LEADER 00000cam  22000004a 4500 
001    ocn227205932 
003    OCoLC 
005    20091021133605.0 
008    080505t20082008njua     b    001 0 eng   
010      2008020450 
015    GBA898752|2bnb 
016 7  014691695|2Uk 
020    9780691118802|qhardcover|qalkaline paper 
020    0691118809|qhardcover|qalkaline paper 
035    (OCoLC)227205932 
040    DLC|beng|cDLC|dYDXCP|dBAKER|dBTCTA|dUKM|dC#P|dBWX|dCDX
       |dIXA|dNLGGC|dIGR|dNOR|dE5G|dTSU|dAKP|dSTJ 
049    STJR 
050 00 QA11.2|b.P745 2008 
082 00 510|222 
084    31.00|2bcl 
092    510|bP957P 
245 04 The Princeton companion to mathematics /|ceditor, Timothy 
       Gowers ; associate editors, June Barrow-Green, Imre 
       Leader. 
264  1 Princeton :|bPrinceton University Press,|c[2008] 
264  4 |c©2008 
300    xx, 1034 pages :|billustrations ;|c26 cm 
336    text|btxt|2rdacontent 
337    unmediated|bn|2rdamedia 
338    volume|bnc|2rdacarrier 
504    Includes bibliographical references and index. 
505 00 |tPreface --|tContributors --|gpt. 1.|tIntroduction --
       |g1.1.|tWhat is mathematics about? --|g1.2. The|tlanguage 
       and grammar of mathematics --|g1.3.|tSome fundamental 
       mathematical definitions --|g1.4. The|tgeneral goals of 
       mathematical research --|gpt. 2. The|torigins of modern 
       mathematics --|g2.1.|tFrom numbers to number systems --
       |g2.2.|tGeometry --|g2.3. The|tdevelopment of abstract 
       algebra --|g2.4.|tAlgorithms --|g2.5. The|tdevelopment of 
       rigor in mathematical analysis --|g2.6. The|tdevelopment 
       of the idea of proof --|g2.7. The|tcrisis in the 
       foundations of mathematics --|gpt. 3.|tMathematical 
       concepts --|g3.1. The|taxiom of choice --|g3.2. The|taxiom
       of determinacy --|g3.3.|tBayesian analysis --|g3.4.|tBraid
       groups --|g3.5.|tBuildings --|g3.6.|tCalabi-Yau manifolds 
       --|g3.7.|tCardinals --|g3.8.|tCategories --|g3.9.
       |tCompactness and compactification --|g3.10.
       |tComputational complexity classes --|g3.11.|tCountable 
       and uncountable sets --|g3.12.|tC* - algebras --|g3.13.
       |tCurvature --|g3.14.|tDesigns --|g3.15.|tDeterminants --
       |g3.15.|tDifferential forms and integration --|g3.17.
       |tDimension --|g3.18.|tDistributions -- 
505 00 |g3.19.|tDuality --|g3.20.|tDynamical systems and chaos --
       |g3.21.|tElliptic curves --|g3.22. The|tEuclidean 
       algorithm and continued fractions --|g3.23. The|tEuler and
       Navier-Stokes equations --|g3.24.|tExpanders --|g3.25. The
       |texponential and logarithmic functions --|g3.26. The
       |tfast Fourier transform --|g3.27. The|tFourier transform 
       --|g3.28.|tFuchsian groups --|g3.29.|tFunction spaces --
       |g3.30.|tGalois groups --|g3.31. The|tgamma function --
       |g3.32.|tGenerating functions --|g3.33.|tGenus --|g3.34.
       |tGraphs --|g3.35.|tHamiltonians --|g3.36. The|theat 
       equation --|g3.37.|tHilbert spaces --|g3.38.|tHomology and
       cohomology --|g3.39.|tHomotopy Groups --|g3.40. The|tideal
       class group --|g3.41.|tIrrational and transcendental 
       numbers --|g3.42. The|tIsing model --|g3.43.|tJordan 
       normal form --|g3.44.|tKnot polynomials --|g3.45.|tK-
       theory --|g3.46. The|tleech lattice --|g3.47.|tL-function 
       --|g3.48.|tLie theory --|g3.49.|tLinear and nonlinear 
       waves and solitons --|g3.50.|tLinear operators and their 
       properties --|g3.51.|tLocal and global in number theory --
       |g3.52. The|tMandelbrot set --|g3.53.|tManifolds --|g3.54.
