The Princeton companion to mathematics 1st Edition by Timothy Gowers, June Barrow Green, Imre Leader ISBN 0691118809 9780691118802

The Princeton companion to mathematics 1st Edition by Timothy Gowers, June Barrow Green, Imre Leader – Ebook PDF Instant Download/Delivery: 0691118809, 9780691118802
Full download The Princeton companion to mathematics 1st Edition after payment

Product details:

ISBN 10: 0691118809 
ISBN 13: 9780691118802
Author: Timothy Gowers, June Barrow Green, Imre Leader

The ultimate mathematics reference book 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. Accessible in 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 contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors include: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, and Doron Zeilberger

The Princeton companion to mathematics 1st Table of contents:

Part I Introduction
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
Part II The Origins of Modern Mathematics
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
Part III Mathematical Concepts
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
III.36 The Heat Equation
III.37 Hilbert Spaces
III.38 Homology and Cohomology
III.39 Homotopy Groups
III.40 The Ideal Class Group
III.41 Irrational and Transcendental Numbers
III.42 The Ising Model
III.43 Jordan Normal Form
III.44 Knot Polynomials
III.45 K-Theory
III.46 The Leech Lattice
III.47 L-Functions
III.48 Lie Theory
III.49 Linear and Nonlinear Waves and Solitons
III.50 Linear Operators and Their Properties
III.51 Local and Global in Number Theory
III.52 The Mandelbrot Set
III.53 Manifolds
III.54 Matroids
III.55 Measures
III.56 Metric Spaces
III.57 Models of Set Theory
III.58 Modular Arithmetic
III.59 Modular Forms
III.60 Moduli Spaces
III.61 The Monster Group
III.62 Normed Spaces and Banach Spaces
III.63 Number Fields
III.64 Optimization and Lagrange Multipliers
III.65 Orbifolds
III.66 Ordinals
III.67 The Peano Axioms
III.68 Permutation Groups
III.69 Phase Transitions
III.70 π
III.71 Probability Distributions
III.72 Projective Space
III.73 Quadratic Forms
III.74 Quantum Computation
III.75 Quantum Groups
III.76 Quaternions, Octonions, and Normed Division Algebras
III.77 Representations
III.78 Ricci Flow
III.79 Riemann Surfaces
III.80 The Riemann Zeta Function
III.81 Rings, Ideals, and Modules
III.82 Schemes
III.83 The Schrödinger Equation
III.84 The Simplex Algorithm
III.85 Special Functions
III.86 The Spectrum
III.87 Spherical Harmonics
III.88 Symplectic Manifolds
III.89 Tensor Products
III.90 Topological Spaces
III.91 Transforms
III.92 Trigonometric Functions
III.93 Universal Covers
III.94 Variational Methods
III.95 Varieties
III.96 Vector Bundles
III.97 Von Neumann Algebras
III.98 Wavelets
III.99 The Zermelo–Fraenkel Axioms
Part IV Branches of Mathematics
IV.1 Algebraic Numbers
IV.2 Analytic Number Theory
IV.3 Computational Number Theory
IV.4 Algebraic Geometry
IV.5 Arithmetic Geometry
IV.6 Algebraic Topology
IV.7 Differential Topology
IV.8 Moduli Spaces
IV.9 Representation Theory
IV.10 Geometric and Combinatorial Group Theory
IV.11 Harmonic Analysis
IV.12 Partial Differential Equations
IV.13 General Relativity and the Einstein Equations
IV.14 Dynamics
IV.15 Operator Algebras
IV.16 Mirror Symmetry
IV.17 Vertex Operator Algebras
IV.18 Enumerative and Algebraic Combinatorics
IV.19 Extremal and Probabilistic Combinatorics
IV.20 Computational Complexity
IV.21 Numerical Analysis
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
Part V Theorems and Problems
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 Dirichiet’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 Gödel’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 Liouvflle’s Theorem and Roth’s Theorem
V.23 Mostow’s Strong Rigidity Theorem
V.24 The P versus NP Problem
V.25 The Poincaré 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
Part VI Mathematicians
VI.1 Pythagoras (ca. 569 B.C.E.–ca.494 B.C.E.)
VI.2 Euclid (ca. 325 B.C.E.–ca. 265 B.C.E.)
VI.3 Archimedes (ca. 287 B.C.E.–212 B.C.E.)
VI.4 Apollonius (ca. 262 B.C.E.–ca. 190 B.C.E.)
VI.5 Abu Ja’far Muhammad ibn Mūsā al-Khwārizmī (800–847)
VI.6 Leonardo of Pisa (known as Fibonacci) (ca. 1170–ca. 1250)
VI.7 Girolamo Cardano (1501–1576)
VI.8 Rafael Bombelli (1526-after 1572)
VI.9 François Viète (1540–1603)
VI.10 Simon Stevin (1548–1620)
VI.11 René Descartes (1596–1650)
