| Description |
1 online resource (xx, 1034 pages) : illustrations |
| Physical Medium |
monochrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references and index. |
| Summary |
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. |
| Contents |
pt. 1. Introduction ; What is mathematics about? ; Language and grammar of mathematics ; Some fundamental mathematical definitions ; General goals of mathematical research -- pt. 2. Origins of modern mathematics ; From numbers to number systems ; Geometry ; Development of abstract algebra ; Algorithms ; Development of rigor in mathematical analysis ; Development of the idea of proof ; Crisis in the foundations of mathematics -- pt. 3. Mathematical concepts ; Axiom of choice ; Axiom of determinacy ; Bayesian analysis ; Braid groups ; Buildings ; Calabi-Yau manifolds ; Cardinals ; Categories ; Compactness and compactification ; Computational complexity classes ; Countable and uncountable sets ; C*-algebras ; Curvature ; Designs ; Determinants ; Differential forms and integration ; Dimension ; Distributions ; Duality ; Dynamical systems and chaos ; Elliptic curves ; Euclidean algorithm and continued fractions ; Euler and Navier-Stokes equations ; Expanders ; Exponential and logarithmic functions ; Fast Fourier transform ; Fourier transform ; Fuchsian groups ; Function spaces ; Galois groups ; Gamma function ; Generating functions ; Genus ; Graphs ; Hamiltonians ; Heat equation ; Hilbert spaces ; Homology and cohomology ; Homotopy Groups ; Ideal class group ; Irrational and transcendental numbers ; Ising model ; Jordan normal form ; Knot polynomials ; K-theory ; The leech lattice ; L-function ; Lie theory ; Linear and nonlinear waves and solitons ; Linear operators and their properties ; Local and global in number theory ; Mandelbrot set ; Manifolds ; Matroids ; Measures ; Metric spaces ; Models of set theory ; Modular arithmetic ; Modular forms ; Moduli spaces ; Monster group ; Normed spaces and banach spaces ; Number fields ; Optimization and Lagrange multipliers ; Orbifolds ; Ordinals. |
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Peano axioms ; Permutation groups ; Phase transitions ; [pi] ; Probability distributions ; Projective space ; Quadratic forms ; Quantum computation ; Quantum groups ; Quaternions, octonions, and normed division algebras ; Representations ; Ricci flow ; Riemann surfaces ; Riemann zeta function ; Rings, ideals, and modules ; Schemes ; Schrödinger equation ; Simplex algorithm ; Special functions ; Spectrum ; Spherical harmonics ; Symplectic manifolds ; Tensor products ; Topological spaces ; Transforms ; Trigonometric functions ; Universal covers ; Variational methods ; Varieties ; Vector bundles ; Von Neumann algebras ; Wavelets ; Zermelo-Fraenkel axioms ; Metric spaces ; Models of set theory ; Modular arithmetic ; Modular forms ; Moduli spaces ; Monster group ; Normed spaces and banach spaces ; Number fields ; Optimization and Lagrange multipliers ; Orbifolds ; Ordinals ; Peano axioms ; Permutation groups ; Phase transitions ; [pi] ; Probability distributions ; Projective space ; Quadratic forms ; Quantum computation ; Quantum groups ; Quaternions, octonions, and normed division algebras ; Representations ; Ricci flow ; Riemann surfaces ; Riemann zeta function ; Rings, ideals, and modules ; Schemes ; Schrödinger equation ; Simplex algorithm ; Special functions ; Spectrum ; Spherical harmonics ; Symplectic manifolds ; Tensor products ; Topological spaces ; Transforms ; Trigonometric functions ; Universal covers ; Variational methods ; Varieties ; Vector bundles ; Von Neumann algebras ; Wavelets ; Zermelo-Fraenkel axioms. |
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pt. 4. Branches of mathematics ; Algebraic numbers ; Analytic number theory ; Computational number theory ; Algebraic geometry ; Arithmetic geometry ; Algebraic topology ; Differential topology ; Moduli spaces ; Representation theory ; Geometric and combinatorial group theory ; Harmonic analysis ; Partial differential equations ; General relativity and the Einstein equations ; Dynamics ; Operator algebras ; Mirror symmetry ; Vertex operator algebras ; Enumerative and algebraic combinatorics ; Extremal and probabilistic combinatorics ; Computational complexity ; Numerical analysis ; Set theory ; Logic and model theory ; Stochastic processes ; Probabilistic models of critical phenomena ; High-dimensional geometry and its probabilistic analogues -- pt. 5. Theorems and problems ; ABC conjecture ; Atiyah-Singer index theorem ; Banach-Tarski paradox ; Birch-Swinnerton-Dyer conjecture ; Carleson's theorem ; Central limit theorem ; Classification of finite simple groups ; Dirichlet's theorem ; Ergodic theorems ; Fermat's last theorem ; Fixed point theorems ; Four-color theorem ; Fundamental theorem of algebra ; Fundamental theorem of arithmetic ; Gödel's theorem ; Gromov's polynomial-growth theorem ; Hilbert's nullstellensatz ; Independence of the continuum hypothesis ; Inequalities ; Insolubility of the halting problem ; Insolubility of the quintic ; Liouville's theorem and Roth's theorem ; Mostow's strong rigidity theorem ; P versus NP problem ; Poincaré conjecture ; Prime number theorem and the Riemann hypothesis ; Problems and results in additive number theory ; From quadratic reciprocity to class field theory ; Rational points on curves and the Mordell conjecture ; Resolution of singularities ; Riemann-Roch theorem ; Robertson-Seymour theorem ; Three-body problem ; Uniformization theorem ; Weil conjecture. |
