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001399204 020__ $$a9781400830398 (electronic bk.)
001399204 020__ $$a1400830397 (electronic bk.)
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001399204 24504 $$aThe Princeton companion to mathematics$$h[electronic resource] /$$ceditor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader.
001399204 260__ $$aPrinceton, N. J. :$$bPrinceton University Press,$$cc2008.
001399204 300__ $$a1 online resource (xx, 1034 p.) :$$bill.
001399204 500__ $$aAccess restricted to authorized users.
001399204 504__ $$aIncludes bibliographical references and index.
001399204 50500 $$tPreface --$$tContributors --$$gpt. 1.$$tIntroduction --$$g1.1.$$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.
001399204 50500 $$g3.19.$$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.
001399204 50500 $$g3.56.$$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 Schrödinger 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.
001399204 50500 $$gpt. 4.$$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.
001399204 50500 $$gpt. 5.$$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 --$$g5.15.$$tGödel'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 Poincaré 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.
001399204 50500 $$tpt. 6.$$tMathematicians --$$g6.1.$$tPythagoras --$$g6.2.$$tEuclid --$$g6.3.$$tArchimedes --$$g6.4.$$tApollonius --$$g6.5.$$tAbu Jaʾfar 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 --$$g6.18.$$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 --$$g6.27.$$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.
001399204 50500 $$g6.41.$$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.
001399204 50500 $$g6.75.$$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.
001399204 50500 $$gpt. 7.$$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 --$$tIndex.
001399204 506__ $$aAccess limited to authorized users.
001399204 520__ $$aThis text features nearly 200 entries which introduce basic mathematical tools and vocabulary, trace the development of modern mathematics, define essential terms and concepts and put them in context, explain core ideas in major areas of mathematics, and much more.
001399204 588__ $$aBased on print version record.
001399204 650_0 $$aMathematics.
001399204 655_0 $$aElectronic books.
001399204 7001_ $$aGowers, Timothy.
001399204 7001_ $$aBarrow-Green, June,$$d1953-
001399204 7001_ $$aLeader, Imre.
001399204 7102_ $$aPrinceton University.
001399204 77608 $$iPrint version:$$tPrinceton companion to mathematics.$$dPrinceton : Princeton University Press, c2008$$z9780691118802$$w(DLC)  2008020450$$w(OCoLC)227205932
001399204 85280 $$bebk$$hProquest Ebook Central Academic Complete
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