| courant institute prize for mathematical talent: Poincare's Prize George G. Szpiro, 2008-07-29 The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. |
| courant institute prize for mathematical talent: The Abel Prize Helge Holden, Ragni Piene, 2009-12-01 The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com . |
| courant institute prize for mathematical talent: Notices of the American Mathematical Society American Mathematical Society, 1994 |
| courant institute prize for mathematical talent: Supersonic Flow and Shock Waves Richard Courant, K.O. Friedrichs, 1999-02-11 Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. However, many aspects make the book just as interesting as a text and a reference today. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it should appeal to engineers, physicists and mathematicians alike. |
| courant institute prize for mathematical talent: Poincare's Prize George G. Szpiro, 2008-07-29 The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. |
| courant institute prize for mathematical talent: How to Appeal for More College Financial Aid Mark Kantrowitz, 2019-01-11 College financial aid is not like negotiating with a car dealership, where bluff and bluster will get you a bigger, better deal. Appealing for more financial aid depends on presenting the college financial aid office with adequate documentation of special circumstances that affect the family's ability to pay for college.This book provides a guide for students and their families on how to appeal for more financial aid for college and how to improve the likelihood of a successful appeal. This book also discusses techniques for increasing eligibility for need-based financial aid and merit aid.The topics covered by this book include corrections, updates, special circumstances, writing an effective financial aid appeal letter, adequate documentation, professional judgment adjustments, unusual circumstances, dependency overrides and the differences between the FAFSA and CSS Profile forms. |
| courant institute prize for mathematical talent: Stochastic Integrals Henry P. McKean, 2024-05-23 This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. —E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications. |
| courant institute prize for mathematical talent: Algorithms, Probability, Networks, and Games Christos Zaroliagis, Grammati Pantziou, Spyros Kontogiannis, 2015-09-07 This Festschrift volume is published in honor of Professor Paul G. Spirakis on the occasion of his 60th birthday. It celebrates his significant contributions to computer science as an eminent, talented, and influential researcher and most visionary thought leader, with a great talent in inspiring and guiding young researchers. The book is a reflection of his main research activities in the fields of algorithms, probability, networks, and games, and contains a biographical sketch as well as essays and research contributions from close collaborators and former PhD students. |
| courant institute prize for mathematical talent: Poincaré's Prize George Szpiro, 2007 With a reclusive and eccentric hero, dramatic turns, and a million-dollar payoff, Poincare's Prize is the stuff of great fiction. Amazingly, the story unveiled in it is true. >In the world of math, the Poincare Conjecture was a holy grail. Decade after decade the theorem that informs how we understand the shape of the universe defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of our time, earning the right to claim the first one-million-dollar Millennium math prize. >George Szpiro begins his masterfully told story in 1904 when Frenchman Henri Poincare formulated a conjecture about a seemingly simple problem. Imagine an ant crawling around on a large surface. How would it know whether the surface is a flat plane, a round sphere, or a bagel- shaped object? The ant would need to lift off into space to observe the object. How could you prove the shape was spherical without actually seeing it? Simply, this is what Poincare sought to solve. |
| courant institute prize for mathematical talent: Engaging Young Students In Mathematics Through Competitions - World Perspectives And Practices: Volume Ii - Mathematics Competitions And How They Relate To Research, Teaching And Motivation Robert Geretschlager, 2020-04-15 The two volumes of 'Engaging Young Students in Mathematics through Competitions' present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume II contains background information on connections between the mathematics of competitions and the organization of such competitions, their interplay with research, teaching and more.It will be of interest to anyone involved with mathematics competitions at any level, be they researchers, competition participants, teachers or theoretical educators.The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018. |
| courant institute prize for mathematical talent: Freshman Calculus Robert A. Bonic, 1971 |
| courant institute prize for mathematical talent: The Probabilistic Method Noga Alon, Joel H. Spencer, 2015-11-02 Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley. |
| courant institute prize for mathematical talent: Newsletter Association for Women in Mathematics (U.S.), 1986 |
