Screen LibraryThe princeton companion to mathematics /
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematic...
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| Corporate Authors: | |
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| Group Author: | ; ; |
| Published: |
Princeton University Press,
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| Publisher Address: | Princeton, N.J. : |
| Publication Dates: |
[2008] ©2008 |
| Literature type: | eBook |
| Language: | English |
| Edition: | Core Textbook. |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1515/9781400830398 http://www.degruyter.com/doc/cover/9781400830398.jpg |
| Summary: |
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.Features nearly 200 entries, organized thematically and written by an international team of distinguished contributorsPresents major ideas and branches of pure mathematics in a clear, accessible styleDefines and explains important mathematical concepts, methods, theorems, and open problemsIntroduces the language of mathematics and the goals of mathematical researchCovers number theory, algebra, analysis, geometry, logic, probability, and moreTraces the history and development of modern mathematicsProfiles more than ninety-five mathematicians who influenced those working todayExplores the influence of mathematics on other disciplinesIncludes bibliographies, cross-references, and a comprehensive indexContributors incude:Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Be |
| Carrier Form: | 1 online resource (1056 pages) : illustrations |
| ISBN: | 9781400830398 |
| Index Number: | QA11 |
| CLC: | O1-4 |
| Contents: |
Frontmatter -- Contents -- Preface -- Contributors -- I.1 What Is Mathematics About? -- I.2 The Language and Grammar of Mathematics -- I.3 Some Fundamental Mathematical Definitions -- I.4 The General Goals of Mathematical Research -- II.1 From Numbers to Number Systems / II.2 Geometry / II.3 The Development of Abstract Algebra / II.4 Algorithms / II.5 The Development of Rigor in Mathematical Analysis / II.6 The Development of the Idea of Proof / II.7 The Crisis in the Foundations of Mathematics / III.1 The Axiom of Choice -- III.2 The Axiom of Determinacy -- III.3 Bayesian Analysis -- III.4 Braid Groups / III.5 Buildings / III.6 Calabi Yau Manifolds / III.7 Cardinals -- III.8 Categories / III.9 Compactness and Compactification / III.10 Computational Complexity Classes -- III.11 Countable and Uncountable Sets -- III.12 C*-Algebras -- III.13 Curvature -- III.14 Designs / III.15 Determinants -- III.16 Differential Forms and Integration / III.17 Dimension -- III.18 Distributions / III.19 Duality -- III.20 Dynamical Systems and Chaos -- III.21 Elliptic Curves / III.22 The Euclidean Algorithm and Continued Fractions / III.23 The Euler and Navier Stokes Equations / III.24 Expanders / III.25 The Exponential and Logarithmic Functions -- III.26 The Fast Fourier Transform -- III.27 The Fourier Transform / III.28 Fuchsian Groups / III.29 Function Spaces / III.30 Galois Groups -- III.31 The Gamma Function / III.32 Generating Functions -- III.33 Genus -- III.34 Graphs -- III.35 Hamiltonians / IV.22 Set Theory / IV.23 Logic and Model Theory / IV.24 Stochastic Processes / IV.25 Probabilistic Models of Critical Phenomena / IV.26 High-Dimensional Geometry and Its Probabilistic Analogues / V.1 The ABC Conjecture -- V.2 The Atiyah Singer Index Theorem / V.3 The Banach Tarski Paradox / V.4 The Birch Swinnerton-Dyer Conjecture -- V.5 Carleson s Theorem / V.6 The Central Limit Theorem -- V.7 The Classification of Finite Simple Groups / V.8 Dirichlet s Theorem -- V.9 Ergodic Theorems / V.10 Fermat s Last Theorem -- V.11 Fixed Point Theorems -- V.12 The Four-Color Theorem / V.13 The Fundamental Theorem of Algebra -- V.14 The Fundamental Theorem of Arithmetic -- V.15 G del s Theorem / V.16 Gromov s Polynomial-Growth Theorem -- V.17 Hilbert s Nullstellensatz -- V.18 The Independence of the Continuum Hypothesis -- V.19 Inequalities -- V.20 The Insolubility of the Halting Problem -- V.21 The Insolubility of the Quintic / V.22 Liouville s Theorem and Roth s Theorem -- V.23 Mostow s Strong Rigidity Theorem / V.24 The P versus NP Problem -- V.25 The Poincar Conjecture -- V.26 The Prime Number Theorem and the Riemann Hypothesis -- V.27 Problems and Results in Additive Number Theory -- V.28 From Quadratic Reciprocity to Class Field Theory / V.29 Rational Points on Curves and the Mordell Conjecture -- V.30 The Resolution of Singularities -- V.31 The Riemann Roch Theorem -- V.32 The Robertson Seymour Theorem / V.33 The Three-Body Problem -- V.34 The Uniformization Theorem -- V.35 The Weil Conjectures / VI.1 Pythagoras / VI.2 Euclid / VI.3 Archimedes |