The Princeton companion to mathematics / (Record no. 143731)

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008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 080505s2008 njua b 001 0 eng
010 ## - LIBRARY OF CONGRESS CONTROL NUMBER
LC control number 2008020450
035 ## - SYSTEM CONTROL NUMBER
System control number (Sirsi) i9780691118802
040 ## - CATALOGING SOURCE
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Language of cataloging eng
Transcribing agency DLC
Modifying agency YDXCP
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015 ## - NATIONAL BIBLIOGRAPHY NUMBER
National bibliography number GBA898752
Source bnb
016 7# - NATIONAL BIBLIOGRAPHIC AGENCY CONTROL NUMBER
Record control number 014691695
Source Uk
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780691118802 (hardcover : alk. paper)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0691118809 (hardcover : alk. paper)
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)227205932
050 00 - LIBRARY OF CONGRESS CALL NUMBER
Classification number REF QA 11.2
Item number .P745 2008
049 ## - LOCAL HOLDINGS (OCLC)
Holding library VF$R
245 04 - TITLE STATEMENT
Title The Princeton companion to mathematics /
Statement of responsibility, etc. editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader.
260 ## - PUBLICATION, DISTRIBUTION, ETC.
Place of publication, distribution, etc. Princeton :
Name of publisher, distributor, etc. Princeton University Press,
Date of publication, distribution, etc. c2008.
300 ## - PHYSICAL DESCRIPTION
Extent xx, 1034 p. :
Other physical details ill. ;
Dimensions 26 cm.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc. note Includes bibliographical references and index.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information Preface --
-- Contributors --
-- pt. 1.
-- Introduction --
-- 1.1.
Title What is mathematics about? --
Miscellaneous information 1.2.
Title The language and grammar of mathematics --
Miscellaneous information 1.3.
Title Some fundamental mathematical definitions --
Miscellaneous information 1.4.
Title The general goals of mathematical research --
Miscellaneous information pt. 2.
Title The origins of modern mathematics --
Miscellaneous information 2.1.
Title From numbers to number systems --
Miscellaneous information 2.2.
Title Geometry --
Miscellaneous information 2.3.
Title The development of abstract algebra --
Miscellaneous information 2.4.
Title Algorithms --
Miscellaneous information 2.5.
Title The development of rigor in mathematical analysis --
Miscellaneous information 2.6.
Title The development of the idea of proof --
Miscellaneous information 2.7.
Title The crisis in the foundations of mathematics --
Miscellaneous information pt. 3.
Title Mathematical concepts --
Miscellaneous information 3.1.
Title The axiom of choice --
Miscellaneous information 3.2.
Title The axiom of determinacy --
Miscellaneous information 3.3.
Title Bayesian analysis --
Miscellaneous information 3.4.
Title Braid groups --
Miscellaneous information 3.5.
Title Buildings --
Miscellaneous information 3.6.
Title Calabi-Yau manifolds --
Miscellaneous information 3.7.
Title Cardinals --
Miscellaneous information 3.8.
Title Categories --
Miscellaneous information 3.9.
Title Compactness and compactification --
Miscellaneous information 3.10.
Title Computational complexity classes --
Miscellaneous information 3.11.
Title Countable and uncountable sets --
Miscellaneous information 3.12.
Title C*-algebras --
Miscellaneous information 3.13.
Title Curvature --
Miscellaneous information 3.14.
Title Designs --
Miscellaneous information 3.15.
Title Determinants --
Miscellaneous information 3.15.
Title Differential forms and integration --
Miscellaneous information 3.17.
Title Dimension --
Miscellaneous information 3.18.
Title Distributions.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information 3.19.
Title Duality --
Miscellaneous information 3.20.
Title Dynamical systems and chaos --
Miscellaneous information 3.21.
Title Elliptic curves --
Miscellaneous information 3.22.
Title The Euclidean algorithm and continued fractions --
Miscellaneous information 3.23.
Title The Euler and Navier-Stokes equations --
Miscellaneous information 3.24.
Title Expanders --
Miscellaneous information 3.25.
Title The exponential and logarithmic functions --
Miscellaneous information 3.26.
Title The fast Fourier transform --
Miscellaneous information 3.27.
Title The Fourier transform --
Miscellaneous information 3.28.
Title Fuchsian groups --
Miscellaneous information 3.29.
Title Function spaces --
Miscellaneous information 3.30.