       |tMatroids --|g3.55.|tMeasures -- 
505 00 |g3.56.|tMetric spaces --|g3.57.|tModels of set theory --
       |g3.58.|tModular arithmetic --|g3.59.|tModular forms --
       |g3.60.|tModuli spaces --|g3.61. The|tmonster group --
       |g3.62.|tNormed spaces and banach spaces --|g3.63.|tNumber
       fields --|g3.64.|tOptimization and Lagrange multipliers --
       |g3.65.|tOrbifolds --|g3.66.|tOrdinals --|g3.67. The
       |tPeano axioms --|g3.68.|tPermutation groups --|g3.69.
       |tPhase transitions --|g3.70.|t[pi] --|g3.71.|tProbability
       distributions --|g3.72.|tProjective space --|g3.73.
       |tQuadratic forms --|g3.74.|tQuantum computation --|g3.75.
       |tQuantum groups --|g3.76.|tQuaternions, octonions, and 
       normed division algebras --|g3.77.|tRepresentations --
       |g3.78.|tRicci flow --|g3.79.|tRiemann surfaces --|g3.80. 
       The|tRiemann zeta function --|g3.81.|tRings, ideals, and 
       modules --|g3.82.|tSchemes --|g3.83. The|tSchrödinger 
       equation --|g3.84. The|tsimplex algorithm --|g3.85.
       |tSpecial functions --|g3.86. The|tspectrum --|g3.87.
       |tSpherical harmonics --|g3.88.|tSymplectic manifolds --
       |g3.89.|tTensor products --|g3.90.|tTopological spaces --
       |g3.91.|tTransforms --|g3.92.|tTrigonometric functions --
       |g3.93.|tUniversal covers --|g3.94.|tVariational methods -
       -|g3.95.|tVarieties --|g3.96.|tVector bundles --|g3.97.
       |tVon Neumann algebras --|g3.98.|tWavelets --|g3.99. The
       |tZermelo-Fraenkel axioms -- 
505 00 |gpt. 4.|tBranches of mathematics --|g4.1.|tAlgebraic 
       numbers --|g4.2.|tAnalytic number theory --|g4.3.
       |tComputational number theory --|g4.4.|tAlgebraic geometry
       --|g4.5.|tArithmetic geometry --|g4.6.|tAlgebraic topology
       --|g4.7.|tDifferential topology --|g4.8.|tModuli spaces --
       |g4.9.|tRepresentation theory --|g4.10.|tGeometric and 
       combinatorial group theory --|g4.11.|tHarmonic analysis --
       |g4.12.|tPartial differential equations --|g4.13.|tGeneral
       relativity and the Einstein equations --|g4.14.|tDynamics 
       --|g4.15.|tOperator algebras --|g4.16.|tMirror symmetry --
       |g4.17.|tVertex operator algebras --|g4.18.|tEnumerative 
       and algebraic combinatorics --|g4.19.|tExtremal and 
       probabilistic combinatorics --|g4.20.|tComputational 
       complexity --|g4.21.|tNumerical analysis --|g4.22.|tSet 
       theory --|g4.23.|tLogic and model theory --|g4.24.
       |tStochastic processes --|g4.25.|tProbabilistic models of 
       critical phenomena --|g4.26.|tHigh-dimensional geometry 
       and its probabilistic analogues -- 
505 00 |gpt. 5.|tTheorems and problems --|g5.1. The|tABC 
       conjecture --|g5.2. The|tAtiyah-Singer index theorem --
       |g5.3. The|tBanach-Tarski paradox --|g5.4. The|tBirch-
       Swinnerton-Dyer conjecture --|g5.5.|tCarleson's theorem --
       |g5.6. The|tcentral limit theorem --|g5.7. The
       |tclassification of finite simple groups --|g5.8.