| courant institute prize for mathematical talent: A History of Mathematics in the United States and Canada David E. Zitarelli, Della Dumbaugh, Stephen F. Kennedy, 2022-07-28 This is the first truly comprehensive and thorough history of the development of a mathematical community in the United States and Canada. This second volume starts at the turn of the twentieth century with a mathematical community that is firmly established and traces its growth over the next forty years, at the end of which the American mathematical community is pre-eminent in the world. In the preface to the first volume of this work Zitarelli reveals his animating philosophy, I find that the human factor lends life and vitality to any subject. History of mathematics, in the Zitarelli conception, is not just a collection of abstract ideas and their development. It is a community of people and practices joining together to understand, perpetuate, and advance those ideas and each other. Telling the story of mathematics means telling the stories of these people: their accomplishments and triumphs; the institutions and structures they built; their interpersonal and scientific interactions; and their failures and shortcomings. One of the most hopeful developments of the period 19001941 in American mathematics was the opening of the community to previously excluded populations. Increasing numbers of women were welcomed into mathematics, many of whomincluding Anna Pell Wheeler, Olive Hazlett, and Mayme Logsdonare profiled in these pages. Black mathematicians were often systemically excluded during this period, but, in spite of the obstacles, Elbert Frank Cox, Dudley Woodard, David Blackwell, and others built careers of significant accomplishment that are described here. The effect on the substantial community of European immigrants is detailed through the stories of dozens of individuals. In clear and compelling prose Zitarelli, Dumbaugh, and Kennedy spin a tale accessible to experts, general readers, and anyone interested in the history of science in North America. |
| courant institute prize for mathematical talent: Strengthening the Linkages Between the Sciences and the Mathematical Sciences National Research Council, Commission on Physical Sciences, Mathematics, and Applications, Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences, 2000-04-05 Over three hundred years ago, Galileo is reported to have said, The laws of nature are written in the language of mathematics. Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance. To encourage new collaboration between the mathematical sciences and other fields and to sustain present collaboration, the National Research Council (NRC) formed a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. The goal of the committee was to examine the mechanisms for strengthening interdisciplinary research between mathematical sciences and the sciences, with a strong focus on suggesting the most effective mechanisms of collaboration. Strengthening the Linkages Between the Sciences and the Mathematical Sciences provides the findings and recommendations of the committee as well as case studies of cross-discipline collaboration, the workshop agenda, and federal agencies that provide funding for such collaboration. |
| courant institute prize for mathematical talent: Polynomial Methods in Combinatorics Larry Guth, 2016-06-10 This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book. |
| courant institute prize for mathematical talent: The Survival of a Mathematician Steven George Krantz, 2009 One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration. In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide.--BOOK JACKET. |
| courant institute prize for mathematical talent: Courant Constance Reid, 2013-06-05 ...a story of great mathematicians and their achievements, of practical successes and failures, and of human perfidy and generosity...this is one of the still too rare occasions in which mathematicians are shown as frail, flesh-and-blood creatures...a very worthwhile book. -CHOICE |
| courant institute prize for mathematical talent: Information Theory and Stochastics for Multiscale Nonlinear Systems Andrew Majda, Rafail V. Abramov, Marcus J. Grote, 2005 This book introduces mathematicians to the fascinating mathematical interplay between ideas from stochastics and information theory and practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of complex nonlinear systems. After a general discussion, a new elementary model, motivated by issues in climate dynamics, is utilized to develop a self-contained example of stochastic mode reduction. Based on A. Majda's Aisenstadt lectures at the University of Montreal, the book is appropriate for both pure and applied mathematics graduate students, postdocs and faculty, as well as interested researchers in other scientific disciplines. No background in geophysical flows is required. About the authors: Andrew Majda is a member of the National Academy of Sciences and has received numerous honors and awards, including the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the Society of Industrial and Applied Mathematics, the Gibbs Prize of the American Mathematical Society, and the Medal of the College de France. In the past several years at the Courant Institute, Majda and a multi-disciplinary faculty have created the Center for Atmosphere Ocean Science to promote cross-disciplinary research with modern applied mathematics in climate modeling and prediction. R.V. Abramov is a young researcher; he received his PhD in 2002. M. J. Grote received his Ph.D. under Joseph B. Keller at Stanford University in 1995. |
