It provides an extensive overview of mathematics, and is noted for the high caliber. 0000001915 00000 n
Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics … Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics … princeton companion to mathematics this volume is an indispensable resource for undergraduate and ... mathematics 8 i3 methods of solution 27 the princeton companion to applied mathematics table of contents author edited by nicholas j higham subject mathematics reference works and anthologies %%EOF
"The Princeton Companion to Applied Mathematics is a tour de force, an incredible collection that should be on the shelf of every mathematician, of every scientist, and indeed of anyone fascinated with mathematics. 0000007894 00000 n
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Transcluding specific-source templates rather than writing out citations reduces code duplication across articles and allows improvements — such as adding a zbMATH number or wikilinking the name of an author or editor — to apply to all uses of the source at once. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. 0000004611 00000 n
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Its goal is to assist these readers in cultivating a global view of mathematics. .It has been a major project that eventually resulted in this amazing product." 0000096455 00000 n
Modeled on the popularPrinceton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. It has something for everyone from beginner to advanced … 0000094970 00000 n
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Unparalleled in its depth of coverage,The Princeton Companion to Mathematicssurveys 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. He is assisted by more than 150 experts in applied mathematics. 0000040434 00000 n
Slightly off as the ToC available from the library of congress is different from the current editions. --Mathematics Teacher "Overall [The Princeton Companion to Mathematics] is an enormous achievement for which the authors deserve to be thanked. <<4B1B01B569861A44B259DD2B0A1A099C>]/Prev 493818>>
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--S.J. It is a monumental work aimed at readers ranging from undergraduate math majors to established researchers. The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. The Princeton Companion to Applied Mathematics Nicholas J. Higham , Mark R. Dennis , Paul Glendinning , Paul A. Martin , Fadil Santosa , Jared Tanner (eds.) The princeton companion to mathematics is a friendly informative reference book that attempts to explain what mathematics is about and what mathematicians do. ���Ӡ��V������8~a�zE
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Contents Preface Contributors Parti Introduction LI 1.2 1.3 1.4 What Is Mathematics About? Title: The Princeton Companion to Mathematics Format: Hardcover Product dimensions: 1056 pages, 10 X 8 X 0 in Shipping dimensions: 1056 pages, 10 X 8 X 0 in Published: 28 septembre 2008 Publisher: Princeton University Press Language: English. ;�@ !u�H=�Ck�;
�Cz迟��nC Get this from a library! The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. The Princeton Companion to Applied Mathematics Editors: Dennis, Mark R., Glendinning, Paul and Martin, Paul A. You Might Ask" 957, 1 "VIII.3 The Ubiquity of Mathematics" 968, 1 "VIII.5 Mathematics: An Experimental Science" 982, 1 "VIII.6 Advice to a Young Mathematician" 991, "1 I.2 The Language and Grammar of Mathematics 8", "1 I.3 Some Fundamental Mathematical Definitions 16", "1 I.4 The General Goals of Mathematical Research 46", "1 Part II The Origins of Modern Mathematics", "1 II.1 From Numbers to Number Systems 77", "1 II.3 The Development of Abstract Algebra 96", "1 II.5 The Development of Rigor in Mathematical Analysis 118", "1 II.6 The Development of the Idea of Proof 130", "1 II.7 The Crisis in the Foundations of Mathematics 143", "1 III.9 Compactness and Compactification 169", "1 III.10 Computational Complexity Classes 171", "1 III.11 Countable and Uncountable Sets 172", "1 III.16 Differential Forms and Integration 176", "1 III.20 Dynamical Systems and Chaos 191", "1 III.22 The Euclidean Algorithm and Continued Fractions 193", "1 III.23 The Euler and Navier-Stokes Equations 195", "1 III.24 The Exponential and Logarithmic