       |tDirichlet's theorem --|g5.9.|tErgodic theorems --|g5.10.
       |tFermat's last theorem --|g5.11.|tFixed point theorems --
       |g5.12. The|tfour-color theorem --|g5.13. The|tfundamental
       theorem of algebra --|g5.14. The|tfundamental theorem of 
       arithmetic --|g5.15.|tGödel's theorem --|g5.16.|tGromov's 
       polynomial-growth theorem --|g5.17.|tHilbert's 
       nullstellensatz --|g5.18. The|tindependence of the 
       continuum hypothesis --|g5.19.|tInequalities --|g5.20. The
       |tinsolubility of the halting problem --|g5.21. The
       |tinsolubility of the quintic --|g5.22.|tLiouville's 
       theorem and Roth's theorem --|g5.23.|tMostow's strong 
       rigidity theorem --|g5.24. The|tp versus NP problem --
       |g5.25. The|tPoincaré conjecture --|g5.26. The|tprime 
       number theorem and the Riemann hypothesis --|g5.27.
       |tProblems and results in additive number theory --|g5.28.
       |tFrom quadratic reciprocity to class field theory --
       |g5.29.|tRational points on curves and the Mordell 
       conjecture --|g5.30. The|tresolution of singularities --
       |g5.31. The|tRiemann-Roch theorem --|g5.32. The|tRobertson
       -Seymour theorem --|g5.33. The|tthree-body problem --
       |g5.34. The|tuniformization theorem --|g5.35. The|tWeil 
       conjecture -- 
505 00 |tpt. 6.|tMathematicians --|g6.1.|tPythagoras --|g6.2.
       |tEuclid --|g6.3.|tArchimedes --|g6.4.|tApollonius --
       |g6.5.|tAbu Jaʼfar Muhammad ibn Mūsā al-Khwārizmī --|g6.6.
       |tLeonardo of Pisa (known as Fibonacci) --|g6.7.|tGirolamo
       Cardano --|g6.8.|tRafael Bombelli --|g6.9.|tFrançois Viète
       --|g6.10.|tSimon Stevin --|g6.11.|tRené Descartes --
       |g6.12.|tPierre Fermat --|g6.13.|tBlaise Pascal --|g6.14.
       |tIsaac Newton --|g6.15.|tGottfried Wilhelm Leibniz --
       |g6.16.|tBrook Taylor --|g6.17.|tChristian Goldbach --
       |g6.18. The|tBernoullis --|g6.19.|tLeonhard Euler --
       |g6.20.|tJean Le Rond d'Alembert --|g6.21.|tEdward Waring 
       --|g6.22.|tJoseph Louis Lagrange --|g6.23.|tPierre-Simon 
       Laplace --|g6.24.|tAdrien-Marie Legendre --|g6.25.|tJean-
       Baptiste Joseph Fourier --|g6.26.|tCarl Friedrich Gauss --
       |g6.27.|tSiméon-Denis Poisson --|g6.28.|tBernard Bolzano -
       -|g6.29.|tAugustin-Louis Cauchy --|g6.30.|tAugust 
       Ferdinand Möbius --|g6.31.|tNicolai Ivanovich Lobachevskii
       --|g6.32.|tGeorge Green --|g6.33.|tNiels Henrik Abel --
       |g6.34.|tJános Bolyai --|g6.35.|tCarl Gustav Jacob Jacobi 
       --|g6.36.|tPeter Gustav Lejeune Dirichlet --|g6.37.
       |tWilliam Rowan Hamilton --|g6.38.|tAugustus De Morgan --
       |g6.39.|tJoseph Liouville --|g6.40.|tEduard Kummer -- 
505 00 |g6.41.|tÉvariste Galois --|g6.42.|tJames Joseph Sylvester
       --|g6.43.|tGeorge Boole --|g6.44.|tKarl Weierstrass --
       |g6.45.|tPafnuty Chebyshev --|g6.46.|tArthur Cayley --
       |g6.47.|tCharles Hermite --|g6.48.|tLeopold Kronecker --
       |g6.49.|tGeorg Friedrich Bernhard Riemann --|g6.50.