| courant institute prize for mathematical talent: Exterior Differential Systems Robert L. Bryant, S.S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P.A. Griffiths, 2013-06-29 This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object. |
| courant institute prize for mathematical talent: Libertas Mathematica , 1996 |
| courant institute prize for mathematical talent: J-holomorphic Curves and Symplectic Topology Dusa McDuff, Dietmar Salamon, 2012 The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology. |
| courant institute prize for mathematical talent: Methods in Computational Science Johan Hoffman, 2021-10-19 Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory. |
| courant institute prize for mathematical talent: Mind, Modernity, Madness Liah Greenfeld, 2013-04-01 A leading interpreter of modernity argues that our culture of limitless self-fulfillment is making millions mentally ill. Training her analytic eye on manic depression and schizophrenia, Liah Greenfeld, in the culminating volume of her trilogy on nationalism, traces these dysfunctions to society’s overburdening demands for self-realization. |
| courant institute prize for mathematical talent: Predictive Analytics For Dummies Anasse Bari, Mohamed Chaouchi, Tommy Jung, 2014-03-06 Combine business sense, statistics, and computers in a new and intuitive way, thanks to Big Data Predictive analytics is a branch of data mining that helps predict probabilities and trends. Predictive Analytics For Dummies explores the power of predictive analytics and how you can use it to make valuable predictions for your business, or in fields such as advertising, fraud detection, politics, and others. This practical book does not bog you down with loads of mathematical or scientific theory, but instead helps you quickly see how to use the right algorithms and tools to collect and analyze data and apply it to make predictions. Topics include using structured and unstructured data, building models, creating a predictive analysis roadmap, setting realistic goals, budgeting, and much more. Shows readers how to use Big Data and data mining to discover patterns and make predictions for tech-savvy businesses Helps readers see how to shepherd predictive analytics projects through their companies Explains just enough of the science and math, but also focuses on practical issues such as protecting project budgets, making good presentations, and more Covers nuts-and-bolts topics including predictive analytics basics, using structured and unstructured data, data mining, and algorithms and techniques for analyzing data Also covers clustering, association, and statistical models; creating a predictive analytics roadmap; and applying predictions to the web, marketing, finance, health care, and elsewhere Propose, produce, and protect predictive analytics projects through your company with Predictive Analytics For Dummies. |
| courant institute prize for mathematical talent: Archimedes in the 21st Century Chris Rorres, 2017-08-26 This book is a collection of papers presented at the “Archimedes in the 21st Century” world conference, held at the Courant Institute of Mathematical Sciences in 2013. This conference focused on the enduring and continuing influence of Archimedes in our modern world, celebrating his centuries of influence on mathematics, science, and engineering. Archimedes planted the seeds for a myriad of seminal ideas that would grow over the ages. Each chapter surveys the growth of one or more of these seeds, and the fruit that they continue to bear to this day. The conference speakers contributing to this book are actively involved in STEM fields whose origins trace back to Archimedes, many of whom have conducted and published research that extends Archimedes’ work into the 21st century. The speakers are not historians, so while historical context is provided, this book is uniquely focused on the works themselves as opposed to their history. The breadth and depth of Archimedes’ influence will inspire, delight, and even surprise readers from a variety of fields and interests including historians, mathematicians, scientists, and engineers. Only a modest background in math is required to read this book, making it accessible to curious readers of all ages. |
| courant institute prize for mathematical talent: Convex Geometric Analysis Keith M. Ball, Vitali Milman, 1999-01-28 Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999. |
| courant institute prize for mathematical talent: Numerical Methods for Two-Point Boundary-Value Problems Herbert B. Keller, 2018-11-14 Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition. |
| courant institute prize for mathematical talent: Vortices in the Magnetic Ginzburg-Landau Model Etienne Sandier, Sylvia Serfaty, 2008-05-14 This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field. |
