised by Edward Odell and Haskell Rosenthal. Career and contributions Schumacher joined Kenyon College as Dana Assistant Professor in 1988, has been full professor there since 2002, and has been department chair for several terms. She was elected vice president of the Mathematical Association of America for the 2018–2020 term. Schumacher is the author of two inquiry-based learning textbooks: Chapter Zero: Fundamental Notions of Abstract Mathematics, on the transition to proofs (Addison-Wesley, 1996; 2nd edition, 2001) and Closer and Closer: Introducing Real Analysis, on real analysis (Jones and Bartlett, 2008). Recognition Kenyon College gave Schumacher their Senior Trustee Teaching Excellence Award in 2005. She was the 2017 winner of the Distinguished Teaching Award of the Ohio Section of the Mathematical Association of America. References External links Home page 1960 births Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians American textbook writers Mathematics educators Bolivian emigrants to the United States Bolivian scientists Bolivian women scientists Women textbook writers Writers from La Paz Hendrix College alumni University of Texas at Austin alumni Kenyon College faculty 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Lucio%20Barroca	Lucio Fernando Barroca (born 30 May 1993) is an Argentine professional footballer who plays as an attacking midfielder. Career statistics References External links 1993 births Living people Men's association football midfielders Argentine men's footballers People from Tres Arroyos Argentine expatriate men's footballers Expatriate men's footballers in Costa Rica Argentine expatriate sportspeople in Costa Rica Expatriate men's footballers in Nicaragua Argentine expatriate sportspeople in Nicaragua Huracán de Tres Arroyos footballers Bella Vista de Bahía Blanca footballers Huracán de Comodoro Rivadavia footballers Club Atlético Los Andes footballers Real Estelí FC players Torneo Argentino A players Torneo Argentino B players Primera Nacional players Liga FPD players Nicaraguan Primera División players Footballers from Buenos Aires Province
https://en.wikipedia.org/wiki/Pedro%20Perlaza	Pedro Pablo Perlaza Caicedo (born 3 February 1991) is an Ecuadorian footballer who plays for S.D. Aucas. Club career He began his career with Juventus in 2009. Career statistics Honours Aucas Ecuadorian Serie A: 2022 Delfín Ecuadorian Serie A: 2019 LDU Quito Supercopa Ecuador: 2020, 2021 References External links 1991 births Living people Men's association football midfielders Ecuadorian men's footballers Ecuadorian Serie A players C.D. Quevedo footballers C.S.D. Macará footballers L.D.U. Portoviejo footballers Delfín S.C. footballers L.D.U. Quito footballers Ecuador men's international footballers Footballers from Esmeraldas, Ecuador
https://en.wikipedia.org/wiki/M%C3%A1ri%C3%B3%20Zeke	Márió Zeke (born 1 September 2000) is a Hungarian football defender who plays for Kecskemét. Club career Zeke joined Kecskemét on loan for the 2022–23 season. Career statistics As of 19 December 2022 References External links 2000 births Sportspeople from Sopron Footballers from Győr-Moson-Sopron County Living people Hungarian men's footballers Hungary men's youth international footballers Men's association football defenders Győri ETO FC players Fehérvár FC players Gyirmót FC Győr players Budaörsi SC footballers Budafoki MTE footballers Kecskeméti TE players Nemzeti Bajnokság I players Nemzeti Bajnokság II players
https://en.wikipedia.org/wiki/Ahmed%20Abbes	Ahmed Abbes (born 24 May 1970) is a Tunisian-French mathematician and a at the Institut des Hautes Études Scientifiques (IHÉS). He is known for his work in arithmetic geometry. Early life and education Abbes was born on 24 May 1970 in Sfax, Tunisia. Abbes received a bronze medal in 1988 and a silver medal in 1989 at the International Mathematical Olympiad while representing Tunisia. Abbes has both French and Tunisian citizenship. Abbes studied at the École Normale Supérieure from 1990 to 1994 and then received his doctorate from Paris-Sud University in 1995 under the supervision of Lucien Szpiro, with the thesis Théorie d'Arakelov et courbes modulaires on Arakelov theory and modular curves. At Paris-Sud, Michel Raynaud was one of his mentors. Abbes received his habilitation in 2003. Career Abbes was a post-doctoral researcher at the Institut des Hautes Études Scientifiques (IHÉS) from 1995 to 1996 and was also a post-doctoral researcher at the Max Planck Institute for Mathematics in 1996. From 1996 to 2007, he was a Chargé de recherche at the CNRS at Paris-Sud University. From 2007 to 2011, he was a CNRS Director of Research (2nd class) at the University of Rennes 1. In 2011, he moved to the IHÉS where he was a CNRS Director of Research (2nd class) until 2013 and where he has been a CNRS Director of Research (1st class) since 2013. Abbes was an editor for Astérisque from 2010 to 2018 and is the co-editor-in-chief of the Tunisian Journal of Mathematics. Abbes is a Coordinator of the Tunisian Campaign for the Academic and Cultural Boycott of Israel (TACBI). He is also a Secretary of the French Association of Academics for Respect for International Law in Palestine (AURDIP). Research Abbes's research concerns the geometric and cohomological properties of sheaves on manifolds over perfect fields of positive characteristic and p-adic fields. He has worked on a p-adic Simpson correspondence and other topics in p-adic Hodge theory with Michel Gros. Awards In 2005, Abbes was awarded the CNRS Bronze Medal. He is a corresponding member of the Tunisian Academy of Sciences, Letters, and Arts. References External links Tunisian mathematicians Arithmetic geometers People from Sfax 1970 births École Normale Supérieure alumni Paris-Sud University alumni Academic staff of Paris-Sud University Research directors of the French National Centre for Scientific Research Academic staff of the University of Rennes International Mathematical Olympiad participants 20th-century French mathematicians 21st-century French mathematicians French people of Tunisian descent 20th-century Tunisian people 21st-century Tunisian people Members of the Tunisian Academy of Sciences, Letters, and Arts Living people
https://en.wikipedia.org/wiki/Roger%20C.%20Alperin	Roger Charles Alperin (January 8, 1947 – November 21, 2019) was an American mathematician, best known for his work in group theory, including its connections with geometry and topology. He was a professor at the University of Oklahoma and at San Jose State University. Education and career Alperin was born on January 8, 1947, in Cambridge, Massachusetts. He received a bachelor's degree from the University of Chicago, and his PhD from Rice University in 1973. His thesis was supervised by Stephen M. Gersten, and was titled Whitehead Torsion of Finite Abelian Groups. After temporary positions at Brown University, Haverford College, and Washington University in St. Louis, Alperin took a permanent position at the University of Oklahoma in 1978. He was eventually promoted to full professor at the University of Oklahoma, but resigned his position to move to California in 1987. Upon moving to California, he found a position at San Jose State University, which he held until his retirement in 2015. Alperin died on November 21, 2019, at his home in Carlsbad, California. Research Alperin's work on real trees in the 80s (partly joint with Hyman Bass and Kenneth Moss) helped to stimulate interest in these objects, and helped establish them as a basic tool in geometric group theory. Alperin has also done foundational work on the mathematical theory of origami. References External links 1947 births Group theorists Topologists 20th-century American mathematicians 21st-century American mathematicians Rice University alumni University of Oklahoma faculty San Jose State University faculty 2019 deaths Brown University faculty Haverford College faculty Washington University in St. Louis faculty University of Chicago alumni
https://en.wikipedia.org/wiki/Pao-sheng%20Hsu	Pao-sheng Hsu is a mathematics educator, Career Hsu completed her PhD under George Bachman at Polytechnic University (previously the Polytechnic Institute of New York, now the New York University Tandon School of Engineering) in 1975; her dissertation was titled An Application of Compactification: Some Theorems on Maximal Ideals. In 1999, 2000, and 2001, Hsu served in the "Human Rights of Mathematicians" committee of the American Mathematical Society. In 2006, Hsu, mathematician and past Association for Women in Mathematics (AWM) president Suzanne Lenhart and middle school teacher Erica Voolich founded the AWM Teacher Partnership Program. "The goal of the program is to link teachers of mathematics in schools, museums, technical institutes, two-year colleges, and universities with other teachers working in an environment different from their own and with mathematicians working in business, government, and industry." , she is an organizer of the AWM Teacher Partnership, with Suzanne Lenhart and Erica Voolich. She also translated a news article about the discussion "Complexities and Opportunities for Women in Mathematics" at the 2002 International Congress of Mathematicians for the AWM newsletter. With Jacqueline Dewar and Harriet Pollatsek, she edited the volume Mathematics Education: A Spectrum of Work in Mathematical Sciences Departments, which was published by Springer International Publishing on 26 November 2016 as part of the Association for Women in Mathematics series. Awards Hsu was presented with an Association for Women in Mathematics (AWM) Service Award in 2013 "for her role in establishing the Teacher Partnership, long-time service on the [Math] Education Committee which included representing AWM at the CBMS Forum in 2009 and 2010, and service on the AWM Web Task Force (2008–2010)." She was elected a fellow of the Association for Women in Mathematics in the Class of 2019 "for her sustained efforts and achievements as a researcher and leader in mathematics education, especially for AWM; for her building of bridges connecting the communities of mathematicians, mathematics educators, and K–12 teachers; and for her work as a teacher and scholar of mathematics". References Year of birth missing (living people) Living people 20th-century women mathematicians 21st-century women mathematicians Fellows of the Association for Women in Mathematics