Title Galois groups --
Miscellaneous information 3.31.
Title The gamma function --
Miscellaneous information 3.32.
Title Generating functions --
Miscellaneous information 3.33.
Title Genus --
Miscellaneous information 3.34.
Title Graphs --
Miscellaneous information 3.35.
Title Hamiltonians --
Miscellaneous information 3.36.
Title The heat equation --
Miscellaneous information 3.37.
Title Hilbert spaces --
Miscellaneous information 3.38.
Title Homology and cohomology --
Miscellaneous information 3.39.
Title Homotopy Groups --
Miscellaneous information 3.40.
Title The ideal class group --
Miscellaneous information 3.41.
Title Irrational and transcendental numbers --
Miscellaneous information 3.42.
Title The Ising model --
Miscellaneous information 3.43.
Title Jordan normal form --
Miscellaneous information 3.44.
Title Knot polynomials --
Miscellaneous information 3.45.
Title K-theory --
Miscellaneous information 3.46.
Title The leech lattice --
Miscellaneous information 3.47.
Title L-function --
Miscellaneous information 3.48.
Title Lie theory --
Miscellaneous information 3.49.
Title Linear and nonlinear waves and solitons --
Miscellaneous information 3.50.
Title Linear operators and their properties --
Miscellaneous information 3.51.
Title Local and global in number theory --
Miscellaneous information 3.52.
Title The Mandelbrot set --
Miscellaneous information 3.53.
Title Manifolds --
Miscellaneous information 3.54.
Title Matroids --
Miscellaneous information 3.55.
Title Measures.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information 3.56.
Title Metric spaces --
Miscellaneous information 3.57.
Title Models of set theory --
Miscellaneous information 3.58.
Title Modular arithmetic --
Miscellaneous information 3.59.
Title Modular forms --
Miscellaneous information 3.60.
Title Moduli spaces --
Miscellaneous information 3.61.
Title The monster group --
Miscellaneous information 3.62.
Title Normed spaces and banach spaces --
Miscellaneous information 3.63.
Title Number fields --
Miscellaneous information 3.64.
Title Optimization and Lagrange multipliers --
Miscellaneous information 3.65.
Title Orbifolds --
Miscellaneous information 3.66.
Title Ordinals --
Miscellaneous information 3.67.
Title The Peano axioms --
Miscellaneous information 3.68.
Title Permutation groups --
Miscellaneous information 3.69.
Title Phase transitions --
Miscellaneous information 3.70.
Title [pi] --
Miscellaneous information 3.71.
Title Probability distributions --
Miscellaneous information 3.72.
Title Projective space --
Miscellaneous information 3.73.
Title Quadratic forms --
Miscellaneous information 3.74.
Title Quantum computation --
Miscellaneous information 3.75.
Title Quantum groups --
Miscellaneous information 3.76.
Title Quaternions, octonions, and normed division algebras --
Miscellaneous information 3.77.
Title Representations --
Miscellaneous information 3.78.
Title Ricci flow --
Miscellaneous information 3.79.
Title Riemann surfaces --
Miscellaneous information 3.80.
Title The Riemann zeta function --
Miscellaneous information 3.81.
Title Rings, ideals, and modules --
Miscellaneous information 3.82.
Title Schemes --
Miscellaneous information 3.83.
Title The Schr�odinger equation --
Miscellaneous information 3.84.
Title The simplex algorithm --
Miscellaneous information 3.85.
Title Special functions --
Miscellaneous information 3.86.
Title The spectrum --
Miscellaneous information 3.87.
Title Spherical harmonics --
Miscellaneous information 3.88.
Title Symplectic manifolds --
Miscellaneous information 3.89.
Title Tensor products --
Miscellaneous information 3.90.
Title Topological spaces --
Miscellaneous information 3.91.
Title Transforms --
Miscellaneous information 3.92.
Title Trigonometric functions --
Miscellaneous information 3.93.
Title Universal covers --
Miscellaneous information 3.94.
Title Variational methods --
Miscellaneous information 3.95.
Title Varieties --
Miscellaneous information 3.96.
Title Vector bundles --
Miscellaneous information 3.97.
Title Von Neumann algebras --
Miscellaneous information 3.98.
Title Wavelets --
Miscellaneous information 3.99.
Title The Zermelo-Fraenkel axioms.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information pt. 4.
Title Branches of mathematics --
Miscellaneous information 4.1.
