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015 _aGBA898752
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020 _a9780691118802 (hardcover : alk. paper)
020 _a0691118809 (hardcover : alk. paper)
035 _a(OCoLC)227205932
050 0 0 _aREF QA 11.2
_b.P745 2008
049 _aVF$R
245 0 4 _aThe Princeton companion to mathematics /
_ceditor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader.
260 _aPrinceton :
_bPrinceton University Press,
_cc2008.
300 _axx, 1034 p. :
_bill. ;
_c26 cm.
504 _aIncludes bibliographical references and index.
505 0 0 _gPreface --
_gContributors --
_gpt. 1.
_gIntroduction --
_g1.1.
_tWhat is mathematics about? --
_g1.2.
_tThe language and grammar of mathematics --
_g1.3.
_tSome fundamental mathematical definitions --
_g1.4.
_tThe general goals of mathematical research --
_gpt. 2.
_tThe origins of modern mathematics --
_g2.1.
_tFrom numbers to number systems --
_g2.2.
_tGeometry --
_g2.3.
_tThe development of abstract algebra --
_g2.4.
_tAlgorithms --
_g2.5.
_tThe development of rigor in mathematical analysis --
_g2.6.
_tThe development of the idea of proof --
_g2.7.
_tThe crisis in the foundations of mathematics --
_gpt. 3.
_tMathematical concepts --
_g3.1.
_tThe axiom of choice --
_g3.2.
_tThe axiom 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 0 0 _g3.19.
_tDuality --
_g3.20.
_tDynamical systems and chaos --
_g3.21.
_tElliptic curves --
_g3.22.
_tThe Euclidean algorithm and continued fractions --
_g3.23.
_tThe Euler and Navier-Stokes equations --
_g3.24.
_tExpanders --
_g3.25.
_tThe exponential and logarithmic functions --
_g3.26.
_tThe fast Fourier transform --
_g3.27.
_tThe Fourier transform --
_g3.28.
_tFuchsian groups --
_g3.29.
_tFunction spaces --
_g3.30.
_tGalois groups --
_g3.31.
_tThe gamma function --
_g3.32.
_tGenerating functions --
_g3.33.
_tGenus --
_g3.34.
_tGraphs --
_g3.35.
_tHamiltonians --
_g3.36.
_tThe heat equation --
_g3.37.
_tHilbert spaces --
_g3.38.
_tHomology and cohomology --
_g3.39.
_tHomotopy Groups --
_g3.40.
_tThe ideal class group --
_g3.41.
_tIrrational and transcendental numbers --
_g3.42.
_tThe Ising model --
_g3.43.
_tJordan normal form --
_g3.44.
_tKnot polynomials --
_g3.45.
_tK-theory --
_g3.46.
_tThe leech 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.
_tThe Mandelbrot set --
_g3.53.
_tManifolds --
_g3.54.
_tMatroids --
_g3.55.
_tMeasures.
505 0 0 _g3.56.
_tMetric spaces --
_g3.57.
_tModels of set theory --
_g3.58.
_tModular arithmetic --
_g3.59.
_tModular forms --
_g3.60.
_tModuli spaces --
_g3.61.
_tThe monster 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.
_tThe Peano 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.
_tThe Riemann zeta function --
_g3.81.
_tRings, ideals, and modules --
_g3.82.
_tSchemes --
_g3.83.
_tThe Schr�odinger equation --
_g3.84.
_tThe simplex algorithm --
_g3.85.
_tSpecial functions --
_g3.86.
_tThe spectrum --
_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.
_tThe Zermelo-Fraenkel axioms.
505 0 0 _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 0 0 _gpt. 5.
_tTheorems and problems --
_g5.1.
_tThe ABC conjecture --
_g5.2.
_tThe Atiyah-Singer index theorem --
_g5.3.
_tThe Banach-Tarski paradox --
_g5.4.
_tThe Birch-Swinnerton-Dyer conjecture --
_g5.5.
_tCarleson's theorem --
_g5.6.
_tThe central limit theorem --
_g5.7.
_tThe classification 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.
_tThe four-color theorem --
_g5.13.
_tThe fundamental theorem of algebra --
_g5.14.
_tThe fundamental theorem of arithmetic --
_g5.15.
_tG�odel's theorem --
_g5.16.