https://en.wikipedia.org/wiki/Guido%20Mislin	Guido Mislin (born April 13, 1941 in Basel) is a Swiss mathematician, academic and researcher. He is a Professor Emeritus of Mathematics at ETH Zurich. He is also associated with Ohio State University as a guest at Mathematics Department. Mislin's main area of research is algebraic topology, focusing especially on questions regarding general localization theory, as they occur in the context of homotopy theory. He has also conducted research in the field of cohomology of groups and algebraic K-Theory of group rings. He has published over 90 research articles and several books including Localization of Nilpotent Groups and Spaces and Proper Group Actions and the Baum-Connes Conjecture. Education Mislin completed his undergraduate studies and diploma in Mathematics in 1964 and received his Ph.D. in 1967 from ETH Zūrich. He then moved to U.S. and completed his post-doctoral studies from Cornell University and University of California, Berkeley. Career Following his post-doctoral studies, Mislin was appointed as an assistant professor at the Ohio State University. In 1972, he moved back to Switzerland and joined ETH Zurich as an Associate Professor of Mathematics. He was promoted to Professor of Mathematics in 1979. Mislin headed the Department of Mathematics from 1998 till 2002. He retired in 2006 and was gifted with Guido's Book of Conjectures, which is a collection of short notes written by 91 different authors. Mislin is associated with ETH Zurich as a Professor Emeritus of Mathematics. Research Mislin specializes in algebraic topology, and has conducted research focusing especially on questions regarding general localization theory. He has also worked on cohomology of groups and algebraic K-Theory of group rings. Mislin studied the cohomology of classifying spaces of complex Lie groups and related discrete groups. His work proved that the Generalized Isomorphism Conjecture is equivalent to a Finite Subgroup Conjecture, generalizing earlier results due to Mark Feshbach and John Milnor, without using Becker-Gottlieb transfer. He presented a theorem regarding constructing torsion classes in systemic manner, by using Chern classes of canonical representation. He discussed the results and also proved certain properties regarding the Chern classes of representations of cyclic groups. Mislin authored a paper in 1990s regarding group homomorphisms inducing mod-p cohomology isomorphisms and highlighted the conditions on p in group theoretic terms for p to induce an H'Z/p-isomorphism. He applied the concept of satellites in order to define Tate cohomology groups for an arbitrary group G and G-module M. Mislin focused on Bass conjecture and conducted a study to prove that the Bost Conjecture on the L1-assembly map for discrete groups implies the Bass Conjecture. He reformulated the weak Bass Conjecture as a comparison of ordinary and L2-Lefschetz numbers. Mislin studied and extended the work conducted by several authors on theory of topological loc
https://en.wikipedia.org/wiki/Geometric%20Constructions	Geometric Constructions is a mathematics textbook on constructible numbers, and more generally on using abstract algebra to model the sets of points that can be created through certain types of geometric construction, and using Galois theory to prove limits on the constructions that can be performed. It was written by George E. Martin, and published by Springer-Verlag in 1998 as volume 81 of their Undergraduate Texts in Mathematics book series. Topics Geometric Constructions has ten chapters. The first two discuss straightedge and compass constructions, including many of the constructions from Euclid's Elements, and their algebraic model, the constructible numbers. They also include impossibility results for the classical Greek problems of straightedge and compass construction the impossibility of doubling the cube and trisecting the angle are proved algebraically, while the impossibility of squaring the circle and constructing some regular polygons is mentioned but not proved. The next four chapters study what happens when the use of the compass or straightedge is restricted: by the Mohr–Mascheroni theorem there is no loss in constructibility if one uses only a compass, but a straightedge without a compass has significantly less power, unless an auxiliary circle is provided (the Poncelet–Steiner theorem). These chapters also discuss the restriction of compasses to dividers, tools that can transfer line segments onto equal segments of other lines but cannot be used to find intersections of circles with other curves, or to rusty compasses, compasses that cannot change radius, and they use dividers to construct the Malfatti circles. The final three chapters go beyond the straightedge and compass to other construction tools. A highly restricted form of construction, the "match-stick geometry" of Thomas Rayner Dawson from the 1930s, uses only unit line segments, which can be placed along each other, intersected, or pivoted around one of their endpoints; despite its limited nature, this turns out to be as powerful as straightedge and compass. Chapter 9 considers neusis constructions with a marked ruler, and the final chapter investigates the mathematics of paper folding; the marked ruler and paper folding models are equivalent algebraically, and both allow constructions for angle trisection. As well as the mathematics it describes, Geometric Constructions includes many pieces of historical background, quotations and pointers to source material for additional reading, and solutions and hints to its many exercises. Audience and reception Martin originally intended his book to be a graduate-level textbook for students planning to become mathematics teachers. However, as well as this use, it can also be read by anyone who is interested in the history of geometry and has an undergraduate-level background in abstract algebra, or used as a reference work on the topic of geometric constructions. Reviewer Horst Martini writes that it "conveys joy in the
https://en.wikipedia.org/wiki/Gila%20Hanna	Gila Hanna is a Canadian mathematics educator and philosopher of mathematics whose research interests include the nature and educational role of mathematical proofs, and gender in mathematics education. She is professor emerita in the Department of Curriculum, Teaching and Learning at the University of Toronto, affiliated with the Ontario Institute for Studies in Education, the former director of mathematics education at the Fields Institute, and the founder of the Canadian Journal of Mathematics, Science and Technology Education. Books Hanna is the author of Contact and Communication: An Evaluation of Bilingual Student Exchange Programs (OISE Press, 1980) and Rigorous Proof in Mathematics Education (OISE Press, 1983). Her numerous edited volumes include: Creativity, Thought and Mathematical Proof (edited with Ian Winchester, 1990) Towards Gender Equity in Mathematics Education (1996) Proof Technology in Mathematics Research and Teaching (edited with David Reid and Michael de Villiers, 2019) Recognition Hanna was named a Fields Institute Fellow in 2003. She was the 2020 winner of the Partners in Research Dr. Jonathon Borwein Mathematics Ambassador Award. References External links Home page Living people 20th-century Canadian mathematicians 21st-century Canadian mathematicians 20th-century Canadian philosophers 21st-century Canadian philosophers Canadian women mathematicians Canadian women philosophers Mathematics educators Philosophers of mathematics Year of birth missing (living people) 20th-century Canadian women scientists
https://en.wikipedia.org/wiki/Arthur%20von%20Abramson	Arthur von Abramson (born 3 March 1854) was an Imperial Russian civil engineer. He was born to a Jewish family in Odessa, and was educated at the city's gymnasium. He studied mathematics at the University of Odessa, but left to take a course in civil engineering at the Zurich Polytechnikum, from which he was graduated in 1876. Returning to Russia in 1879, von Abramson passed the state examination at the Russian Imperial Institute of Roads and Communications, and was appointed one of the directors of the Russian state railway at Kiev. He devised, built, and managed the sewer system of Kiev, and constructed the street-railroad of that city. In 1881 he founded and became editor-in-chief of a technical monthly, Inzhener ('The Engineer'). He was appointed president of the local sewer company and director of the Kiev city railroad. Publications Published in English as References 1854 births Year of death unknown ETH Zurich alumni Civil engineers from the Russian Empire Editors from the Russian Empire Odesa Jews Print editors Railway civil engineers People from the Russian Empire in rail transport
https://en.wikipedia.org/wiki/Ir%C3%A8ne%20Waldspurger	Irène Waldspurger is a French mathematician and a researcher at the Research Centre in Mathematics of Decision (CEREMADE) where her research focuses on algorithm to solve phase problems, a class of problem relevant for a large number of imaging techniques used in science and medicine. She is also a professor at Paris Sciences et Lettres University. Education and career Waldspurger competed for France in the 2006 International Mathematical Olympiad, winning a bronze medal. Waldspurger was a student of the prestigious Ecole Normale Superieure, in Paris, France, where she was ranked first at the entrance exam in 2006. She pursued her doctoral research at École Normale Supérieure, working on phase retrieval techniques using wavelet transforms under the supervision of Stephane Mallat, which she completed in 2015. She then joined the Massachusetts Institute of Technology for a postdoctoral fellowship, before returning to France in 2017 to join the French National Centre for Scientific Research. Recognition In 2020, Waldspurger was one of the Peccot Lecturers and Peccot Prize winners of the College de France, and won the CNRS Bronze Medal. References External links Irène Waldspurger French mathematicians French National Centre for Scientific Research awards École Normale Supérieure alumni Living people Year of birth missing (living people)