Title Algebraic numbers --
Miscellaneous information 4.2.
Title Analytic number theory --
Miscellaneous information 4.3.
Title Computational number theory --
Miscellaneous information 4.4.
Title Algebraic geometry --
Miscellaneous information 4.5.
Title Arithmetic geometry --
Miscellaneous information 4.6.
Title Algebraic topology --
Miscellaneous information 4.7.
Title Differential topology --
Miscellaneous information 4.8.
Title Moduli spaces --
Miscellaneous information 4.9.
Title Representation theory --
Miscellaneous information 4.10.
Title Geometric and combinatorial group theory --
Miscellaneous information 4.11.
Title Harmonic analysis --
Miscellaneous information 4.12.
Title Partial differential equations --
Miscellaneous information 4.13.
Title General relativity and the Einstein equations --
Miscellaneous information 4.14.
Title Dynamics --
Miscellaneous information 4.15.
Title Operator algebras --
Miscellaneous information 4.16.
Title Mirror symmetry --
Miscellaneous information 4.17.
Title Vertex operator algebras --
Miscellaneous information 4.18.
Title Enumerative and algebraic combinatorics --
Miscellaneous information 4.19.
Title Extremal and probabilistic combinatorics --
Miscellaneous information 4.20.
Title Computational complexity --
Miscellaneous information 4.21.
Title Numerical analysis --
Miscellaneous information 4.22.
Title Set theory --
Miscellaneous information 4.23.
Title Logic and model theory --
Miscellaneous information 4.24.
Title Stochastic processes --
Miscellaneous information 4.25.
Title Probabilistic models of critical phenomena --
Miscellaneous information 4.26.
Title High-dimensional geometry and its probabilistic analogues.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information pt. 5.
Title Theorems and problems --
Miscellaneous information 5.1.
Title The ABC conjecture --
Miscellaneous information 5.2.
Title The Atiyah-Singer index theorem --
Miscellaneous information 5.3.
Title The Banach-Tarski paradox --
Miscellaneous information 5.4.
Title The Birch-Swinnerton-Dyer conjecture --
Miscellaneous information 5.5.
Title Carleson's theorem --
Miscellaneous information 5.6.
Title The central limit theorem --
Miscellaneous information 5.7.
Title The classification of finite simple groups --
Miscellaneous information 5.8.
Title Dirichlet's theorem --
Miscellaneous information 5.9.
Title Ergodic theorems --
Miscellaneous information 5.10.
Title Fermat's last theorem --
Miscellaneous information 5.11.
Title Fixed point theorems --
Miscellaneous information 5.12.
Title The four-color theorem --
Miscellaneous information 5.13.
Title The fundamental theorem of algebra --
Miscellaneous information 5.14.
Title The fundamental theorem of arithmetic --
Miscellaneous information 5.15.
Title G�odel's theorem --
Miscellaneous information 5.16.
Title Gromov's polynomial-growth theorem --
Miscellaneous information 5.17.
Title Hilbert's nullstellensatz --
Miscellaneous information 5.18.
Title The independence of the continuum hypothesis --
Miscellaneous information 5.19.
Title Inequalities --
Miscellaneous information 5.20.
Title The insolubility of the halting problem --
Miscellaneous information 5.21.
Title The insolubility of the quintic --
Miscellaneous information 5.22.
Title Liouville's theorem and Roth's theorem --
Miscellaneous information 5.23.
Title Mostow's strong rigidity theorem --
Miscellaneous information 5.24.
Title The p versus NP problem --
Miscellaneous information 5.25.
Title The Poincar�e conjecture --
Miscellaneous information 5.26.
Title The prime number theorem and the Riemann hypothesis --
Miscellaneous information 5.27.
Title Problems and results in additive number theory --
Miscellaneous information 5.28.
Title From quadratic reciprocity to class field theory --
Miscellaneous information 5.29.
Title Rational points on curves and the Mordell conjecture --
Miscellaneous information 5.30.
Title The resolution of singularities --
Miscellaneous information 5.31.
Title The Riemann-Roch theorem --
Miscellaneous information 5.32.
Title The Robertson-Seymour theorem --
Miscellaneous information 5.33.
Title The three-body problem --
Miscellaneous information 5.34.
Title The uniformization theorem --
Miscellaneous information 5.35.
Title The Weil conjecture.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information pt. 6.
Title Mathematicians --
Miscellaneous information 6.1.
Title Pythagoras --
Miscellaneous information 6.2.