| courant institute prize for mathematical talent: Math Bytes Tim P. Chartier, 2014-04-06 An inviting collection of fun, hands-on applications in mathematics and computing This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie's opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson’s method for disproving Fermat’s Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or result--such as Google’s PageRank and the traveling salesman problem--and the applications grow more challenging as you progress through the chapters. But don’t worry, helpful solutions are provided each step of the way. Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Bird--and much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace--a bit and a byte at a time. |
| courant institute prize for mathematical talent: MAA Notes , 1983 |
| courant institute prize for mathematical talent: Domain Decomposition Methods - Algorithms and Theory Andrea Toselli, Olof Widlund, 2006-06-20 This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods. |
| courant institute prize for mathematical talent: Intermediate Algebra James Hall, 1999-07 |
| courant institute prize for mathematical talent: Symmetric Bilinear Forms John Milnor, Dale Husemoller, 2013-04-17 The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper Theorie der quadratischen Formen in beliebigen Körpern. We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts ... |
| courant institute prize for mathematical talent: Elliptic Partial Differential Equations Qing Han, Fanghua Lin, 2011 This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems. |
| courant institute prize for mathematical talent: The Mathematician's Brain David Ruelle, 2007-08-05 Examines mathematical ideas and the visionary minds behind them. This book provides an account of celebrated mathematicians and their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the beauty of their mathematical discoveries. |
| courant institute prize for mathematical talent: Data India , 2007 |
| courant institute prize for mathematical talent: Filtering Complex Turbulent Systems Andrew J. Majda, John Harlim, 2012-02-23 The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems. The book contains background material from filtering, turbulence theory and numerical analysis, making it suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required. |
| courant institute prize for mathematical talent: Mathematicians of the World, Unite! Guillermo Curbera, 2009-02-23 This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int |
| courant institute prize for mathematical talent: The Abel Prize 2008-2012 Helge Holden, Ragni Piene, 2017-04-30 Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners. |
| courant institute prize for mathematical talent.: Poincare's Prize George G. Szpiro, 2008-07-29 The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. |
| courant institute prize for mathematical talent.: The Abel Prize Helge Holden, Ragni Piene, 2009-12-01 The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com . |
| courant institute prize for mathematical talent.: Notices of the American Mathematical Society American Mathematical Society, 1994 |
| courant institute prize for mathematical talent.: Supersonic Flow and Shock Waves Richard Courant, K.O. Friedrichs, 1999-02-11 Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. However, many aspects make the book just as interesting as a text and a reference today. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it should appeal to engineers, physicists and mathematicians alike. |
| courant institute prize for mathematical talent.: Poincare's Prize George G. Szpiro, 2008-07-29 The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius. |
| courant institute prize for mathematical talent.: How to Appeal for More College Financial Aid Mark Kantrowitz, 2019-01-11 College financial aid is not like negotiating with a car dealership, where bluff and bluster will get you a bigger, better deal. Appealing for more financial aid depends on presenting the college financial aid office with adequate documentation of special circumstances that affect the family's ability to pay for college.This book provides a guide for students and their families on how to appeal for more financial aid for college and how to improve the likelihood of a successful appeal. This book also discusses techniques for increasing eligibility for need-based financial aid and merit aid.The topics covered by this book include corrections, updates, special circumstances, writing an effective financial aid appeal letter, adequate documentation, professional judgment adjustments, unusual circumstances, dependency overrides and the differences between the FAFSA and CSS Profile forms. |
| courant institute prize for mathematical talent.: Stochastic Integrals Henry P. McKean, 2024-05-23 This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. —E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications. |
| courant institute prize for mathematical talent.: Algorithms, Probability, Networks, and Games Christos Zaroliagis, Grammati Pantziou, Spyros Kontogiannis, 2015-09-07 This Festschrift volume is published in honor of Professor Paul G. Spirakis on the occasion of his 60th birthday. It celebrates his significant contributions to computer science as an eminent, talented, and influential researcher and most visionary thought leader, with a great talent in inspiring and guiding young researchers. The book is a reflection of his main research activities in the fields of algorithms, probability, networks, and games, and contains a biographical sketch as well as essays and research contributions from close collaborators and former PhD students. |