https://en.wikipedia.org/wiki/Playing%20with%20Infinity	Playing with Infinity: Mathematical Explorations and Excursions is a book in popular mathematics by Hungarian mathematician Rózsa Péter, published in German in 1955 and in English in 1961. Publication history and translations Playing with Infinity was originally written in 1943 by mathematician Rózsa Péter, based on a series of letters Péter had written to a non-mathematical friend, . Because of World War II, it was not published until 1955, in German, under the title Das Spiel mit dem Unendlichen, by Teubner. An English translation by Zoltán Pál Dienes was published in 1961 by G. Bell & Sons in England, and by Simon & Schuster in the US. The English version was reprinted in 1976 by Dover Books, The German version was also reprinted, in 1984, by Verlag Harri Deutsch; the book has also been translated into Polish in 1962, and into Russian in 1967. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Topics Playing with Infinity presents a broad panorama of mathematics for a popular audience. It is divided into three parts, the first of which concerns counting, arithmetic, and connections from numbers to geometry both through visual proofs of results in arithmetic like the sum of finite arithmetic series, and in the other direction through counting problems for geometric objects like the diagonals of polygons. These ideas lead to more advanced topics including Pascal's triangle, the Seven Bridges of Königsberg, the prime number theorem and the sieve of Eratosthenes, and the beginnings of algebra and its use in proving the impossibility of certain straightedge and compass constructions. The second part begins with the power of inverse operations to construct more powerful systems of numbers: negative numbers from subtraction, and rational numbers from division. Later topics in this part include the countability of the rationals, the irrationality of the square root of 2, exponentiation and logarithms, graphs of functions, slopes and areas of curves, and complex numbers. Topics in the third part include non-Euclidean geometry, higher dimensions, mathematical logic, the failings of naive set theory, and Gödel's incompleteness theorems. In keeping with its title, these topics allow Playing with Infinity to introduce many different ways in which ideas of infinity have entered mathematics, in the notions of infinite series and limits in the first part, countability and transcendental numbers in the second, and the introduction of infinite points in projective geometry, higher dimensions, metamathematics, and undecidability in the third. Audience and reception Reviewer Philip Peak writes that the book succeeds in showing readers the joy of mathematics without getting them bogged down in calculations and formulas. On a similar note, Michael Holt recommends the book to mathematics teachers, as a sample of the more conceptual style of mathematics taught in Hunga
https://en.wikipedia.org/wiki/Sami%20Habib%20Beldi	Sami Beldi (; born 23 September 1998), is an Algerian professional footballer who plays as a goalkeeper for Qatar Stars League side Umm Salal. Career statistics Club References External links 1998 births Living people Qatari men's footballers Qatari people of Algerian descent Naturalised citizens of Qatar Men's association football goalkeepers Al-Duhail SC players Umm Salal SC players Qatar Stars League players
https://en.wikipedia.org/wiki/Shephard%20Prize	The Shephard Prize is awarded by the London Mathematical Society to a mathematician or mathematicians for making a contribution to mathematics with a strong intuitive component which can be explained to those with little or no knowledge of university mathematics, though the work itself may involve more advanced ideas. The prize will be awarded in even-numbered years and is the result of a donation made to the Society by Geoffrey Shephard. The Shephard Prize may not be awarded to any person who has received the De Morgan Medal or the Pólya Prize. Winners The winners of the Shephard Prize have been: 2015 Keith Ball 2020 Desmond Higham 2020 Kenneth Falconer 2022 Andrew Lobb See also List of mathematics awards References Awards of the London Mathematical Society
https://en.wikipedia.org/wiki/Peng%20Shuai%20career%20statistics	This is a list of the main career statistics of professional Chinese tennis player Peng Shuai. Performance timelines Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup and Olympic Games are included in win–loss records. Singles Doubles Significant finals Grand Slam tournaments Doubles: 3 (2 titles, 1 runner-up) Year-end championships Doubles: 2 (1 title, 1 runner-up) Premier Mandatory/Premier 5 tournaments Doubles: 11 (8 titles, 3 runner-ups) WTA career finals Singles: 9 (2 titles, 7 runner-ups) Doubles: 32 (23 titles, 9 runner-ups) WTA 125 finals Singles: 3 (2 titles, 1 runner–up) Doubles: 1 (1 title) ITF Circuit finals Singles: 16 (12 titles, 4 runner–ups) Doubles: 6 (3 titles, 3 runner–ups) Head-to-head record Record against top 10 players Peng's record against players who have been ranked in the top 10. Active players are in boldface. Wins over top 10 players References Peng, Shuai
https://en.wikipedia.org/wiki/Topological%20Hochschild%20homology	In mathematics, Topological Hochschild homology is a topological refinement of Hochschild homology which rectifies some technical issues with computations in characteristic . For instance, if we consider the -algebra then but if we consider the ring structure on (as a divided power algebra structure) then there is a significant technical issue: if we set , so , and so on, we have from the resolution of as an algebra over , i.e. This calculation is further elaborated on the Hochschild homology page, but the key point is the pathological behavior of the ring structure on the Hochschild homology of . In contrast, the Topological Hochschild Homology ring has the isomorphism giving a less pathological theory. Moreover, this calculation forms the basis of many other THH calculations, such as for smooth algebras Construction Recall that the Eilenberg–MacLane spectrum can be embed ring objects in the derived category of the integers into ring spectrum over the ring spectrum of the stable homotopy group of spheres. This makes it possible to take a commutative ring and constructing a complex analogous to the Hochschild complex using the monoidal product in ring spectra, namely, acts formally like the derived tensor product over the integers. We define the Topological Hochschild complex of (which could be a commutative differential graded algebra, or just a commutative algebra) as the simplicial complex, pg 33-34 called the Bar complexof spectra (note that the arrows are incorrect because of Wikipedia formatting...). Because simplicial objects in spectra have a realization as a spectrum, we form the spectrumwhich has homotopy groups defining the topological Hochschild homology of the ring object . See also Revisiting THH(F_p) Topological cyclic homology of the integers Homological algebra Algebraic topology
https://en.wikipedia.org/wiki/1945%20in%20Estonia	This article lists events that occurred during 1945 in Estonia. Incumbents Events World War II aftermaths: 282,000 dead people (about 1/4 of population of Estonia). Arrests, nationalization of industry. Guerilla warfare was intensified. About 15,000 men in underground and in the forests (Forest Brothers). Births 21 December – Mari Lill, actress Deaths References 1940s in Estonia Estonia Estonia Years of the 20th century in Estonia
https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Singapore	This article presents official statistics gathered during the COVID-19 pandemic in Singapore. The Ministry of Health of Singapore has been publishing official numbers on a daily basis since the first confirmed case of SARS-CoV-2 virus on 23 January 2020. In their situation reports, the cases are broken down into several categories: imported cases, non-imported community cases, non-imported dormitory cases. Prior to 16 April 2020, MOH had released the data only at the end of the day. However upon discovery of a civil servant leaking information before the official release of data, since 17 April 2020, MOH has been providing a preliminary update of summarised figures at around noon of each day with the details released at the end of the day. Classifying COVID-19 cases Singapore adheres strictly to World Health Organization's case definition for classifying COVID-19 deaths, which does not include non-pneumonia fatalities like those caused by blood or heart issues among COVID-19 patients in its official tally. This was exemplified in three cases which the cause of death was recorded as either ischaemic heart disease or heart attack, and a suicide committed by an Indian migrant worker who was tested positive for the virus. Untraced cases prior to 11 April 2020 Charts The linear plot shows the total number of cases as a function of time (by date) since 23 January 2020, the date of the first reported case in Singapore, while the graph plotted on a logarithmic scale, or a semi-log plot, shows an exponential growth in the number of cases as a straight line on the graph. In the logarithmic scale plot, the slope of the straight line determines the rate of growth of the number of cases, with a steeper slope representing a higher growth rate. The third and fourth plot shows the number of daily new cases and total active cases respectively as reported. Overview Cases per day Active cases per day Recoveries per day Deaths per day Total tests performed The linear plot shows the total number of tests performed as a function of time (by date) from 7 April 2020, the date of the first testing data given in Singapore. Cumulative number of cases, hospitalizations, ICU admissions, recoveries and deaths Notes References 2020 in Singapore 2021 in Singapore COVID-19 pandemic in Singapore COVID-19 COVID-19 Singapore
https://en.wikipedia.org/wiki/1972%E2%80%9373%20Rochdale%20A.F.C.%20season	The 1972–73 season saw Rochdale compete for their 4th consecutive season in the Football League Third Division. Statistics \|} Final League Table Competitions Football League Third Division F.A. Cup League Cup Lancashire Cup Rose Bowl References Rochdale A.F.C. seasons Rochdale
https://en.wikipedia.org/wiki/Yerambam	Yerambam () was an ancient Indian mathematical treatise in the Tamil language. It was among the few ancient Tamil works on mathematics such as the work of Kanakkadhigaram and the manuscripts of Kilvaai and Kulimaattru. The work Yerambam was one of the works in the corpus of ancient Tamil mathematical works, which includes several other works such as Kilaralaabam, Adhisaram, Kalambagam, Thribuvana Thilagam, Kanidha Rathinam, and Sirukanakku. In addition to these, there were two other works for which the name of the author is known: Kanakku Nool by Kaakkai Paadiniyaar and Kanakkadhigaram by Kaarinaayanar. Kaarinaayanar cites Yerambam and the six other works in the ancient corpus as the sources of his work Kanakkadhigaram. Yerambam is also explicitly mentioned by name by Parimelalhagar in his commentary on Thirukkural. According to Devaneya Pavanar, the work is completely lost to modern times. See also Tamil literature References External links Yerambam, Tamil Wiktionary entry Sangam literature Books about mathematics Ancient Indian mathematical works