Title Euclid --
Miscellaneous information 6.3.
Title Archimedes --
Miscellaneous information 6.4.
Title Apollonius --
Miscellaneous information 6.5.
Title Abu Ja'far Muhammad ibn M?s? al-Khw?rizm? --
Miscellaneous information 6.6.
Title Leonardo of Pisa (known as Fibonacci) --
Miscellaneous information 6.7.
Title Girolamo Cardano --
Miscellaneous information 6.8.
Title Rafael Bombelli --
Miscellaneous information 6.9.
Title Fran�cois Vi�ete --
Miscellaneous information 6.10.
Title Simon Stevin --
Miscellaneous information 6.11.
Title Ren�e Descartes --
Miscellaneous information 6.12.
Title Pierre Fermat --
Miscellaneous information 6.13.
Title Blaise Pascal --
Miscellaneous information 6.14.
Title Isaac Newton --
Miscellaneous information 6.15.
Title Gottfried Wilhelm Leibniz --
Miscellaneous information 6.16.
Title Brook Taylor --
Miscellaneous information 6.17.
Title Christian Goldbach --
Miscellaneous information 6.18.
Title The Bernoullis --
Miscellaneous information 6.19.
Title Leonhard Euler --
Miscellaneous information 6.20.
Title Jean Le Rond d'Alembert --
Miscellaneous information 6.21.
Title Edward Waring --
Miscellaneous information 6.22.
Title Joseph Louis Lagrange --
Miscellaneous information 6.23.
Title Pierre-Simon Laplace --
Miscellaneous information 6.24.
Title Adrien-Marie Legendre --
Miscellaneous information 6.25.
Title Jean-Baptiste Joseph Fourier --
Miscellaneous information 6.26.
Title Carl Friedrich Gauss --
Miscellaneous information 6.27.
Title Sim�eon-Denis Poisson --
Miscellaneous information 6.28.
Title Bernard Bolzano --
Miscellaneous information 6.29.
Title Augustin-Louis Cauchy --
Miscellaneous information 6.30.
Title August Ferdinand M�obius --
Miscellaneous information 6.31.
Title Nicolai Ivanovich Lobachevskii --
Miscellaneous information 6.32.
Title George Green --
Miscellaneous information 6.33.
Title Niels Henrik Abel --
Miscellaneous information 6.34.
Title J�anos Bolyai --
Miscellaneous information 6.35.
Title Carl Gustav Jacob Jacobi --
Miscellaneous information 6.36.
Title Peter Gustav Lejeune Dirichlet --
Miscellaneous information 6.37.
Title William Rowan Hamilton --
Miscellaneous information 6.38.
Title Augustus De Morgan --
Miscellaneous information 6.39.
Title Joseph Liouville --
Miscellaneous information 6.40.
Title Eduard Kummer.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information 6.41.
Title �Evariste Galois --
Miscellaneous information 6.42.
Title James Joseph Sylvester --
Miscellaneous information 6.43.
Title George Boole --
Miscellaneous information 6.44.
Title Karl Weierstrass --
Miscellaneous information 6.45.
Title Pafnuty Chebyshev --
Miscellaneous information 6.46.
Title Arthur Cayley --
Miscellaneous information 6.47.
Title Charles Hermite --
Miscellaneous information 6.48.
Title Leopold Kronecker --
Miscellaneous information 6.49.
Title Georg Friedrich Bernhard Riemann --
Miscellaneous information 6.50.
Title Julius Wilhelm Richard Dedekind --
Miscellaneous information 6.51.
Title �Emile L�eonard Mathieu --
Miscellaneous information 6.52.
Title Camille Jordan --
Miscellaneous information 6.53.
Title Sophus Lie --
Miscellaneous information 6.54.
Title Georg Cantor --
Miscellaneous information 6.55.
Title William Kingdon Clifford --
Miscellaneous information 6.56.
Title Gottlob Frege --
Miscellaneous information 6.57.
Title Christian Felix Klein --
Miscellaneous information 6.58.
Title Ferdinand Georg Frobenius --
Miscellaneous information 6.59.
Title Sofya (Sonya) Kovalevskaya --
Miscellaneous information 6.60.
Title William Burnside --
Miscellaneous information 6.61.
Title Jules Henri Poincar�e --
Miscellaneous information 6.62.
Title Giuseppe Peano --
Miscellaneous information 6.63.