| courant institute prize for mathematical talent.: Poincaré's Prize George Szpiro, 2007 With a reclusive and eccentric hero, dramatic turns, and a million-dollar payoff, Poincare's Prize is the stuff of great fiction. Amazingly, the story unveiled in it is true. >In the world of math, the Poincare Conjecture was a holy grail. Decade after decade the theorem that informs how we understand the shape of the universe defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of our time, earning the right to claim the first one-million-dollar Millennium math prize. >George Szpiro begins his masterfully told story in 1904 when Frenchman Henri Poincare formulated a conjecture about a seemingly simple problem. Imagine an ant crawling around on a large surface. How would it know whether the surface is a flat plane, a round sphere, or a bagel- shaped object? The ant would need to lift off into space to observe the object. How could you prove the shape was spherical without actually seeing it? Simply, this is what Poincare sought to solve. |
| courant institute prize for mathematical talent.: Engaging Young Students In Mathematics Through Competitions - World Perspectives And Practices: Volume Ii - Mathematics Competitions And How They Relate To Research, Teaching And Motivation Robert Geretschlager, 2020-04-15 The two volumes of 'Engaging Young Students in Mathematics through Competitions' present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment.Volume II contains background information on connections between the mathematics of competitions and the organization of such competitions, their interplay with research, teaching and more.It will be of interest to anyone involved with mathematics competitions at any level, be they researchers, competition participants, teachers or theoretical educators.The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018. |
| courant institute prize for mathematical talent.: Freshman Calculus Robert A. Bonic, 1971 |
| courant institute prize for mathematical talent.: The Probabilistic Method Noga Alon, Joel H. Spencer, 2015-11-02 Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley. |
| courant institute prize for mathematical talent.: Newsletter Association for Women in Mathematics (U.S.), 1986 |
| courant institute prize for mathematical talent.: A History of Mathematics in the United States and Canada David E. Zitarelli, Della Dumbaugh, Stephen F. Kennedy, 2022-07-28 This is the first truly comprehensive and thorough history of the development of a mathematical community in the United States and Canada. This second volume starts at the turn of the twentieth century with a mathematical community that is firmly established and traces its growth over the next forty years, at the end of which the American mathematical community is pre-eminent in the world. In the preface to the first volume of this work Zitarelli reveals his animating philosophy, I find that the human factor lends life and vitality to any subject. History of mathematics, in the Zitarelli conception, is not just a collection of abstract ideas and their development. It is a community of people and practices joining together to understand, perpetuate, and advance those ideas and each other. Telling the story of mathematics means telling the stories of these people: their accomplishments and triumphs; the institutions and structures they built; their interpersonal and scientific interactions; and their failures and shortcomings. One of the most hopeful developments of the period 19001941 in American mathematics was the opening of the community to previously excluded populations. Increasing numbers of women were welcomed into mathematics, many of whomincluding Anna Pell Wheeler, Olive Hazlett, and Mayme Logsdonare profiled in these pages. Black mathematicians were often systemically excluded during this period, but, in spite of the obstacles, Elbert Frank Cox, Dudley Woodard, David Blackwell, and others built careers of significant accomplishment that are described here. The effect on the substantial community of European immigrants is detailed through the stories of dozens of individuals. In clear and compelling prose Zitarelli, Dumbaugh, and Kennedy spin a tale accessible to experts, general readers, and anyone interested in the history of science in North America. |
| courant institute prize for mathematical talent.: Strengthening the Linkages Between the Sciences and the Mathematical Sciences National Research Council, Commission on Physical Sciences, Mathematics, and Applications, Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences, 2000-04-05 Over three hundred years ago, Galileo is reported to have said, The laws of nature are written in the language of mathematics. Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance. To encourage new collaboration between the mathematical sciences and other fields and to sustain present collaboration, the National Research Council (NRC) formed a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. The goal of the committee was to examine the mechanisms for strengthening interdisciplinary research between mathematical sciences and the sciences, with a strong focus on suggesting the most effective mechanisms of collaboration. Strengthening the Linkages Between the Sciences and the Mathematical Sciences provides the findings and recommendations of the committee as well as case studies of cross-discipline collaboration, the workshop agenda, and federal agencies that provide funding for such collaboration. |