https://en.wikipedia.org/wiki/List%20of%20Mumbai%20City%20FC%20records%20and%20statistics	Mumbai City Football Club is an Indian professional football club based in Mumbai, Maharashtra. The club was established on 30 August 2014 and began their first competitive season in the Indian Super League a few months later on 2014. Club All time performance record As of 27th August 2023 Season by season record Correct as the end of the 2022–23 season. General Note: When scores are mentioned, score Mumbai City FC are given first. First match: 0–3 (vs ATK, 12 October 2014) First win: 5–0 (vs Pune City, Indian Super League, 18 October 2014) Biggest win (in Indian Super League): 6–1 (vs Kerala Blasters FC, 16 December 2018) 6-1 (vs Odisha FC, 24 February 2021) Biggest loss (in Indian Super League): 0-7 (vs FC Goa, 17 November 2015) Highest scoring draw: 3-3 (vs FC Goa, 8 February 2021 ) 3-3 (vs Hyderabad FC, 9 October 2022) Biggest win (in Super Cup): 2-1 (vs Indian Arrows, 16 March 2018) Biggest loss (in Super Cup): 0–2 (vs Chennaiyin FC, 2019) Biggest win (in Durand Cup): 5-0 (vs Jamshedpur FC, 8 August 2023) Biggest loss (in Durand Cup): 1-3 (vs Mohun Bagan AC, 27 August 2023) Biggest win (in AFC Champions League): 2-1 (vs Al-Quwa Al-Jawiya, 11 April 2022) 1-0 (vs Al-Quwa Al-Jawiya, 26 April 2022) Biggest loss (in AFC Champions League): 0-6 (vs Al Shabab FC), 18 April 2022) Most wins in an ISL season:14 (out of 20 games), during the 2022-23 season Fewest wins in an ISL season:4 (out of 14 games), during the 2014 and 2015 season Most defeats in an ISL season:9 (out of 18 matches), during the 2017-18 season Fewest defeats in an ISL season:2 (out of 20 matches), during the 2022-23 season Most goals scored in an ISL season:54 goals in 20 games, during the 2022-23 season Fewest goals scored in an ISL season:14 goals in 14 games, during the 2014 season Most goals conceded in an ISL season:32 goals in 18 games, during the 2019-20 season Fewest goals conceded in an ISL season:11 goals in 14 games, during the 2014 season Highest goal difference in a single ISL season:+33 in 20 games, during the 2022-23 season Most points in an ISL season:46 in 20 games, during the 2022-23 season Fewest points in an ISL season:16 in 14 games, during the 2014 and 2015 seasons Highest attendance: 28000 (vs Pune City, 18 October 2014) Highest average home attendance in a season :22712 (2015) Team Records League winners (2016) (2020–21) (2022–23) Fewest goals conceded in a season: (11), Mumbai City (2016) (2020-21) Highest Points tally in the Indian Super League (46 Points) (2022-23) (also an ISL record) Quickest League Shield winners in Indian Super League history (18) Games (2022-23) Quickest semi-final qualification in Indian Super League history (15) Games (2020-21) Scored in (28) successive ISL games between 2021–22 and 2022-23 ISL seasons Most no. of goals scored by a team in a single season (54) Goals Mumbai City (2022-23) Most no. of goals scored by Indian players in a single season (25) Goals Mumbai City (2022-23) Most Nu
https://en.wikipedia.org/wiki/Strong%20and%20weak%20sampling	Strong and weak sampling are two sampling approach in Statistics, and are popular in computational cognitive science and language learning. In strong sampling, it is assumed that the data are intentionally generated as positive examples of a concept, while in weak sampling, it is assumed that the data are generated without any restrictions. Formal Definition In strong sampling, we assume observation is randomly sampled from the true hypothesis: In weak sampling, we assume observations randomly sampled and then classified: Consequence: Posterior computation under Weak Sampling Therefore the likelihood for all hypotheses will be "ignored". References External links Lecture 20: Strong vs weak sampling Sampling (statistics)
https://en.wikipedia.org/wiki/Reinhardt%20polygon	In geometry, a Reinhardt polygon is an equilateral polygon inscribed in a Reuleaux polygon. As in the regular polygons, each vertex of a Reinhardt polygon participates in at least one defining pair of the diameter of the polygon. Reinhardt polygons with sides exist, often with multiple forms, whenever is not a power of two. Among all polygons with sides, the Reinhardt polygons have the largest possible perimeter for their diameter, the largest possible width for their diameter, and the largest possible width for their perimeter. They are named after Karl Reinhardt, who studied them in 1922. Definition and construction A Reuleaux polygon is a convex shape with circular-arc sides, each centered on a vertex of the shape and all having the same radius; an example is the Reuleaux triangle. These shapes are curves of constant width. Some Reuleaux polygons have side lengths that are irrational multiples of each other, but if a Reuleaux polygon has sides that can be partitioned into a system of arcs of equal length, then the polygon formed as the convex hull of the endpoints of these arcs is defined as a Reinhardt polygon. Necessarily, the vertices of the underlying Reuleaux polygon are also endpoints of arcs and vertices of the Reinhardt polygon, but the Reinhardt polygon may also have additional vertices, interior to the sides of the Reuleaux polygon. If is a power of two, then it is not possible to form a Reinhardt polygon with sides. If is an odd number, then the regular polygon with sides is a Reinhardt polygon. Any other natural number must have an odd divisor , and a Reinhardt polygon with sides may be formed by subdividing each arc of a regular -sided Reuleaux polygon into smaller arcs. Therefore, the possible numbers of sides of Reinhardt polygons are the polite numbers, numbers that are not powers of two. When is an odd prime number, or two times a prime number, there is only one shape of -sided Reinhardt polygon, but all other values of have Reinhardt polygons with multiple shapes. Dimensions and optimality The diameter pairs of a Reinhardt polygon form many isosceles triangles with the sides of the triangle, with apex angle , from which the dimensions of the polygon may be calculated. If the side length of a Reinhardt polygon is 1, then its perimeter is just . The diameter of the polygon (the longest distance between any two of its points) equals the side length of these isosceles triangles, . The curves of constant width of the polygon (the shortest distance between any two parallel supporting lines) equals the height of this triangle, . These polygons are optimal in three ways: They have the largest possible perimeter among all -sided polygons with their diameter, and the smallest possible diameter among all -sided polygons with their perimeter. They have the largest possible width among all -sided polygons with their diameter, and the smallest possible diameter among all -sided polygons with their width. They have the largest
https://en.wikipedia.org/wiki/Birahim%20Gaye	Birahim Gaye (born 27 February 1994), is a Senegalese footballer who plays as a forward. Career statistics References External links 1994 births Living people Senegalese men's footballers Senegalese expatriate men's footballers Men's association football forwards Diambars FC players Al-Shabab SC (Kuwait) players Al Shahaniya SC players Hassania Agadir players Ligue 1 (Senegal) players Kuwait Premier League players Qatari Second Division players Botola players Expatriate men's footballers in Kuwait Expatriate men's footballers in Qatar Expatriate men's footballers in Morocco Senegalese expatriate sportspeople in Kuwait Senegalese expatriate sportspeople in Qatar Senegalese expatriate sportspeople in Morocco Senegal men's international footballers
https://en.wikipedia.org/wiki/Benjamin%20Breyer	Benjamin N. Breyer is an American urologic surgeon. As a Professor of Urology, Epidemiology, and Biostatistics at the University of California, San Francisco, he specializes in complex urethral and penile reconstruction, male incontinence, male fistula, surgical treatment for erectile dysfunction. Early life and education Breyer completed his Bachelor of Science degree in Cell and Structural Biology from the University of Illinois at Urbana–Champaign and his Medical Degree from the Pritzker School of Medicine. He earned a Master of Science Degree in Clinical Research from the University of California, San Francisco. Career After completing his residency and fellowship at University of California, San Francisco (UCSF), Breyer joined the faculty of Urology in 2011. Breyer’s research focuses on genitourinary reconstruction particularly urethral stricture disease, trauma, sexual medicine, and health disparities. His research has had support from the National Institutes of Health, the Department of Defense and Foundation support. Breyer is a Past President of the Trauma Urologic Reconstructive Network of Surgeons, a collaborative research group focused on genitourinary reconstruction and trauma, Breyer’s research group has published over 300 peer-reviewed papers and scholarly works. In his first year as an assistant professor, he collaborated with Michael Eisenberg to use "Google Insights for Search" to see if the varying popularity of search terms would reflect seasonal and geographic differences in kidney stone prevalence. The following year, Breyer led the largest study looking at major and minor "genitourinary" injuries amongst 142,144 U.S. adults went to emergency rooms from injuries caused by clothing, furniture, tools and toys between 2002 and 2010. He followed up this study in 2019 by using GoFundMe to study the most popular crowdfunding projects on the website. His research team found that cancer patients raise approximately a quarter of their goal of $10,000 using GoFundMe. By 2014, Breyer was appointed chief of urology at San Francisco General Hospital, succeeding Jack W. McAninch, his mentor and fellowship director. In addition to his role as chief, Breyer continued to direct the UCSF male genitourinary reconstruction and trauma surgery fellowship. According to ExpertScape, Breyer is one of the top experts in urethral stricture disease and treatment worldwide. During the COVID-19 pandemic in North America, Breyer was named Residency Program Director and Associate Chair of Education for the Department of Urology. References External links American urologists Pritzker School of Medicine alumni University of California, San Francisco faculty Living people Year of birth missing (living people) University of Illinois College of Liberal Arts and Sciences alumni