       |tJulius Wilhelm Richard Dedekind --|g6.51.|tÉmile Léonard
       Mathieu --|g6.52.|tCamille Jordan --|g6.53.|tSophus Lie --
       |g6.54.|tGeorg Cantor --|g6.55.|tWilliam Kingdon Clifford 
       --|g6.56.|tGottlob Frege --|g6.57.|tChristian Felix Klein 
       --|g6.58.|tFerdinand Georg Frobenius --|g6.59.|tSofya 
       (Sonya) Kovalevskaya --|g6.60.|tWilliam Burnside --|g6.61.
       |tJules Henri Poincaré --|g6.62.|tGiuseppe Peano --|g6.63.
       |tDavid Hilbert --|g6.64.|tHermann Minkowski --|g6.65.
       |tJacques Hadamard --|g6.66.|tIvar Fredholm --|g6.67.
       |tCharles-Jean de la Vallée Poussin --|g6.68.|tFelix 
       Hausdorff --|g6.69.|tÉlie Joseph Cartan --|g6.70.|tEmile 
       Borel --|g6.71.|tBertrand Arthur William Russell --|g6.72.
       |tHenri Lebesgue --|g6.73.|tGodfrey Harold Hardy --|g6.74.
       |tFrigyes (Frédéric) Riesz -- 
505 00 |g6.75.|tLuitzen Egbertus Jan Brouwer --|g6.76.|tEmmy 
       Noether --|g6.77.|tWacław Sierpiński --|g6.78.|tGeorge 
       Birkhoff --|g6.79.|tJohn Edensor Littlewood --|g6.80.
       |tHermann Weyl --|g6.81.|tThoralf Skolem --|g6.82.
       |tSrinivasa Ramanujan --|g6.83.|tRichard Courant --|g6.84.
       |tStefan Banach --|g6.85.|tNorbert Wiener --|g6.86.|tEmil 
       Artin --|g6.87.|tAlfred Tarski --|g6.88.|tAndrei 
       Nikolaevich Kolmogorov --|g6.89.|tAlonzo Church --|g6.90.
       |tWilliam Vallance Douglas Hodge --|g6.91.|tJohn von 
       Neumann --|g6.92.|tKurt Gödel --|g6.93.|tAndré Weil --
       |g6.94.|tAlan Turing --|g6.95.|tAbraham Robinson --|g6.96.
       |tNicolas Bourbaki -- 
505 00 |gpt. 7. The|tinfluence of mathematics --|g7.1.
       |tMathematics and chemistry --|g7.2.|tMathematical biology
       --|g7.3.|tWavelets and applications --|g7.4. The
       |tmathematics of traffic in networks --|g7.5. The
       |tmathematics of algorithm design --|g7.6|tReliable 
       transmission of information --|g7.7.|tMathematics and 
       cryptography --|g7.8.|tMathematics and economic reasoning 
       --|g7.9. The|tmathematics of money --|g7.10.|tMathematical
       statistics --|g7.11.|tMathematics and medical statistics -
       -|g7.12.|tAnalysis, mathematical and philosophical --
       |g7.13.|tMathematics and music --|g7.14.|tMathematics and 
       art --|gpt. 8.|tFinal perspectives --|g8.1. The|tart of 
       problem solving --|g8.2.|t"Why mathematics?" you might ask
       --|g8.3. The|tubiquity of mathematics --|g8.4.|tNumeracy -
       -|g8.5.|tMathematics : an experimental science --|g8.6.
       |tAdvice to a young mathematician --|g8.7. A|tchronology 
       of mathematical events --|tIndex. 
650  0 Mathematics. 
700 1  Gowers, Timothy. 
700 1  Barrow-Green, June,|d1953- 
700 1  Leader, Imre. 
710 2  Princeton University. 
856 41 |3Table of contents only|uhttp://www.loc.gov/catdir/toc/
       ecip0818/2008020450.html 
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