| courant institute prize for mathematical talent.: Polynomial Methods in Combinatorics Larry Guth, 2016-06-10 This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book. |
| courant institute prize for mathematical talent.: The Survival of a Mathematician Steven George Krantz, 2009 One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration. In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide.--BOOK JACKET. |
| courant institute prize for mathematical talent.: Courant Constance Reid, 2013-06-05 ...a story of great mathematicians and their achievements, of practical successes and failures, and of human perfidy and generosity...this is one of the still too rare occasions in which mathematicians are shown as frail, flesh-and-blood creatures...a very worthwhile book. -CHOICE |
| courant institute prize for mathematical talent.: Information Theory and Stochastics for Multiscale Nonlinear Systems Andrew Majda, Rafail V. Abramov, Marcus J. Grote, 2005 This book introduces mathematicians to the fascinating mathematical interplay between ideas from stochastics and information theory and practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of complex nonlinear systems. After a general discussion, a new elementary model, motivated by issues in climate dynamics, is utilized to develop a self-contained example of stochastic mode reduction. Based on A. Majda's Aisenstadt lectures at the University of Montreal, the book is appropriate for both pure and applied mathematics graduate students, postdocs and faculty, as well as interested researchers in other scientific disciplines. No background in geophysical flows is required. About the authors: Andrew Majda is a member of the National Academy of Sciences and has received numerous honors and awards, including the National Academy of Science Prize in Applied Mathematics, the John von Neumann Prize of the Society of Industrial and Applied Mathematics, the Gibbs Prize of the American Mathematical Society, and the Medal of the College de France. In the past several years at the Courant Institute, Majda and a multi-disciplinary faculty have created the Center for Atmosphere Ocean Science to promote cross-disciplinary research with modern applied mathematics in climate modeling and prediction. R.V. Abramov is a young researcher; he received his PhD in 2002. M. J. Grote received his Ph.D. under Joseph B. Keller at Stanford University in 1995. |
| courant institute prize for mathematical talent.: Exterior Differential Systems Robert L. Bryant, S.S. Chern, Robert B. Gardner, Hubert L. Goldschmidt, P.A. Griffiths, 2013-06-29 This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object. |
| courant institute prize for mathematical talent.: Libertas Mathematica , 1996 |
| courant institute prize for mathematical talent.: J-holomorphic Curves and Symplectic Topology Dusa McDuff, Dietmar Salamon, 2012 The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology. |
| courant institute prize for mathematical talent.: Methods in Computational Science Johan Hoffman, 2021-10-19 Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory. |
| courant institute prize for mathematical talent.: Mind, Modernity, Madness Liah Greenfeld, 2013-04-01 A leading interpreter of modernity argues that our culture of limitless self-fulfillment is making millions mentally ill. Training her analytic eye on manic depression and schizophrenia, Liah Greenfeld, in the culminating volume of her trilogy on nationalism, traces these dysfunctions to society’s overburdening demands for self-realization. |
| courant institute prize for mathematical talent.: Predictive Analytics For Dummies Anasse Bari, Mohamed Chaouchi, Tommy Jung, 2014-03-06 Combine business sense, statistics, and computers in a new and intuitive way, thanks to Big Data Predictive analytics is a branch of data mining that helps predict probabilities and trends. Predictive Analytics For Dummies explores the power of predictive analytics and how you can use it to make valuable predictions for your business, or in fields such as advertising, fraud detection, politics, and others. This practical book does not bog you down with loads of mathematical or scientific theory, but instead helps you quickly see how to use the right algorithms and tools to collect and analyze data and apply it to make predictions. Topics include using structured and unstructured data, building models, creating a predictive analysis roadmap, setting realistic goals, budgeting, and much more. Shows readers how to use Big Data and data mining to discover patterns and make predictions for tech-savvy businesses Helps readers see how to shepherd predictive analytics projects through their companies Explains just enough of the science and math, but also focuses on practical issues such as protecting project budgets, making good presentations, and more Covers nuts-and-bolts topics including predictive analytics basics, using structured and unstructured data, data mining, and algorithms and techniques for analyzing data Also covers clustering, association, and statistical models; creating a predictive analytics roadmap; and applying predictions to the web, marketing, finance, health care, and elsewhere Propose, produce, and protect predictive analytics projects through your company with Predictive Analytics For Dummies. |