https://en.wikipedia.org/wiki/Nedret%20Billor	Nedret Billor is a Turkish statistician known for her work on robust statistics and outlier detection. She is a professor of statistics at Auburn University. Education and career Billor graduated from Ankara University in 1983, and earned a master's degree at Çukurova University in 1985. She completed a Ph.D. in statistics at the University of Sheffield in 1992; her dissertation, Diagnostic Methods in Ridge Regression and Errors-in-variables Model, was supervised by Robert Loynes. She returned to Çukurova University as an assistant professor in 1993 and was promoted to associate professor in 1997 and professor in 2003. In 2014, she moved to her present position at Auburn University. In 2019–2020, she served as chair of the Auburn University Senate. Recognition Billor became an Elected Member of the International Statistical Institute in 2012. References External links Year of birth missing (living people) Living people American statisticians Turkish statisticians Women statisticians Ankara University alumni Çukurova University alumni Alumni of the University of Sheffield Auburn University faculty Elected Members of the International Statistical Institute
https://en.wikipedia.org/wiki/Argentina%20national%20football%20team%20results%20%281960%E2%80%931979%29	This page details the match results and statistics of the Argentina national football team from 1960 to 1979. Key Key to matches Att.=Match attendance (H)=Home ground (A)=Away ground (N)=Neutral ground Key to record by opponent Pld=Games played W=Games won D=Games drawn L=Games lost GF=Goals for GA=Goals against Results Argentina's score is shown first in each case. Notes Record by opponent References Argentina national football team results
https://en.wikipedia.org/wiki/Jimmy%20Cooke	James "Jay" Cooke was an American baseball pitcher in the Negro leagues. He played with the Baltimore Black Sox in 1932. Among available statistics, Cooke had a 2-1 win-loss record with a 4.74 earned run average in 10 games, including a shutout against the Hilldale Club on May 20. References External links and Seamheads Baltimore Black Sox players Year of birth unknown Year of death unknown Baseball pitchers
https://en.wikipedia.org/wiki/Gabriel%20Melo	Gabriel Couto Caetano de Melo (born 23 June 2000), commonly known as Gabriel Melo, is a Brazilian footballer who currently plays for Al Urooba. Career statistics Club Notes References External links 2000 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football wingers UAE Pro League players UAE First Division League players Barra Futebol Clube (SC) players Ittihad Kalba FC players Dibba Al Fujairah FC players Al Urooba Club players Expatriate men's footballers in the United Arab Emirates Brazilian expatriate sportspeople in the United Arab Emirates
https://en.wikipedia.org/wiki/Mohamed%20Awadalla	Mohamed Awadalla (born 16 July 2002) is a Sudanese footballer born in Emirates who currently plays as a forward for Khor Fakkan on loan from Al Ain. Career statistics Club Notes References External links 2002 births Living people Sudanese men's footballers Sudanese expatriate men's footballers Men's association football forwards UAE Pro League players Al Ain FC players Khor Fakkan Club players Expatriate men's footballers in the United Arab Emirates
https://en.wikipedia.org/wiki/Benjamin%20Ayim	Benjamin Ayim (born 19 February 2000) is a Ghanaian footballer who currently plays as a attacking midfielder for Khor Fakkan. Career statistics Club Notes References External links 2000 births Living people Ghanaian men's footballers Ghanaian expatriate men's footballers Men's association football midfielders UAE Pro League players Dreams F.C. (Ghana) players Al Falah FC players Al Dhafra FC players Khor Fakkan Club players Expatriate men's footballers in the United Arab Emirates Ghanaian expatriate sportspeople in the United Arab Emirates
https://en.wikipedia.org/wiki/Representations%20of%20classical%20Lie%20groups	In mathematics, the finite-dimensional representations of the complex classical Lie groups , , , , , can be constructed using the general representation theory of semisimple Lie algebras. The groups , , are indeed simple Lie groups, and their finite-dimensional representations coincide with those of their maximal compact subgroups, respectively , , . In the classification of simple Lie algebras, the corresponding algebras are However, since the complex classical Lie groups are linear groups, their representations are tensor representations. Each irreducible representation is labelled by a Young diagram, which encodes its structure and properties. General linear group, special linear group and unitary group Weyl's construction of tensor representations Let be the defining representation of the general linear group . Tensor representations are the subrepresentations of (these are sometimes called polynomial representations). The irreducible subrepresentations of are the images of by Schur functors associated to partitions of into at most integers, i.e. to Young diagrams of size with . (If then .) Schur functors are defined using Young symmetrizers of the symmetric group , which acts naturally on . We write . The dimensions of these irreducible representations are where is the hook length of the cell in the Young diagram . The first formula for the dimension is a special case of a formula that gives the characters of representations in terms of Schur polynomials, where are the eigenvalues of . The second formula for the dimension is sometimes called Stanley's hook content formula. Examples of tensor representations: General irreducible representations Not all irreducible representations of are tensor representations. In general, irreducible representations of are mixed tensor representations, i.e. subrepresentations of , where is the dual representation of (these are sometimes called rational representations). In the end, the set of irreducible representations of is labeled by non increasing sequences of integers . If , we can associate to the pair of Young tableaux . This shows that irreducible representations of can be labeled by pairs of Young tableaux . Let us denote the irreducible representation of corresponding to the pair or equivalently to the sequence . With these notations, For , denoting the one-dimensional representation in which acts by , . If is large enough that , this gives an explicit description of in terms of a Schur functor. The dimension of where is where . See for an interpretation as a product of n-dependent factors divided by products of hook lengths. Case of the special linear group Two representations of are equivalent as representations of the special linear group if and only if there is such that . For instance, the determinant representation is trivial in , i.e. it is equivalent to . In particular, irreducible representations of can be indexed by
https://en.wikipedia.org/wiki/Mathematics%20in%20India%20%28book%29	Mathematics in India: 500 BCE–1800 CE is a monograph about the history of Indian mathematics. It was written by American historian of mathematics Kim Plofker, and published in 2009 by the Princeton University Press. The Basic Library List Committee of the Mathematical Association of America has classified the book as essential for undergraduate mathematics libraries, their highest rating. Topics Plofker has organized Mathematics in India into nine chapters, roughly chronologically, according to the "mainstream narrative" of Indian chronology in a subject where accurate chronology is difficult and disputed. It covers the mathematics of the entire Indian subcontinent, including the modern areas of Afghanistan, India, and Pakistan, but largely restricts itself to Sanskrit-language sources. Unlike many previous works in this area, it views Indian mathematics as a coherent whole, strongly connected to Indian culture and religion, both influencing and being influenced by the other cultures of the world, rather than as a collection of milestones for measuring relative progress against other cultures. Much of the scholarly work on this subject has been contradictory and contentious, and Plofker is careful to provide evidence for the hypotheses she supports, discuss alternative hypotheses, and view the subject neutrally for itself rather than as a way to boost or put down Indian culture. Her book includes some speculative theories, but is well-grounded in recent scholarship, and focused on evidence from the source material. It carefully maintains a balance between the cultural and scientific context needed to understand the mathematics it describes, the major texts and oral traditions through which that mathematics has come down to us, and the cross-cultural transmission of mathematical knowledge with other cultures. The first introductory chapter provides an overview of Indian history of Indian mathematics and its scholarship, and of the religious and linguistic context of early Sanskrit texts, which leads to important differences from Indian mathematics to other ancient mathematical cultures developing from administrative or scientific works. Chapter two discusses the Vedic period from 1500 to 500 BCE, and the Shulba Sutras, religious instructional texts with significant mathematical content that are generally attributed to this period, although (as the book discusses) the absence of concrete astronomical observations within these texts has made it impossible to date them precisely. Topics from this period include its methods for reckoning time, its fascination with large numbers, the beginnings of decimal numbering and integer factorization, geometric constructions using cords or ropes, the Pythagorean theorem, and accurate approximations to pi and the square root of two. This chapter also includes material on speculative links between Vedic India and ancient Mesopotamia, a pet theory of Plofker's advisor David Pingree, but it notes the weakness of