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pt. 6. Mathematicians ; Pythagoras ; Euclid ; Archimedes ; Apollonius ; Abu Jaʼfar Muhammad ibn Mūsā al-Khwārizmī ; Leonardo of Pisa (known as Fibonacci) ; Girolamo Cardano ; Rafael Bombelli ; François Viète ; Simon Stevin ; René Descartes ; Pierre Fermat ; Blaise Pascal ; Isaac Newton ; Gottfried Wilhelm Leibniz ; Brook Taylor ; Christian Goldbach ; Bernoullis ; Leonhard Euler ; Jean Le Rond d'Alembert ; Edward Waring ; Joseph Louis Lagrange ; Pierre-Simon Laplace ; Adrien-Marie Legendre ; Jean-Baptiste Joseph Fourier ; Carl Friedrich Gauss ; Siméon-Denis Poisson ; Bernard Bolzano ; Augustin-Louis Cauchy ; August Ferdinand Möbius ; Nicolai Ivanovich Lobachevskii ; George Green ; Niels Henrik Abel ; János Bolyai ; Carl Gustav Jacob Jacobi ; Peter Gustav Lejeune Dirichlet ; William Rowan Hamilton ; Augustus De Morgan ; Joseph Liouville ; Eduard Kumme ; Évariste Galois ; James Joseph Sylvester ; George Boole ; Karl Weierstrass ; Pafnuty Chebyshev ; Arthur Cayley ; Charles Hermite ; Leopold Kronecker ; Georg Friedrich Bernhard Riemann ; Julius Wilhelm Richard Dedekind ; Émile Léonard Mathieu ; Camille Jordan ; Sophus Lie ; Georg Cantor ; William Kingdon Clifford ; Gottlob Frege ; Christian Felix Klein ; Ferdinand Georg Frobenius ; Sofya (Sonya) Kovalevskaya ; William Burnside ; Jules Henri Poincaré ; Giuseppe Peano ; David Hilbert ; Hermann Minkowski ; Jacques Hadamard ; Ivar Fredholm ; Charles-Jean de la Vallée Poussin ; Felix Hausdorff ; Élie Joseph Cartan ; Emile Borel ; Bertrand Arthur William Russell ; Henri Lebesgue ; Godfrey Harold Hardy ; Frigyes (Frédéric) Riesz. |
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Luitzen Egbertus Jan Brouwer ; Emmy Noether ; Wacław Sierpiński ; George Birkhoff ; John Edensor Littlewood ; Hermann Weyl ; Thoralf Skolem ; Srinivasa Ramanujan ; Richard Courant ; Stefan Banach ; Norbert Wiener ; Emil Artin ; Alfred Tarski ; Andrei Nikolaevich Kolmogorov ; Alonzo Church ; William Vallance Douglas Hodge ; John von Neumann ; Kurt Gödel ; André Weil ; Alan Turing ; Abraham Robinson ; Nicolas Bourbaki -- pt. 7. Influence of mathematics ; Mathematics and chemistry ; Mathematical biology ; Wavelets and applications ; Mathematics of traffic in networks ; Mathematics of algorithm design ; Reliable transmission of information ; Mathematics and cryptography ; Mathematics and economic reasoning ; Mathematics of money ; Mathematical statistics ; Mathematics and medical statistics ; Analysis, mathematical and philosophical ; Mathematics and music ; Mathematics and art -- pt. 8. Final perspectives ; Art of problem solving ; "Why mathematics?" you might ask ; Ubiquity of mathematics ; Numeracy ; Mathematics : an experimental science ; Advice to a young mathematician ; A chronology of mathematical. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematics.
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Mathematics. |
| Genre/Form |
Electronic reference sources.
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Electronic books.
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Electronic books.
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| Added Author |
Gowers, Timothy.
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Barrow-Green, June, 1953-
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Leader, Imre.
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Princeton University.
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| Other Form: |
Print version: Princeton companion to mathematics. Princeton : Princeton University Press, ©2008 9780691118802 0691118809 (DLC) 2008020450 (OCoLC)227205932 |
| ISBN |
9781400830398 (electronic book) |
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1400830397 (electronic book) |
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9780691118802 (hardcover ; alkaline paper) |
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0691118809 (hardcover ; alkaline paper) |
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1282767194 |
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9781282767195 |
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