Functions 198", "1 III.26 The Fast Fourier Transform 204", "1 III.43 Irrational and Transcendental Numbers 224", "1 III.51 Linear and Nonlinear Waves and Solitons 236", "1 III.52 Linear Operators and Their Properties 241", "1 III.53 Local and Global in Number Theory 243", "1 III.54 Optimization and Lagrange Multipliers 246", "1 III.65 Normed Spaces and Banach Spaces 257", "1 III.78 Quaternions, Octonions, and Normed Division Algebras 277", "1 III.83 Rings, Ideals, and Modules 286", "1 III.101 The Zermelo-Fraenkel Axioms 315", "1 IV.11 Geometric and Combinatorial Group Theory 453", "1 IV.16 Partial Differential Equations 526", "1 IV.17 General Relativity and the Einstein Equations 553", "1 IV.22 Enumerative and Algebraic Combinatorics 613", "1 IV.23 Extremal and Probabilistic Combinatorics 625", "1 IV.24 High-Dimensional Geometry and Its Probabilistic Analogues 639", "1 IV.26 Probabilistic Models of Critical Phenomena 660", "1 V.2 The Atiyah-Singer Index Theorem 673", "1 V.4 The Birch-Swinnerton-Dyer Conjecture 677", "1 V.8 The Classification of Finite Simple Groups 679", "1 V.15 The Fundamental Theorem of Algebra 691", "1 V.16 The Fundamental Theorem of Arithmetic 692", "1 V.17 The Fundamental Theorem of Calculus 693", "1 V.19 Gromovs Polynomial-Growth Theorem 695", "1 V.21 The Independence of the Continuum Hypothesis 696", "1 V.23 The Insolubility of the Halting Problem 699", "1 V.24 The Insolubility of the Quintic 701", "1 V.25 Liouvilles Theorem and Roths Theorem 703", "1 V.26 Rational Points on Curves and the Mordell Conjecture 704", "1 V.27 Mostows Strong Rigidity Theorem 706", "1 V.30 Problems and Results in Additive Number Theory 709", "1 V.31 From Quadratic Reciprocity to Class Field Theory 712", "1 V.32 The Resolution of Singularities 715", "1 V.35 The Robertson-Seymour Theorem 718", "1 VI.5 Leonardo of Pisa (known as Fibonacci) 730", "1 VI.24 Jean-Baptiste Joseph Fourier 748", "1 VI.30 Nicolai Ivanovich Lobachevskii 752", "1 VI.35 Peter Gustav Lejeune Dirichlet 757", "1 VI.48 Georg Bernhard Friedrich Riemann 767", "1 VI.49 Julius Wilhelm Richard Dedekind 769", "1 VI.66 Charles-Jean de la Vallee Poussin 784", "1 VI.70 Bertrand Arthur William Russell 788", "1 VI.74 Luitzen Egbertus Jan Brouwer 792", "1 VI.87 Andrei Nikolaevich Kolmogorov 807", "1 VI.88 William Vallance Douglas Hodge 809", "1 Part VII The Influence of Mathematics", "1 VII.4 The Mathematics of Traffic in Networks 855", "1 VII.5 The Mathematics of Algorithm Design 863", "1 VII.6 Reliable Transmission of Information 871", "1 VII.7 Mathematics and Cryptography 879", "1 VII.8 Mathematics and Economic Reasoning 888", "1 VII.11 Mathematics and Medical Statistics 914", "1 VII.12 Analysis, Mathematical and Philosophical 921", "1 VIII.1 The Art of Problem Solving 949", "1 VIII.2 Why Mathematics? We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Learn more. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. The Princeton Companion to Mathematics EDITOR Timothy Gowers University of Cambridge ASSOCIATE EDITORS June Barrow-Green The Open University Imre Leader University of Cambridge Princeton University Press Princeton and Oxford . The Princeton companion to mathematics. 0000043548 00000 n
"The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. ... Table of Contents. "The perfect companion to the earlier Companion.
O’Reilly members get unlimited access to live online training experiences, plus books, videos, and digital content from 200+ publishers. We use essential cookies to perform essential website functions, e.g. Get this from a library! The Princeton Companion to Mathematics ). 0000081471 00000 n
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This book will be a landmark for decades ahead. Keywords. The book is an excellent reference that successfully compiles into a readable and … 13 0 obj
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Publication Year : 2015 Publisher : Princeton University Press Single-User Purchase Price: $186.50 Unlimited-User Purchase Price: $279.75 ISBN : 978-0-69-115039-0 Category : Mathematics & Statistics - Mathematics Image Count : 410 Book Status: Available Table of Contents Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as … 0000043638 00000 n