https://en.wikipedia.org/wiki/Elementary%20Number%20Theory%2C%20Group%20Theory%20and%20Ramanujan%20Graphs	Elementary Number Theory, Group Theory and Ramanujan Graphs is a book in mathematics whose goal is to make the construction of Ramanujan graphs accessible to undergraduate-level mathematics students. In order to do so, it covers several other significant topics in graph theory, number theory, and group theory. It was written by Giuliana Davidoff, Peter Sarnak, and Alain Valette, and published in 2003 by the Cambridge University Press, as volume 55 of the London Mathematical Society Student Texts book series. Background In graph theory, expander graphs are undirected graphs with high connectivity: every small-enough subset of vertices has many edges connecting it to the remaining parts of the graph. Sparse expander graphs have many important applications in computer science, including the development of error correcting codes, the design of sorting networks, and the derandomization of randomized algorithms. For these applications, the graph must be constructed explicitly, rather than merely having its existence proven. One way to show that a graph is an expander is to study the eigenvalues of its adjacency matrix. For an -regular graph, these are real numbers in the interval , and the largest eigenvalue (corresponding to the all-1s eigenvector) is exactly . The spectral expansion of the graph is defined from the difference between the largest and second-largest eigenvalues, the spectral gap, which controls how quickly a random walk on the graph settles to its stable distribution; this gap can be at most . The Ramanujan graphs are defined as the graphs that are optimal from the point of view of spectral expansion: they are -regular graphs whose spectral gap is exactly . Although Ramanujan graphs with high degree, such as the complete graphs, are easy to construct, expander graphs of low degree are needed for the applications of these graphs. Several constructions of low-degree Ramanujan graphs are now known, the first of which were by and . Reviewer Jürgen Elstrod writes that "while the description of these graphs is elementary, the proof that they have the desired properties is not". Elementary Number Theory, Group Theory and Ramanujan Graphs aims to make as much of this theory accessible at an elementary level as possible. Topics Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are large. This provides additional motivation for the construction of Ramanujan graphs, as the ones constructed in the book provide explicit examples of the same phenomenon. This chapter also provides the expected material on spectral graph theory, needed for the definition of Ramanujan graphs. Chapter 2, on number theory, includ
https://en.wikipedia.org/wiki/Walter%20Richard%20Talbot	Walter Richard Talbot (1909-1977) was the fourth African American to earn a Ph.D. in Mathematics (Geometric Group Theory) from the University of Pittsburgh and Lincoln University's youngest Doctor of Philosophy. He was a member of Sigma Xi and Pi Tau Phi. In 1969 Talbot co-founded the National Association of Mathematics (NAM) at Morgan State University, the organization which, nine years later honored him at a memorial luncheon and created a scholarship in his name. In 1990 the Cox-Talbot lecture was inaugurated recognizing his accomplishments together with Elbert Frank Cox – the first African-American to get a doctoral degree in mathematics. Academic positions Talbot held include: Mathematics Department Chair and Professor (Morgan State University); assistant professor, professor, department chair, dean of men, registrar, acting dean of instruction (Lincoln University). Talbot was most widely known for his introduction of computer technology to the school. Talbot's dissertation was entitled Fundamental Regions in S(sub 6) for the Simple Quaternary G(sub 60), Type I. References 1909 births 1977 deaths African-American mathematicians University of Pittsburgh alumni 20th-century African-American scientists
https://en.wikipedia.org/wiki/Ca%C3%ADque%20%28footballer%2C%20born%2018%20July%202000%29	Caíque de Jesus da Silva (born 18 July 2000), commonly known as Caíque , is a Brazilian footballer who currently plays for Dibba Al-Hisn. Career statistics Club Notes References External links 2000 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football forwards UAE Pro League players UAE First Division League players Esporte Clube Jacuipense players Esporte Clube Bahia players Al-Nasr SC (Dubai) players Khor Fakkan Club players Al Urooba Club players Dibba Al-Hisn Sports Club players Expatriate men's footballers in the United Arab Emirates Brazilian expatriate sportspeople in the United Arab Emirates Footballers from Salvador, Bahia
https://en.wikipedia.org/wiki/Issam%20Shaitit	Issam Shaitit (Arabic:عصام سحيتيت) (born 14 February 2000) is a Moroccan footballer who plays as a winger for Al-Hamriyah. Career statistics Club External links References 2000 births Living people Moroccan men's footballers Moroccan expatriate men's footballers Olympique Club de Khouribga players Ajman Club players Emirates Club players Al Hamriyah Club players UAE Pro League players UAE First Division League players Men's association football wingers Expatriate men's footballers in the United Arab Emirates Moroccan expatriate sportspeople in the United Arab Emirates Place of birth missing (living people)
https://en.wikipedia.org/wiki/Darlington%20Igwekali	Darlington Igwekali (born 4 April 2000) is a Nigerian professional footballer who plays as a defender. Career statistics Club References External links 2000 births Living people Nigerian men's footballers Nigerian expatriate men's footballers Alanyaspor footballers FC Olimpik Donetsk players Ajman Club players Fujairah FC players Emirates Club players UAE Pro League players UAE First Division League players Men's association football defenders Expatriate men's footballers in Turkey Expatriate men's footballers in Ukraine Expatriate men's footballers in the United Arab Emirates Nigerian expatriate sportspeople in Turkey Nigerian expatriate sportspeople in Ukraine Nigerian expatriate sportspeople in the United Arab Emirates Place of birth missing (living people)
https://en.wikipedia.org/wiki/Junior%20Hochou	Junior Hochou Hore (born 30 December 2000) is an Ivorian footballer. He currently plays as a defender for Al Taawon. Career statistics Club External links References 2000 births Living people Ivorian men's footballers Ivorian expatriate men's footballers Hatta Club players Al-Taawon (UAE) Club players UAE Pro League players UAE First Division League players Men's association football defenders Expatriate men's footballers in the United Arab Emirates Ivorian expatriate sportspeople in the United Arab Emirates Place of birth missing (living people)
https://en.wikipedia.org/wiki/Hussein%20Faisal	Hussein Faisal Hussein Abdelkader (; born 4 March 1999) is an Egyptian professional footballer who plays as an attacking midfielder for Egyptian League club Smouha Career statistics Club International References External links 1999 births Living people Egyptian men's footballers Egypt men's youth international footballers Men's association football forwards Zamalek SC players Egyptian Premier League players
https://en.wikipedia.org/wiki/Analytics%20%28disambiguation%29	Analytics is the systematic computational analysis of data or statistics. Analytics may also refer to: Analytics (ice hockey), the analysis of the characteristics of hockey players and teams through the use of statistics and other tools Analytics (basketball), analyzing basketball statistics through objective evidence Adobe Analytics, part of Adobe Experience Cloud Google Analytics, a web analytics service offered by Google See also Analytic (disambiguation) Prior Analytics, a treatise by Aristotle Posterior Analytics, a treatise by Aristotle
https://en.wikipedia.org/wiki/Mina%20Ossiander	Mina Egbert Ossiander is an American mathematician specializing in probability theory and central limit theorems. She is a professor of mathematics at Oregon State University, where she also holds an adjunct appointment in statistics. Education and career Ossiander majored in costume and textile design as an undergraduate at the University of Washington, graduating with a B.A. in 1978. She returned to the university for graduate study in statistics in the late 1970s, intending to go into consumer protection, but studying biostatistics as the only statistics program offered there at the time, and earning a master's degree in 1982. Becoming more interested in the mathematical foundations for the statistics she was studying, she completed a Ph.D. at the University of Washington in 1985. Her dissertation, Weak Convergence and a Law of the Iterated Logarithm for Processes Indexed by Points in a Metric Space, was supervised by Ronald Pyke. She came to her faculty position at Oregon State University in 1988 after postdoctoral research at the University of British Columbia, working with Cindy Greenwood, and after visiting positions at the University of Washington and the University of California, San Diego. Personal life Ossiander is the daughter of Frank J. Ossiander and Helen A. Jones; Frank Ossiander was an Oregon State University alumnus who worked as a biometrician for NOAA and for the Alaska Department of Fish and Game. Her middle name, "Egbert", reflects her marriage to Gary Egbert, an oceanography professor at Oregon State University. References External links Home page Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Probability theorists University of Washington alumni Oregon State University faculty 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Abdullah%20Nasser%20%28footballer%2C%20born%201998%29	Abdullah Nasser (; born 20 August 1998), is an Emirati professional footballer who plays as a left back for Al Urooba. Career statistics Club Career statistics References External links 1998 births Living people Emirati men's footballers Men's association football fullbacks Sharjah FC players Fujairah FC players Al-Nasr SC (Dubai) players Al Urooba Club players UAE Pro League players UAE First Division League players
https://en.wikipedia.org/wiki/Khalfan%20Khalid	Khalfan Khalid (; born 14 August 2000) is an Emirati professional footballer who plays as a left back. Career statistics Club References External links 2000 births Living people Emirati men's footballers Men's association football fullbacks Ajman Club players UAE Pro League players
https://en.wikipedia.org/wiki/Zayed%20Sultan	Zayed Sultan (; born 11 April 2001), is an Emirati professional footballer who plays as a right back for UAE Pro League side Al Jazira. Career statistics Club References External links 2001 births Living people Emirati men's footballers Men's association football fullbacks Al Jazira Club players UAE Pro League players
https://en.wikipedia.org/wiki/Mansoor%20Saeed	Mansoor Saeed Abdulla Al-Menhali (; born 29 September 2003) is an Emirati professional footballer who plays as a forward for UAE Pro League side Al-Wahda. Career statistics Club References External links 2003 births Living people Emirati men's footballers Men's association football forwards Al Wahda FC players UAE Pro League players
