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The Resource The Princeton companion to mathematics, editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader

The Princeton companion to mathematics, editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader

Label
The Princeton companion to mathematics
Title
The Princeton companion to mathematics
Statement of responsibility
editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader
Contributor
Subject
Genre
Language
eng
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
Cataloging source
N$T
Illustrations
illustrations
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1953-
http://library.link/vocab/relatedWorkOrContributorName
  • Gowers, Timothy
  • Barrow-Green, June
  • Leader, Imre
  • Princeton University
http://library.link/vocab/subjectName
  • Mathematics
  • MATHEMATICS
  • MATHEMATICS
  • MATHEMATICS
  • Mathematics
  • Mathematik
  • Mathematics Teaching & Research
  • Mathematics
  • Physical Sciences & Mathematics
Label
The Princeton companion to mathematics, editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • From numbers to number systems
  • Geometry
  • The development of abstract algebra
  • Algorithms
  • The development of rigor in mathematical analysis
  • The development of the idea of proof
  • The crisis in the foundations of mathematics
  • pt. 3.
  • Mathematical concepts
  • The axiom of choice
  • pt. 1.
  • The axiom of determinacy
  • Bayesian analysis
  • Braid groups
  • Buildings
  • Calabi-Yau manifolds
  • Cardinals
  • Categories
  • Compactness and compactification
  • Computational complexity classes
  • Countable and uncountable sets
  • Introduction
  • C*-algebras
  • Curvature
  • Designs
  • Determinants
  • Differential forms and integration
  • Dimension
  • Distributions
  • Duality
  • Dynamical systems and chaos
  • Elliptic curves
  • What is mathematics about?
  • The Euclidean algorithm and continued fractions
  • The Euler and Navier-Stokes equations
  • Expanders
  • The exponential and logarithmic functions
  • The fast Fourier transform
  • The Fourier transform
  • Fuchsian groups
  • Function spaces
  • Galois groups
  • The gamma function
  • The language and grammar of mathematics
  • Generating functions
  • Genus
  • Graphs
  • Hamiltonians
  • The heat equation
  • Hilbert spaces
  • Homology and cohomology
  • Homotopy Groups
  • The ideal class group
  • Irrational and transcendental numbers
  • Some fundamental mathematical definitions
  • The 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
  • The Mandelbrot set
  • The general goals of mathematical research
  • Manifolds
  • Matroids
  • Measures
  • Metric spaces
  • Models of set theory
  • Modular arithmetic
  • Modular forms
  • Moduli spaces
  • The monster group
  • Normed spaces and banach spaces
  • pt. 2.
  • Number fields
  • Optimization and Lagrange multipliers
  • Orbifolds
  • Ordinals
  • The origins of modern mathematics
  • Quantum groups
  • Quaternions, octonions, and normed division algebras
  • Representations
  • Ricci flow
  • Riemann surfaces
  • The Riemann zeta function
  • Rings, ideals, and modules
  • Schemes
  • The Schrödinger equation
  • The simplex algorithm
  • The Peano axioms
  • Special functions
  • The spectrum
  • Spherical harmonics
  • Symplectic manifolds
  • Tensor products
  • Topological spaces
  • Transforms
  • Trigonometric functions
  • Universal covers
  • Variational methods
  • Permutation groups
  • Varieties
  • Vector bundles
  • Von Neumann algebras
  • Wavelets
  • The Zermelo-Fraenkel axioms
  • Metric spaces
  • Models of set theory
  • Modular arithmetic
  • Modular forms
  • Moduli spaces
  • Phase transitions
  • The monster group
  • Normed spaces and banach spaces
  • Number fields
  • Optimization and Lagrange multipliers
  • Orbifolds
  • Ordinals
  • The Peano axioms
  • Permutation groups
  • Phase transitions
  • [pi]
  • [pi]
  • Probability distributions
  • Projective space
  • Quadratic forms
  • Quantum computation
  • Quantum groups
  • Quaternions, octonions, and normed division algebras
  • Representations
  • Ricci flow
  • Riemann surfaces
  • The Riemann zeta function
  • Probability distributions
  • Rings, ideals, and modules
  • Schemes
  • The Schrödinger equation
  • The simplex algorithm
  • Special functions
  • The spectrum
  • Spherical harmonics
  • Symplectic manifolds
  • Tensor products
  • Topological spaces
  • Projective space
  • Transforms
  • Trigonometric functions
  • Universal covers
  • Variational methods
  • Varieties
  • Vector bundles
  • Von Neumann algebras
  • Wavelets
  • The Zermelo-Fraenkel axioms
  • Quadratic forms
  • Quantum computation
  • 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
  • pt. 4.