| courant institute prize for mathematical talent.: Archimedes in the 21st Century Chris Rorres, 2017-08-26 This book is a collection of papers presented at the “Archimedes in the 21st Century” world conference, held at the Courant Institute of Mathematical Sciences in 2013. This conference focused on the enduring and continuing influence of Archimedes in our modern world, celebrating his centuries of influence on mathematics, science, and engineering. Archimedes planted the seeds for a myriad of seminal ideas that would grow over the ages. Each chapter surveys the growth of one or more of these seeds, and the fruit that they continue to bear to this day. The conference speakers contributing to this book are actively involved in STEM fields whose origins trace back to Archimedes, many of whom have conducted and published research that extends Archimedes’ work into the 21st century. The speakers are not historians, so while historical context is provided, this book is uniquely focused on the works themselves as opposed to their history. The breadth and depth of Archimedes’ influence will inspire, delight, and even surprise readers from a variety of fields and interests including historians, mathematicians, scientists, and engineers. Only a modest background in math is required to read this book, making it accessible to curious readers of all ages. |
| courant institute prize for mathematical talent.: Convex Geometric Analysis Keith M. Ball, Vitali Milman, 1999-01-28 Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999. |
| courant institute prize for mathematical talent.: Numerical Methods for Two-Point Boundary-Value Problems Herbert B. Keller, 2018-11-14 Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition. |
| courant institute prize for mathematical talent.: Vortices in the Magnetic Ginzburg-Landau Model Etienne Sandier, Sylvia Serfaty, 2008-05-14 This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field. |
| courant institute prize for mathematical talent.: Math Bytes Tim P. Chartier, 2014-04-06 An inviting collection of fun, hands-on applications in mathematics and computing This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie's opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson’s method for disproving Fermat’s Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or result--such as Google’s PageRank and the traveling salesman problem--and the applications grow more challenging as you progress through the chapters. But don’t worry, helpful solutions are provided each step of the way. Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Bird--and much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace--a bit and a byte at a time. |
| courant institute prize for mathematical talent.: MAA Notes , 1983 |
| courant institute prize for mathematical talent.: Domain Decomposition Methods - Algorithms and Theory Andrea Toselli, Olof Widlund, 2006-06-20 This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods. |
| courant institute prize for mathematical talent.: Intermediate Algebra James Hall, 1999-07 |
| courant institute prize for mathematical talent.: Symmetric Bilinear Forms John Milnor, Dale Husemoller, 2013-04-17 The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper Theorie der quadratischen Formen in beliebigen Körpern. We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts ... |
| courant institute prize for mathematical talent.: Elliptic Partial Differential Equations Qing Han, Fanghua Lin, 2011 This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems. |
| courant institute prize for mathematical talent.: Data India , 2007 |
| courant institute prize for mathematical talent.: Filtering Complex Turbulent Systems Andrew J. Majda, John Harlim, 2012-02-23 The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems. The book contains background material from filtering, turbulence theory and numerical analysis, making it suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required. |
| courant institute prize for mathematical talent.: Mathematicians of the World, Unite! Guillermo Curbera, 2009-02-23 This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int |
| courant institute prize for mathematical talent.: The Abel Prize 2008-2012 Helge Holden, Ragni Piene, 2017-04-30 Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners. |
| courant institute prize for mathematical talent.: The Abel Prize 2013-2017 Helge Holden, Ragni Piene, 2019-02-23 The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize. As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners. |
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