https://en.wikipedia.org/wiki/Khalid%20Ghuloom	Khalid Ghuloom (; born 18 August 1996) is an Emirati professional footballer who plays as a winger for Al-Hamriyah. Career statistics Club Career statistics References External links 1996 births Living people Emirati men's footballers Men's association football wingers Sharjah FC players Khor Fakkan Club players Al Urooba Club players Fujairah FC players Al Hamriyah Club players UAE Pro League players UAE First Division League players
https://en.wikipedia.org/wiki/Hamdan%20Humaid	Hamdan Humaid (; born 6 November 2002), is an Emirati professional footballer who plays as a midfielder for UAE Pro League side Shabab Al-Ahli. Career statistics Club Career statistics References External links 2002 births Living people Emirati men's footballers Men's association football midfielders Shabab Al Ahli Club players UAE Pro League players
https://en.wikipedia.org/wiki/Trena%20Wilkerson	Trena L. Wilkerson (born 1954) is an American mathematician and mathematics educator. She is a Professor of Mathematics Education in the Department of Curriculum & Instruction at Baylor University, and the president of the National Council of Teachers of Mathematics for the 2020–2022 term. Education and career Wilkerson majored in mathematics at Mississippi College, earned a master's degree in mathematics education from Southeastern Louisiana University, and worked as a high school teacher in Louisiana for 18 years, from 1976 to 1994. Returning to graduate study, she earned a Ph.D. in curriculum and instruction in 1994 at the University of Southern Mississippi, specializing in mathematics education, and became an assistant research professor at Louisiana State University from 1994 to 1999, when she moved to her present position at Baylor. References External links Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Mathematics educators Mississippi College alumni Southeastern Louisiana University alumni University of Southern Mississippi alumni Louisiana State University faculty Baylor University faculty 20th-century American women 21st-century American women 1954 births
https://en.wikipedia.org/wiki/List%20of%20Macarthur%20FC%20records%20and%20statistics	Macarthur Football Club is an Australian professional association football club based in Oran Park, Sydney. The club was formed in 2017 as Macarthur South West United before being renamed as Macarthur FC in 2019. The list encompasses the honours won by Macarthur FC, records set by the club, their managers and their players. The player records section itemises the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Macarthur FC players on the international stage. Attendance records at Campbelltown are also included. Macarthur FC has won one top-flight title that being the Australia Cup in 2022. The club's record appearance maker and record goalscorer is Lachlan Rose who made 71 appearances and scored 15 goals between 2020 and the present day. All figures are correct as of 21 October 2023 Honours Domestic Australia Cup Winners (1): 2022 Player records Appearances Most A-League Men appearances: Lachlan Rose, 64 Youngest first-team player: Rhys Youlley, 18 years, 5 days (against Newcastle Jets, A-League Men, 18 February 2023) Oldest first-team player: Adam Federici, 36 years, 140 days (against Melbourne City, A-League, 20 June 2021) Most consecutive appearances: Al Hassan Toure, 38 (from 1 February 2022 to 20 January 2023) Most appearances Competitive matches only, includes appearances as substitute. Numbers in brackets indicate goals scored. Goalscorers Most goals in a match: Matt Derbyshire, 3 goals (against Adelaide United, A-League, 12 February 2021) Youngest goalscorer: Michael Ruhs, 18 years, 266 days (against Melbourne City, A-League, 24 April 2021) Oldest goalscorer: Mark Milligan, 35 years, 300 days (against Western United, A-League, 31 May 2021) Top goalscorers Lachlan Rose is the all-time top goalscorer for Macarthur FC. Competitive matches only. Numbers in brackets indicate appearances made. International This section refers to caps won while a Macarthur FC player. First capped player: Denis Genreau, for Australia against Chinese Taipei on 7 June 2021. Most capped player: Denis Genreau with 1 cap. Managerial records First full-time manager: Ante Milicic managed Macarthur FC 15 from May 2022 to 8 May 2022 Longest-serving manager: Ante Milicic – 2 years, 358 days (15 May 2019 to 8 May 2022) Highest win percentage: Dwight Yorke, 55.56% Lowest win percentage: Mile Sterjovski, 29.41% Club records Matches Firsts First match: Macarthur South West United 0–4 Central Coast Mariners, friendly, 12 October 2018 First A-League Men match: Western Sydney Wanderers 0–1 Macarthur FC, 30 December 2020 First Australia Cup match: Newcastle Olympic 0–3 Macarthur FC, 13 November 2021 First AFC Cup match: Shan United 0–3 Macarthur FC, 21 September 2023 First competitive match at Campbelltown Stadium: Macarthur FC 0–2 Central Coast Mariners, A-League Men, 3 January 2021 Record wins Record A-League Men win: 4–0 against Adelaide United, 12 F
https://en.wikipedia.org/wiki/Lynda%20Wiest	Lynda R. Wiest is an American mathematics education researcher and professor at the University of Nevada, Reno. Research Wiest investigates mathematics education, educational equity, and teacher education. Education Wiest earned her B.S. degree in 1979 and her M.Ed. degree in 1984, both from Bloomsburg University of Pennsylvania. After teaching elementary and middle school students for eleven years in Pennsylvania, she earned her Ph.D. at Indiana University in 1996. Her Ph.D. advisor was Frank Klein Lester, Jr., and her dissertation title is The Role of Fantasy and Real-World Problem Contexts in Fourth- and Sixth-Grade Students' Mathematical Problem Solving. Career In 1996, Wiest joined the faculty at the University of Nevada, Reno in the College of Education. She earned tenure and was promoted to Associate Professor in 2001, and she was promoted to Professor in 2009. In 1998, Wiest founded the Northern Nevada Girls Math and Technology Program. Awards and honors In 2021, Weist received the Association for Women in Mathematics (AWM) Louise Hay Award for "contribut[ing] impactfully to advancing mathematics education in K-12 across a variety of school settings. She has created innovative courses and summer programs, addressing gender equity and diversity issues." She received the Women in Leadership STEM Award, from the Girl Scouts of the Sierra Nevada in 2015. She earned the F. Donald Tibbitts Distinguished Teacher Award from the University of Nevada, Reno in 2015. She won the Nevada Regent’s Academic Advisor Award (graduate level) in 2003. References Living people 21st-century American mathematicians Women mathematicians American women mathematicians Year of birth missing (living people) Bloomsburg University of Pennsylvania alumni Indiana University alumni University of Nevada, Reno faculty 21st-century American women
https://en.wikipedia.org/wiki/Diane%20Briars	Diane Jane Briars (born 1951) is an American mathematics educator, the former president of both the National Council of Supervisors of Mathematics and the National Council of Teachers of Mathematics. She has been an advocate for the Everyday Mathematics, Connected Mathematics, and Common Core State Standards Initiative mathematics education programs. Education and career Briars majored in mathematics at Northwestern University, graduating in 1973. She has a master's degrees in mathematics and a Ph.D. in mathematics education from Northwestern; the topic of her 1984 doctoral dissertation was Individual Differences in Rule Discovery: An Exploratory Study of the Inductive Reasoning Game Eleusis. She has taught mathematics at the middle school level in Evanston, Illinois, where Northwestern is located. After completing her Ph.D., she was a postdoctoral researcher at Carnegie Mellon University, working there with Jill H. Larkin, and briefly held a position as assistant professor of mathematics education at Northern Illinois University. She joined Pittsburgh Public Schools in 1986 as head of mathematics education. At Pittsburgh, she instituted the Everyday Mathematics program for elementary-school mathematics and the Connected Mathematics program for middle-school mathematics. Her state teaching certifications were brought into question in 2005, as part of a political battle with the school board over the continuation of these two programs, and she was placed on leave from her position in 2006. She stepped down to become a consultant and mathematics education developer, and to co-direct the Algebra Intensification Project of the University of Illinois at Chicago and University of Texas at Austin. She served as president of the National Council of Supervisors of Mathematics from 2009 to 2011, and of the National Council of Teachers of Mathematics from 2014 to 2016. As NCTM president, she advocated for the Common Core State Standards Initiative and used her platform to debunk what she has described as widely-spread falsehoods about the initiative. Book Briars is a coauthor of What Principals Need to Know about Teaching and Learning Mathematics (Solution Tree Press, 2012) and of a teacher guide to the mathematics components of the Common Core State Standards Initiative, Common Core Mathematics in a PLC at Work, Grades 6-8 (Solution Tree Press, 2013). Recognition In 2009 the Pennsylvania Council of Supervisors of Mathematics gave Briars their Outstanding Contributions to Mathematics Supervision award. In 2018 the National Council of Supervisors of Mathematics gave her their Ross Taylor/Glenn Gilbert National Leadership Award. References 1951 births Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Mathematics educators Northwestern University alumni Northern Illinois University faculty 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Briars%20%28surname%29	Briars is a surname. Notable people with the surname include: Diane Briars (born 1951), American mathematics educator Gawain Briars (born 1958), British squash player and lawyer