VI.12 Pierre Fermat (160?-1665)
VI.13 Blaise Pascal (1623–1662)
VI.14 Isaac Newton (1642–1727)
VI.15 Gottfried Wilhelm Leibniz (1646–1716)
VI.16 Brook Taylor (1685–1731)
VI.17 Christian Goldbach (1690–1764)
VI.18 The Bernoullis (f1.18th century)
VI.19 Leonhard Euler (1707–1783)
VI.20 Jean Le Rond d’Alembert (1717–1783)
VI.21 Edward Waring (ca.1735–1798)
VI.22 Joseph Louis Lagrange (1736–1813)
VI.23 Pierre-Simon Laplace (1749–1827)
VI.24 Adrien-Marie Legendre (1752–1833)
VI.25 Jean-Baptiste Joseph Fourier (1768–1830)
VI.26 Carl Friedrich Gauss (1777–1855)
VI.27 Siméon-Denis Poisson (1781–1840)
VI.28 Bernard Bolzano (1781–1848)
VI.29 Augustin-Louis Cauchy (1789–1857)
VI.30 August Ferdinand Möbius (1790–1868)
VI.31 Nicolai Ivanovich Lobachevskii (1792–1856)
VI.32 George Green (1793–1841)
VI.33 Niels Henrik Abel (1802–1829)
VI.34 János Bolyai (1802–1860)
VI.35 Carl Gustav Jacob Jacobi (1804–1851)
VI.36 Peter Gustav Lejeune Dirichlet (1805–1859)
VI.37 William Rowan Hamilton (1805–1865)
VI.38 Augustus De Morgan (1806–1871)
VI.39 Joseph Liouville (1809–1882)
VI.40 Ernst Eduard Kummer (1810–1893)
VI.41 Évariste Galois (1811–1832)
VI.42 James Joseph Sylvester (1814–1897)
VI.43 George Boole (1815–1864)
VI.44 Karl Weierstrass (1815–1897)
VI.45 Pafnuty Chebyshev (1821–1894)
VI.46 Arthur Cayley (1821–1895)
VI.47 Charles Hermite (1822–1901)
VI.48 Leopold Kronecker (1823–1891)
VI.49 Georg Friedrich Bernhard Riemann (1826–1866)
VI.50 Julius Wilhelm Richard Dedekind (1831–1916)
VI.51 Émile Léonard Mathieu (1835–1890)
VI.52 Camille Jordan (1838–1922)
VI.53 Sophus Lie (1842–1899)
VI.54 Georg Cantor (1845–1918)
VI.55 William Kingdon Clifford (1845–1879)
VI.56 Gottlob Frege (1848–1925)
VI.57 Christian Felix Klein (1849–1925)
VI.58 Ferdinand Georg Frobenius (1849–1917)
VI.59 Sofya (Sonya) Kovalevskaya (1850–1891)
VI.60 William Burnside (1852–1927)
VI.61 Jules Henri Poincaré (1854–1912)
VI.62 Giuseppe Peano (1858–1932)
VI.63 David Hilbert (1862–1943)
VI.64 Hermann Minkowski (1864–1909)
VI.65 Jacques Hadamard (1865–1963)
VI.66 Ivar Fredholm (1866–1927)
VI.67 Charles-Jean de la Vallée Poussin (1866–1962)
VI.68 Felix Hausdorff (1868–1942)
VI.69 Élie Joseph Cartan (1869–1951)
VI.70 Emile Borel (1871–1956)
VI.71 Bertrand Arthur William Russell (1872–1970)
VI.72 Henri Lebesgue (1875–1941)
VI.73 Godfrey Harold Hardy (1877–1947)
VI.74 Frigyes (Frédéric) Riesz (1880–1956)
VI.75 Luitzen Egbertus Jan Brouwer (1881–1966)
VI.76 Emmy Noether (1882–1935)
VI.77 Waclaw Sierpiński (1882–1969)
VI.78 George Birkhoff (1884–1944)
VI.79 John Edensor Littlewood (1885–1977)
VI.80 Hermann Weyl (1885–1955)
VI.81 Thoralf Skolem (1887–1963)
VI.82 Srinwasa Ramanujan (1887–1920)
VI.83 Richard Courant (1888–1972)
VI.84 Stefan Banach (1892–1945)
VI.85 Norbert Wiener (1894–1964)
VI.86 Emil Artin (1898–1962)
VI.87 Alfred Tarski (1901–1983)
VI.88 Andrei Nikolaevich Kolmogorov (1903–1987)
VI.89 Alonzo Church (1903–1995)
VI.90 William Valiance Douglas Hodge (1903–1975)
VI.91 John von Neumann (1903–1957)
VI.92 Kurt Gödel (1906–1978)
VI.93 André Weil (1906–1998)
VI.94 Alan Turing (1912–1954)
VI.95 Abraham Robinson (1918–1974)
VI.96 Nicolas Bourbaki (1935–)
Part VII The Influence of Mathematics
VII.1 Mathematics and Chemistry
VII.2 Mathematical Biology
VII.3 Wavelets and Applications
VII.4 The Mathematics of Traffic in Networks
VII.5 The Mathematics of Algorithm Design
VII.6 Reliable Transmission of Information
VII.7 Mathematics and Cryptography
VII.8 Mathematics and Economic Reasoning
VII.9 The Mathematics of Money
VII.10 Mathematical Statistics
VII.11 Mathematics and Medical Statistics
VII.12 Analysis, Mathematical and Philosophical
VII.13 Mathematics and Music
VII.14 Mathematics and Art
Part VIII Final Perspectives
VIII.1 The Art of Problem Solving
VIII.2 “Why Mathematics” You Might Ask
VIII.3 The Ubiquity of Mathematics
VIII.4 Numeracy
VIII.5 Mathematics: An Experimental Science
VIII.6 Advice to a Young Mathematician
VIII.7 A Chronology of Mathematical Events
Index

People also search for The Princeton companion to mathematics 1st:

the princeton companion to mathematics
    
synopsis of the princeton companion to mathematics
    
the princeton companion to mathematics pdf
    
the princeton companion to mathematics reddit
    
the princeton companion to mathematics pdf download

Tags: Timothy Gowers, June Barrow Green, Imre Leader, Princeton, companion