"—Nick Trefethen, University of Oxford "The Princeton Companion to Applied Mathematics is a tour de force, an incredible collection that should be on the shelf of every mathematician, of every scientist, and indeed of anyone fascinated with mathematics. But at the heart of The Companion lies Part IV, on “Branches of Mathematics”, covering 26 branches of mathematics, each discussed in ten to twenty pages. 0000001643 00000 n
Higham, N., ed., Princeton, Companion, Applied, Mathematics, Mathematics, Reference Works and Anthologies, Princeton University Press. xref
The following ISBNs are associated with this title: ISBN - 10: 0691118809. Table 1 Relevant articles from The Princeton Companion to Mathematics whose topic is not duplicated here. 1 "I.2 The Language and Grammar of Mathematics" 8, 1 "I.3 Some Fundamental Mathematical Definitions" 17, 1 "I.4 The General Goals of Mathematical Research" 46, 1 "II.1 From Numbers to Number Systems" 74, 1 "II.3 The Development of Abstract Algebra" 93, 1 "II.5 The Development of Rigor in Mathematical Analysis" 115, 1 "II.6 The Development of the Idea of Proof" 127, 1 "II.7 The Crisis in the Foundations of Mathematics" 140, 1 "III.9 Compactness and Compactification" 166, 1 "III.10 Computational Complexity Classes" 168, 1 "III.11 Countable and Uncountable Sets" 169, 1 "III.16 Differential Forms and Integration" 173, 1 "III.20 Dynamical Systems and Chaos" 188, 1 "III.22 The Euclidean Algorithm and Continued Fractions" 190, 1 "III.23 The Euler and Navier-Stokes Equations" 192, 1 "III.24 The Exponential and Logarithmic Functions" 195, 1 "III.26 The Fast Fourier Transform" 201, 1 "III.43 Irrational and Transcendental Numbers" 221, 1 "III.51 Linear and Nonlinear Waves and Solitons" 233, 1 "III.52 Linear Operators and Their Properties" 238, 1 "III.53 Local and Global in Number Theory" 240, 1 "III.54 Optimization and Lagrange Multipliers" 243, 1 "III.65 Normed Spaces and Banach Spaces" 254, 1 "III.78 Quaternions, Octonions, and Normed Division Algebras" 274, 1 "III.83 Rings, Ideals, and Modules" 283, 1 "III.101 The Zermelo-Fraenkel Axioms" 312, 1 "IV.11 Geometric and Combinatorial Group Theory" 450, 1 "IV.16 Partial Differential Equations" 523, 1 "IV.17 General Relativity and the Einstein Equations" 550, 1 "IV.22 Enumerative and Algebraic Combinatorics" 610, 1 "IV.23 Extremal and Probabilistic Combinatorics" 622, 1 "IV.24 High-Dimensional Geometry and Its Probabilistic Analogues" 636, 1 "IV.26 Probabilistic Models of Critical Phenomena" 657, 1 "V.2 The Atiyah-Singer Index Theorem" 670, 1 "V.4 The Birch-Swinnerton-Dyer Conjecture" 674, 1 "V.8 The Classification of Finite Simple Groups" 676, 1 "V.15 The Fundamental Theorem of Algebra" 688, 1 "V.16 The Fundamental Theorem of Arithmetic" 689, 1 "V.17 The Fundamental Theorem of Calculus" 690, 1 "V.19 Gromovs Polynomial-Growth Theorem" 692, 1 "V.21 The Independence of the Continuum Hypothesis" 693, 1 "V.23 The Insolubility of the Halting Problem" 696, 1 "V.24 The Insolubility of the Quintic" 698, 1 "V.25 Liouvilles Theorem and Roths Theorem" 700, 1 "V.26 Rational Points on Curves and the Mordell Conjecture" 701, 1 "V.27 Mostows Strong Rigidity Theorem" 703, 1 "V.30 Problems and Results in Additive Number Theory" 706, 1 "V.31 From Quadratic Reciprocity to Class Field Theory" 709, 1 "V.32 The Resolution of Singularities" 712, 1 "V.35 The Robertson-Seymour Theorem" 715, 1 "VI.5 Leonardo of Pisa (known as Fibonacci)" 727, 1 "VI.24 Jean-Baptiste Joseph Fourier" 745, 1 "VI.30 Nicolai Ivanovich Lobachevskii" 749, 1 "VI.35 Peter Gustav Lejeune Dirichlet" 754, 1 "VI.48 Georg Bernhard Friedrich Riemann" 764, 1 "VI.49 Julius Wilhelm Richard Dedekind" 766, 1 "VI.66 Charles-Jean de la Vallee Poussin" 781, 1 "VI.70 Bertrand Arthur William Russell" 785, 1 "VI.74 Luitzen Egbertus Jan Brouwer" 789, 1 "VI.87 Andrei Nikolaevich Kolmogorov" 804, 1 "VI.88 William Vallance Douglas Hodge" 806, 1 "VII.4 The Mathematics of Traffic in Networks" 852, 1 "VII.5 The Mathematics of Algorithm Design" 860, 1 "VII.6 Reliable Transmission of Information" 868, 1 "VII.7 Mathematics and Cryptography" 876, 1 "VII.8 Mathematics and Economic Reasoning" 885, 1 "VII.11 Mathematics and Medical Statistics" 911, 1 "VII.12 Analysis, Mathematical and Philosophical" 918, 1 "VIII.1 The Art of Problem Solving" 946, 1 "VIII.2 Why Mathematics? 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