https://en.wikipedia.org/wiki/Linda%20Gojak	Linda M. Gojak is an American mathematics educator who was president of the National Council of Supervisors of Mathematics and, in 2012–2014, of the National Council of Teachers of Mathematics. Education and career Gojak is a graduate of Miami University. She earned a master's degree in education, specializing in elementary and middle school mathematics, from Kent State University. She was a mathematics teacher for 28 years, and then in 1999 took a position in the Department of Education and Allied Studies at John Carroll University as director of the Center for Mathematics and Science Education, Teaching, and Technology. Books Gojak is the author of books including: What's Your Math Problem!?!: Getting to the Heart of Teaching Problem (Shell Education, 2011) The Common Core Mathematics Companion: The Standards Decoded (with Ruth Harbin Miles, Corwin, 2016) Mathematize It! Going Beyond Key Words to Make Sense of Word Problems (with Kimberly Morrow-Leong and Sara Delano Moore, Corwin, 2020) Recognition The Ohio Council of Teachers of Mathematics has named their annual state-level award for middle school teaching as the Linda M. Gojak Award. References Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Mathematics educators Miami University alumni Kent State University alumni John Carroll University faculty 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/AWM-SIAM%20Sonia%20Kovalevsky%20Lecture	The AWM-SIAM Sonia Kovalevsky Lecture is an award and lecture series that "highlights significant contributions of women to applied or computational mathematics." The Association for Women in Mathematics (AWM) and the Society for Industrial and Applied Mathematics (SIAM) planned the award and lecture series in 2002 and first awarded it in 2003. The lecture is normally given each year at the SIAM Annual Meeting. Award winners receive a signed certificate from the AWM and SIAM presidents. The lectures are named after Sonia Kovalevsky (1850–1891), a well-known Russian mathematician of the late 19th century. Karl Weierstrass regarded Kovalevsky as his most talented student. In 1874, she received her Doctor of Philosophy degree from the University of Göttingen under the supervision of Weierstrass. She was granted privatdozentin status and taught at the University of Stockholm in 1883; she became an ordinary professor (the equivalent of full professor) at this institution in 1889. She was also an editor of the journal Acta Mathematica. Kovalevsky did her important work in the theory of partial differential equations and the rotation of a solid around a fixed point. Recipients The Kovalevky Lecturers have been: 2003 Linda R. Petzold, University of California, Santa Barbara, “Towards the Multiscale Simulation of Biochemical Networks” 2004 Joyce R. McLaughlin, Rensselaer Polytechnic Institute, “Interior Elastodynamics Inverse Problems: Creating Shear Wave Speed Images of Tissue” 2005 Ingrid Daubechies, Princeton University, “Superfast and (Super)sparse Algorithms” 2006 Irene Fonseca, Carnegie Mellon University, “New Challenges in the Calculus of Variations” 2007 Lai-Sang Young, Courant Institute, “Shear-Induced Chaos” 2008 Dianne P. O'Leary, University of Maryland, “A Noisy Adiabatic Theorem: Wilkinson Meets Schrödinger’s Cat” 2009 Andrea Bertozzi, University of California, Los Angeles 2010 Suzanne Lenhart, University of Tennessee at Knoxville, “Mixing it up: Discrete and Continuous Optimal Control for Biological Models” 2011 Susanne C. Brenner, Louisiana State University, “A Cautionary Tale in Numerical PDEs” 2012 Barbara Keyfitz, Ohio State University, “The Role of Characteristics in Conservation Laws” 2013 Margaret Cheney, Colorado State University, “Introduction to Radar Imaging” 2014 Irene M. Gamba, University of Texas at Austin, “The evolution of complex interactions in non-linear kinetic systems” 2015 Linda J. S. Allen, Texas Tech University, “Predicting Population Extinction” 2016 Lisa J. Fauci, Tulane University, “Biofluids of Reproduction: Oscillators, Viscoelastic Networks and Sticky Situations” 2017 Liliana Borcea, University of Michigan, “Mitigating Uncertainty in Inverse Wave Scattering” 2018 Eva Tardos, Cornell University, “Learning and Efficiency of Outcomes in Games” 2019 Catherine Sulem, University of Toronto, “The Dynamics of Ocean Waves” 2020 Bonnie Berger, MIT, “Compressive g
https://en.wikipedia.org/wiki/Combinatorics%3A%20The%20Rota%20Way	Combinatorics: The Rota Way is a mathematics textbook on algebraic combinatorics, based on the lectures and lecture notes of Gian-Carlo Rota in his courses at the Massachusetts Institute of Technology. It was put into book form by Joseph P. S. Kung and Catherine Yan, two of Rota's students, and published in 2009 by the Cambridge University Press in their Cambridge Mathematical Library book series, listing Kung, Rota, and Yan as its authors (ten years posthumously in the case of Rota). The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Topics Combinatorics: The Rota Way has six chapters, densely packed with material: each could be "a basis for a course at the Ph.D. level". Chapter 1, "Sets, functions and relations", also includes material on partially ordered sets, lattice orders, entropy (formulated in terms of partitions of a set), and probability. The topics in Chapter 2, "Matching theory", as well as matchings in graphs, include incidence matrices, submodular set functions, independent matchings in matroids, the Birkhoff–von Neumann theorem on the Birkhoff polytope of doubly stochastic matrices, and the Gale–Ryser theorem on row and column sums of (0,1) matrices. Chapter 3 returns to partially ordered sets and lattices, including material on Möbius functions of incidence algebras, Sperner's theorem on antichains in power sets, special classes of lattices, valuation rings, and Dilworth's theorem on partitions into chains. One of the things Rota became known for, in the 1970s, was the revival of the umbral calculus as a general technique for the formal manipulation of power series and generating functions, and this is the subject of Chapter 4. Other topics in this chapter include Sheffer sequences of polynomials, and the Riemann zeta function and its combinatorial interpretation. Chapter 5 concerns symmetric functions and Rota–Baxter algebras, including symmetric functions over finite fields. Chapter 6, "Determinants, matrices, and polynomials", concludes the book with material including the roots of polynomials, the Grace–Walsh–Szegő theorem, the spectra of totally positive matrices, and invariant theory formulated in terms of the umbral calculus. Each chapter concludes with a discussion of the history of the problems it covers, and pointers to the literature on these problems. Also included at the end of the book are solutions to some of the "exercises" provided at the end of each chapter, each of which could be (and often is) the basis of a research publication, and which connect the material from the chapters to some of its applications. Audience and reception Combinatorics: The Rota Way is too advanced for undergraduates, but could be used as the basis for one or more graduate-level mathematics courses. However, even as a practicing mathematician in combinatorics, reviewer Jennifer Quinn found the book difficult going, despite the many topics of
https://en.wikipedia.org/wiki/Nay%20Moe%20Naing	Nay Moe Naing (born 13 December 1997) is a Burmese professional footballer currently playing as a midfielder for Myanmar National League side Hanthawaddy United. International statistics International goals References 1997 births Living people Burmese men's footballers Myanmar men's international footballers Myanmar National League players Ayeyawady United F.C. players Magwe F.C. players Hantharwady United F.C. players Men's association football midfielders
https://en.wikipedia.org/wiki/Patrick%20Dove	Patrick Dove may refer to: Patrick Edward Dove (1815–1873), Scottish born author of the book The Theory of Human Progression, and Natural Probability of a Reign of Justice Patrick Dove (sea captain) (1896–1957), British merchant navy officer, author of the book I Was Graf Spee's Prisoner
https://en.wikipedia.org/wiki/Braids%2C%20Links%2C%20and%20Mapping%20Class%20Groups	Braids, Links, and Mapping Class Groups is a mathematical monograph on braid groups and their applications in low-dimensional topology. It was written by Joan Birman, based on lecture notes by James W. Cannon, and published in 1974 by the Princeton University Press and University of Tokyo Press, as volume 82 of the book series Annals of Mathematics Studies. Although braid groups had been introduced in 1891 by Adolf Hurwitz and formalized in 1925 by Emil Artin, this was the first book devoted to them. It has been described as a "seminal work", one that "laid the foundations for several new subfields in topology". Topics Braids, Links, and Mapping Class Groups is organized into five chapters and an appendix. The first introductory chapter defines braid groups, configuration spaces, and the use of configuration spaces to define braid groups on arbitrary two-dimensional manifolds. It provides a solution to the word problem for braids, the question of determining whether two different-looking braid presentations really describe the same group element. It also describes the braid groups as automorphism groups of free groups and of multiply-punctured disks. The next three chapters present connections of braid groups to three different areas of mathematics. Chapter 2 concerns applications to knot theory, via Alexander's theorem that every knot or link can be formed by closing off a braid, and provides the first complete proof of the Markov theorem on equivalence of links formed in this way. It also includes material on the conjugacy problem, important in this area because conjugate braids close off to form the same link, and on the "algebraic link problem" (not to be confused with algebraic links) in which one must determine whether two links can be related to each other by finitely many moves of a certain type, equivalent to the homeomorphism of link complements. Chapter 3 concerns representation theory, and includes Fox derivatives and Fox's free differential calculus, the Magnus representation of free groups and the Gassner and Burau representations of braid groups. Chapter 4 concerns the mapping class groups of 2-manifolds, Dehn twists and the Lickorish twist theorem, and plats, braids closed off in a different way than in Alexander's theorem. Chapter 5 is titled "plats and links". It moves from 2-dimensional topology to 3-dimensional topology, and is more speculative, concerning connections between braid groups, 3-manifolds, and the classification of links. It includes also an analog of Alexander's theorem for plats, where the number of strands of the resulting plat turns out to be determined by the bridge number of a given link. The appendix provides a list of 34 open problems. By the time Wilbur Whitten wrote his review, in June 1975, a handful of these had already been solved. Audience and reception This is a book for advanced mathematics students and professionals, who are expected to already be familiar with algebraic topology and presenta

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