  • 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.
  • Branches of mathematics
  • Theorems and problems
  • The ABC conjecture
  • The Atiyah-Singer index theorem
  • The Banach-Tarski paradox
  • The Birch-Swinnerton-Dyer conjecture
  • Carleson's theorem
  • The central limit theorem
  • The classification of finite simple groups
  • Dirichlet's theorem
  • Ergodic theorems
  • Algebraic numbers
  • Fermat's last theorem
  • Fixed point theorems
  • The four-color theorem
  • The fundamental theorem of algebra
  • The fundamental theorem of arithmetic
  • Gödel's theorem
  • Gromov's polynomial-growth theorem
  • Hilbert's nullstellensatz
  • The independence of the continuum hypothesis
  • Inequalities
  • Analytic number theory
  • The insolubility of the halting problem
  • The insolubility of the quintic
  • Liouville's theorem and Roth's theorem
  • Mostow's strong rigidity theorem
  • The p versus NP problem
  • The Poincaré conjecture
  • The 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
  • Computational number theory
  • The resolution of singularities
  • The Riemann-Roch theorem
  • The Robertson-Seymour theorem
  • The three-body problem
  • The uniformization theorem
  • The Weil conjecture
  • Algebraic geometry
  • Arithmetic geometry
  • Algebraic topology
  • Girolamo Cardano
  • Rafael Bombelli
  • François Viète
  • Simon Stevin
  • René Descartes
  • Pierre Fermat
  • Blaise Pascal
  • Isaac Newton
  • Gottfried Wilhelm Leibniz
  • Brook Taylor
  • pt. 6.
  • Christian Goldbach
  • The 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
  • Mathematicians
  • 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
  • Pythagoras
  • William Rowan Hamilton
  • Augustus De Morgan
  • Joseph Liouville
  • Eduard Kumme
  • Évariste Galois
  • James Joseph Sylvester
  • George Boole
  • Karl Weierstrass
  • Pafnuty Chebyshev
  • Arthur Cayley
  • Euclid
  • 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
  • Archimedes
  • Christian Felix Klein
  • Ferdinand Georg Frobenius
  • Sofya (Sonya) Kovalevskaya
  • William Burnside
  • Jules Henri Poincaré
  • Giuseppe Peano
  • David Hilbert
  • Hermann Minkowski
  • Jacques Hadamard
  • Ivar Fredholm
  • Apollonius
  • 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
  • Abu Jaʼfar Muhammad ibn Mūsā al-Khwārizmī
  • Leonardo of Pisa (known as Fibonacci)
  • Richard Courant
  • Stefan Banach
  • Norbert Wiener
  • Emil Artin
  • Alfred Tarski
  • Andrei Nikolaevich Kolmogorov
  • Alonzo Church
  • William Vallance Douglas Hodge
  • John von Neumann
  • Kurt Gödel
  • Luitzen Egbertus Jan Brouwer
  • André Weil
  • Alan Turing
  • Abraham Robinson
  • Nicolas Bourbaki
  • pt. 7.
  • The influence of mathematics
  • Mathematics and chemistry
  • Mathematical biology
  • Wavelets and applications
  • The mathematics of traffic in networks
  • Emmy Noether
  • The mathematics of algorithm design
  • Reliable transmission of information
  • Mathematics and cryptography
  • Mathematics and economic reasoning
  • The mathematics of money
  • Mathematical statistics
  • Mathematics and medical statistics
  • Analysis, mathematical and philosophical
  • Mathematics and music
  • Mathematics and art
  • Wacław Sierpiński
  • pt. 8.