_tGromov's polynomial-growth theorem --
_g5.17.
_tHilbert's nullstellensatz --
_g5.18.
_tThe independence of the continuum hypothesis --
_g5.19.
_tInequalities --
_g5.20.
_tThe insolubility of the halting problem --
_g5.21.
_tThe insolubility of the quintic --
_g5.22.
_tLiouville's theorem and Roth's theorem --
_g5.23.
_tMostow's strong rigidity theorem --
_g5.24.
_tThe p versus NP problem --
_g5.25.
_tThe Poincar�e conjecture --
_g5.26.
_tThe prime 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.
_tThe resolution of singularities --
_g5.31.
_tThe Riemann-Roch theorem --
_g5.32.
_tThe Robertson-Seymour theorem --
_g5.33.
_tThe three-body problem --
_g5.34.
_tThe uniformization theorem --
_g5.35.
_tThe Weil conjecture.
505 0 0 _gpt. 6.
_tMathematicians --
_g6.1.
_tPythagoras --
_g6.2.
_tEuclid --
_g6.3.
_tArchimedes --
_g6.4.
_tApollonius --
_g6.5.
_tAbu Ja'far Muhammad ibn M?s? al-Khw?rizm? --
_g6.6.
_tLeonardo of Pisa (known as Fibonacci) --
_g6.7.
_tGirolamo Cardano --
_g6.8.
_tRafael Bombelli --
_g6.9.
_tFran�cois Vi�ete --
_g6.10.
_tSimon Stevin --
_g6.11.
_tRen�e 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.
_tThe Bernoullis --
_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.
_tSim�eon-Denis Poisson --
_g6.28.
_tBernard Bolzano --
_g6.29.
_tAugustin-Louis Cauchy --
_g6.30.
_tAugust Ferdinand M�obius --
_g6.31.
_tNicolai Ivanovich Lobachevskii --
_g6.32.
_tGeorge Green --
_g6.33.
_tNiels Henrik Abel --
_g6.34.
_tJ�anos 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 0 0 _g6.41.
_t�Evariste 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.
_t�Emile L�eonard 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 Poincar�e --
_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 Vall�ee Poussin --
_g6.68.
_tFelix Hausdorff --
_g6.69.
_t�Elie Joseph Cartan --
_g6.70.
_tEmile Borel --
_g6.71.
_tBertrand Arthur William Russell --
_g6.72.
_tHenri Lebesgue --
_g6.73.
_tGodfrey Harold Hardy --
_g6.74.
_tFrigyes (Fr�ed�eric) Riesz.
505 0 0 _g6.75.
_tLuitzen Egbertus Jan Brouwer --
_g6.76.
_tEmmy Noether --
_g6.77.
_tWac?aw Sierpi?ski --
_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 G�odel --
_g6.93.
_tAndr�e Weil --
_g6.94.
_tAlan Turing --
_g6.95.
_tAbraham Robinson --
_g6.96.
_tNicolas Bourbaki.
505 0 0 _gpt. 7.
_tThe influence of mathematics --
_g7.1.
_tMathematics and chemistry --
_g7.2.
_tMathematical biology --
_g7.3.
_tWavelets and applications --
_g7.4.
_tThe mathematics of traffic in networks --
_g7.5.
_tThe mathematics of algorithm design --
_g7.6
_tReliable transmission of information --
_g7.7.
_tMathematics and cryptography --
_g7.8.
_tMathematics and economic reasoning --
_g7.9.
_tThe mathematics 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.
_tThe art of problem solving --
_g8.2.
_t"Why mathematics?" you might ask --
_g8.3.
_tThe ubiquity of mathematics --
_g8.4.
_tNumeracy --
_g8.5.
_tMathematics : an experimental science --
_g8.6.
_tAdvice to a young mathematician --
_g8.7.
_tA chronology of mathematical events --
_gIndex.
520 8 _aThis 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 _aMathematics.
700 1 _aGowers, Timothy.
700 1 _aBarrow-Green, June,
_d1953-
700 1 _aLeader, Imre.
710 2 _aPrinceton University.
856 4 1 _3Table of contents only
_uhttp://catdir.loc.gov/catdir/toc/ecip0818/2008020450.html
856 4 1 _3Table of contents
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