Title David Hilbert --
Miscellaneous information 6.64.
Title Hermann Minkowski --
Miscellaneous information 6.65.
Title Jacques Hadamard --
Miscellaneous information 6.66.
Title Ivar Fredholm --
Miscellaneous information 6.67.
Title Charles-Jean de la Vall�ee Poussin --
Miscellaneous information 6.68.
Title Felix Hausdorff --
Miscellaneous information 6.69.
Title �Elie Joseph Cartan --
Miscellaneous information 6.70.
Title Emile Borel --
Miscellaneous information 6.71.
Title Bertrand Arthur William Russell --
Miscellaneous information 6.72.
Title Henri Lebesgue --
Miscellaneous information 6.73.
Title Godfrey Harold Hardy --
Miscellaneous information 6.74.
Title Frigyes (Fr�ed�eric) Riesz.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information 6.75.
Title Luitzen Egbertus Jan Brouwer --
Miscellaneous information 6.76.
Title Emmy Noether --
Miscellaneous information 6.77.
Title Wac?aw Sierpi?ski --
Miscellaneous information 6.78.
Title George Birkhoff --
Miscellaneous information 6.79.
Title John Edensor Littlewood --
Miscellaneous information 6.80.
Title Hermann Weyl --
Miscellaneous information 6.81.
Title Thoralf Skolem --
Miscellaneous information 6.82.
Title Srinivasa Ramanujan --
Miscellaneous information 6.83.
Title Richard Courant --
Miscellaneous information 6.84.
Title Stefan Banach --
Miscellaneous information 6.85.
Title Norbert Wiener --
Miscellaneous information 6.86.
Title Emil Artin --
Miscellaneous information 6.87.
Title Alfred Tarski --
Miscellaneous information 6.88.
Title Andrei Nikolaevich Kolmogorov --
Miscellaneous information 6.89.
Title Alonzo Church --
Miscellaneous information 6.90.
Title William Vallance Douglas Hodge --
Miscellaneous information 6.91.
Title John von Neumann --
Miscellaneous information 6.92.
Title Kurt G�odel --
Miscellaneous information 6.93.
Title Andr�e Weil --
Miscellaneous information 6.94.
Title Alan Turing --
Miscellaneous information 6.95.
Title Abraham Robinson --
Miscellaneous information 6.96.
Title Nicolas Bourbaki.
505 00 - FORMATTED CONTENTS NOTE
Miscellaneous information pt. 7.
Title The influence of mathematics --
Miscellaneous information 7.1.
Title Mathematics and chemistry --
Miscellaneous information 7.2.
Title Mathematical biology --
Miscellaneous information 7.3.
Title Wavelets and applications --
Miscellaneous information 7.4.
Title The mathematics of traffic in networks --
Miscellaneous information 7.5.
Title The mathematics of algorithm design --
Miscellaneous information 7.6
Title Reliable transmission of information --
Miscellaneous information 7.7.
Title Mathematics and cryptography --
Miscellaneous information 7.8.
Title Mathematics and economic reasoning --
Miscellaneous information 7.9.
Title The mathematics of money --
Miscellaneous information 7.10.
Title Mathematical statistics --
Miscellaneous information 7.11.
Title Mathematics and medical statistics --
Miscellaneous information 7.12.
Title Analysis, mathematical and philosophical --
Miscellaneous information 7.13.
Title Mathematics and music --
Miscellaneous information 7.14.
Title Mathematics and art --
Miscellaneous information pt. 8.
Title Final perspectives --
Miscellaneous information 8.1.
Title The art of problem solving --
Miscellaneous information 8.2.
Title "Why mathematics?" you might ask --
Miscellaneous information 8.3.
Title The ubiquity of mathematics --
Miscellaneous information 8.4.
Title Numeracy --
Miscellaneous information 8.5.
Title Mathematics : an experimental science --
Miscellaneous information 8.6.
Title Advice to a young mathematician --
Miscellaneous information 8.7.
Title A chronology of mathematical events --
Miscellaneous information Index.
520 8# - SUMMARY, ETC.
Summary, etc. This text features nearly 200 entries which introduce basic mathematical tools and vocabulary, trace the development of modern mathematics, define essential terms and concepts and put them in context, explain core ideas in major areas of mathematics, and much more.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Mathematics.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Gowers, Timothy.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Barrow-Green, June,
Dates associated with a name 1953-
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Leader, Imre.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element Princeton University.
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