  • Final perspectives
  • The art of problem solving
  • "Why mathematics?" you might ask
  • The ubiquity of mathematics
  • Numeracy
  • Mathematics : an experimental science
  • Advice to a young mathematician
  • A chronology of mathematical
  • George Birkhoff
  • John Edensor Littlewood
  • Hermann Weyl
  • Thoralf Skolem
  • Srinivasa Ramanujan
Control code
ocn659590835
Dimensions
unknown
Extent
1 online resource (xx, 1034 pages)
Form of item
online
Isbn
9786612767197
Lccn
2008020450
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
2831458
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
  • cl0500000161
  • 22573/ctt10z4n
Specific material designation
remote
System control number
(OCoLC)659590835
Label
The Princeton companion to mathematics, editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • From numbers to number systems
  • Geometry
  • The development of abstract algebra
  • Algorithms
  • The development of rigor in mathematical analysis
  • The development of the idea of proof
  • The crisis in the foundations of mathematics
  • pt. 3.
  • Mathematical concepts
  • The axiom of choice
  • pt. 1.
  • The axiom of determinacy
  • Bayesian analysis
  • Braid groups
  • Buildings
  • Calabi-Yau manifolds
  • Cardinals
  • Categories
  • Compactness and compactification
  • Computational complexity classes
  • Countable and uncountable sets
  • Introduction
  • C*-algebras
  • Curvature
  • Designs
  • Determinants
  • Differential forms and integration
  • Dimension
  • Distributions
  • Duality
  • Dynamical systems and chaos
  • Elliptic curves
  • What is mathematics about?
  • The Euclidean algorithm and continued fractions
  • The Euler and Navier-Stokes equations
  • Expanders
  • The exponential and logarithmic functions
  • The fast Fourier transform
  • The Fourier transform
  • Fuchsian groups
  • Function spaces
  • Galois groups
  • The gamma function
  • The language and grammar of mathematics
  • Generating functions
  • Genus
  • Graphs
  • Hamiltonians
  • The heat equation
  • Hilbert spaces
  • Homology and cohomology
  • Homotopy Groups
  • The ideal class group
  • Irrational and transcendental numbers
  • Some fundamental mathematical definitions
  • The 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
  • The Mandelbrot set
  • The general goals of mathematical research
  • Manifolds
  • Matroids
  • Measures
  • Metric spaces
  • Models of set theory
  • Modular arithmetic
  • Modular forms
  • Moduli spaces
  • The monster group
  • Normed spaces and banach spaces
  • pt. 2.
  • Number fields
  • Optimization and Lagrange multipliers
  • Orbifolds
  • Ordinals
  • The origins of modern mathematics
  • Quantum groups
  • Quaternions, octonions, and normed division algebras
  • Representations
  • Ricci flow
  • Riemann surfaces
  • The Riemann zeta function
  • Rings, ideals, and modules
  • Schemes
  • The Schrödinger equation
  • The simplex algorithm
  • The Peano axioms
  • Special functions
  • The spectrum
  • Spherical harmonics
  • Symplectic manifolds
  • Tensor products
  • Topological spaces
  • Transforms
  • Trigonometric functions
  • Universal covers
  • Variational methods
  • Permutation groups
  • Varieties
  • Vector bundles
  • Von Neumann algebras
  • Wavelets
  • The Zermelo-Fraenkel axioms
  • Metric spaces
  • Models of set theory
  • Modular arithmetic
  • Modular forms
  • Moduli spaces
  • Phase transitions
  • The monster group
  • Normed spaces and banach spaces
  • Number fields
  • Optimization and Lagrange multipliers
  • Orbifolds
  • Ordinals
  • The Peano axioms
  • Permutation groups
  • Phase transitions
  • [pi]
  • [pi]
  • Probability distributions
  • Projective space
  • Quadratic forms
  • Quantum computation
  • Quantum groups
  • Quaternions, octonions, and normed division algebras
  • Representations
  • Ricci flow
  • Riemann surfaces
  • The Riemann zeta function
  • Probability distributions
  • Rings, ideals, and modules
  • Schemes
  • The Schrödinger equation
  • The simplex algorithm
  • Special functions
  • The spectrum
  • Spherical harmonics
  • Symplectic manifolds
  • Tensor products
  • Topological spaces
  • Projective space
  • Transforms
  • Trigonometric functions
  • Universal covers
  • Variational methods
  • Varieties
  • Vector bundles
  • Von Neumann algebras
  • Wavelets
  • The Zermelo-Fraenkel axioms
  • Quadratic forms
  • Quantum computation
  • 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
  • pt. 4.
  • 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.
  • Branches of mathematics
  • Theorems and problems
  • The ABC conjecture
  • The Atiyah-Singer index theorem
  • The Banach-Tarski paradox
  • The Birch-Swinnerton-Dyer conjecture
  • Carleson's theorem
  • The central limit theorem
  • The classification of finite simple groups
  • Dirichlet's theorem
  • Ergodic theorems
  • Algebraic numbers
  • Fermat's last theorem
  • Fixed point theorems
  • The four-color theorem
  • The fundamental theorem of algebra
  • The fundamental theorem of arithmetic
  • Gödel's theorem
  • Gromov's polynomial-growth theorem
  • Hilbert's nullstellensatz
  • The independence of the continuum hypothesis
  • Inequalities
  • Analytic number theory
  • The insolubility of the halting problem
  • The insolubility of the quintic
  • Liouville's theorem and Roth's theorem
  • Mostow's strong rigidity theorem
  • The p versus NP problem
  • The Poincaré conjecture
  • The 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
  • Computational number theory
  • The resolution of singularities
  • The Riemann-Roch theorem
  • The Robertson-Seymour theorem
  • The three-body problem
  • The uniformization theorem
  • The Weil conjecture
  • Algebraic geometry
  • Arithmetic geometry
  • Algebraic topology
  • Girolamo Cardano
  • Rafael Bombelli
  • François Viète
  • Simon Stevin
  • René Descartes
  • Pierre Fermat
  • Blaise Pascal
  • Isaac Newton
  • Gottfried Wilhelm Leibniz
  • Brook Taylor
  • pt. 6.
  • Christian Goldbach
  • The 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
  • Mathematicians
  • 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
  • Pythagoras
  • William Rowan Hamilton
  • Augustus De Morgan
  • Joseph Liouville
  • Eduard Kumme
  • Évariste Galois
  • James Joseph Sylvester
  • George Boole
  • Karl Weierstrass
  • Pafnuty Chebyshev
  • Arthur Cayley
  • Euclid
  • 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
  • Archimedes
  • Christian Felix Klein
  • Ferdinand Georg Frobenius
  • Sofya (Sonya) Kovalevskaya
  • William Burnside
  • Jules Henri Poincaré
  • Giuseppe Peano
  • David Hilbert
  • Hermann Minkowski
  • Jacques Hadamard
  • Ivar Fredholm
  • Apollonius
  • 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
  • Abu Jaʼfar Muhammad ibn Mūsā al-Khwārizmī
  • Leonardo of Pisa (known as Fibonacci)
  • Richard Courant
  • Stefan Banach
  • Norbert Wiener
  • Emil Artin
  • Alfred Tarski
  • Andrei Nikolaevich Kolmogorov
  • Alonzo Church
  • William Vallance Douglas Hodge
  • John von Neumann
  • Kurt Gödel
  • Luitzen Egbertus Jan Brouwer
  • André Weil
  • Alan Turing
  • Abraham Robinson
  • Nicolas Bourbaki
  • pt. 7.
  • The influence of mathematics
  • Mathematics and chemistry
  • Mathematical biology
  • Wavelets and applications
  • The mathematics of traffic in networks
  • Emmy Noether
  • The mathematics of algorithm design
  • Reliable transmission of information
  • Mathematics and cryptography
  • Mathematics and economic reasoning
  • The mathematics of money
  • Mathematical statistics
  • Mathematics and medical statistics
  • Analysis, mathematical and philosophical
  • Mathematics and music
  • Mathematics and art
  • Wacław Sierpiński
  • pt. 8.
  • Final perspectives
  • The art of problem solving
  • "Why mathematics?" you might ask
  • The ubiquity of mathematics
  • Numeracy
  • Mathematics : an experimental science
  • Advice to a young mathematician
  • A chronology of mathematical
  • George Birkhoff
  • John Edensor Littlewood
  • Hermann Weyl
  • Thoralf Skolem
  • Srinivasa Ramanujan
Control code
ocn659590835
Dimensions
unknown
Extent
1 online resource (xx, 1034 pages)
Form of item
online
Isbn
9786612767197
Lccn
2008020450
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other control number
2831458
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
  • cl0500000161
  • 22573/ctt10z4n
Specific material designation
remote
System control number
(OCoLC)659590835

Library Locations

    • Copley LibraryBorrow it
      5998 Alcalá Park, San Diego, CA, 92110-2492, US
      32.771354 -117.193327
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