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Encyclopedia of Mathematics and its Applications

Back to Mathematics

Editors: R. Doran, M. Ismail, T.-Y. Lam, E. Lutwak

This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in The Encyclopedia of Mathematics and Its Applications cover their subject comprehensively. Less important results may be summarized as exercises at the ends of chapters. For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects.

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There are 411 books in this series...

[120] Absolute Measurable Spaces

[92] Abstract Regular Polytopes

Volume 0, Part 0,

[127] Aggregation Functions

[90] Algebraic Combinatorics on Words

[90] Algebraic Combinatorics on Words

[30] Algorithmic Algebraic Number Theory

[123] Algorithmic Aspects of Graph Connectivity

Volume 0, Part 0,

[123] Algorithmic Aspects of Graph Connectivity

Volume 0, Part 0,

[87] An Algebraic Introduction to K-Theory

[87] An Algebraic Introduction to K-Theory

[106] Analytic Tomography

Volume 0, Part 0,

[8] Angular Momentum in Quantum Physics

Theory and Application

  • L. C. Biedenharn, James D. Louck, Foreword by Peter A. Carruthers
  • Hardback | Published February 1985
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[8] Angular Momentum in Quantum Physics

Theory and Application

  • L. C. Biedenharn, James D. Louck, Foreword by Peter A. Carruthers
  • Paperback | Published March 2009
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[166] Aperiodic Order

Volume 2, Crystallography and Almost Periodicity
Part 0,

[149] Aperiodic Order

Volume 1, A Mathematical Invitation
Part 0,

[105] Applied Combinatorics on Words

[118] Asymptotic Analysis of Random Walks

Heavy-Tailed Distributions
Volume 0, Part 0,

[85] Asymptotics and Mellin-Barnes Integrals

Volume 0, Part 0,

[49] Banach Algebras and the General Theory of *-Algebras

Volume 1, Algebras and Banach Algebras

[49] Banach Algebras and the General Theory of *-Algebras

Volume 1, Algebras and Banach Algebras

[79] Banach Algebras and the General Theory of *-Algebras 2 Part Paperback Set

Volume 2, *-Algebras
Part 0,

[96] Basic Hypergeometric Series

Volume 0, Part 0, 2nd Edition

[19] Birkhoff Interpolation

[19] Birkhoff Interpolation

[145] Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations

Boolean Functions

Theory, Algorithms, and Applications

[134] Boolean Models and Methods in Mathematics, Computer Science, and Engineering

Volume 0, Part 0,

[60] Bounded Arithmetic, Propositional Logic and Complexity Theory

[97] Categorical Foundations

Special Topics in Order, Topology, Algebra, and Sheaf Theory
Volume 0, Part 0,

[98] Classical and Quantum Orthogonal Polynomials in One Variable

[129] Codes and Automata

[114] Combinatorial Games

Tic-Tac-Toe Theory

[114] Combinatorial Games

Tic-Tac-Toe Theory

[29] Combinatorial Geometries

[29] Combinatorial Geometries

[108] Combinatorial Matrix Classes

[39] Combinatorial Matrix Theory

Volume 0, Part 0,

[55] Combinatorial Methods in Discrete Mathematics

[55] Combinatorial Methods in Discrete Mathematics

[67] Combinatorial Species and Tree-like Structures

  • François Bergeron, Gilbert Labelle, Pierre Leroux, Translated by Margaret Readdy
  • Hardback | Published December 1997
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[135] Combinatorics, Automata and Number Theory

Volume 0, Part 0,

[159] Combinatorics, Words and Symbolic Dynamics

Volume 0, Part 0,

[36] Comparison of Statistical Experiments

[36] Comparison of Statistical Experiments

[25] Computation and Automata

[25] Computation and Automata

[48] Computation with Finitely Presented Groups

Volume 0, Part 0,

[48] Computation with Finitely Presented Groups

Volume 0, Part 0,

[101] Contact Geometry and Nonlinear Differential Equations

Volume 0, Part 0,

[11] Continued Fractions

Analytic Theory and Applications

[93] Continuous Lattices and Domains

Volume 0, Part 0,

  • G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott
  • Hardback | Published March 2003
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[75] Control Theory for Partial Differential Equations

Continuous and Approximation Theories
Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon

[75] Control Theory for Partial Differential Equations

Continuous and Approximation Theories
Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon

[74] Control Theory for Partial Differential Equations

Continuous and Approximation Theories
Volume 1, Abstract Parabolic Systems

[74] Control Theory for Partial Differential Equations

Continuous and Approximation Theories
Volume 1, Abstract Parabolic Systems

[151] Convex Bodies: The Brunn–Minkowski Theory

Volume 0, Part 0, 2nd Edition

[109] Convex Functions

Constructions, Characterizations and Counterexamples

[78] Design Theory

Volume 2, Part 0, 2nd Edition

[104] Dynamic Data Assimilation

A Least Squares Approach

[66] Eigenspaces of Graphs

[66] Eigenspaces of Graphs

[146] Ellipsoidal Harmonics

Theory and Applications

[165] Equivalents of the Riemann Hypothesis

Volume 2, Analytic Equivalents
Part 0,

[164] Equivalents of the Riemann Hypothesis

Volume 1, Arithmetic Equivalents
Part 0,

Equivalents of the Riemann Hypothesis 2 Hardback Volume Set

Volume 0, Part 0,

[143] Ergodic Control of Diffusion Processes

Volume 0, Part 0,

[38] Exact Constants in Approximation Theory

[38] Exact Constants in Approximation Theory

[117] Exact and Approximate Controllability for Distributed Parameter Systems

A Numerical Approach

[33] Factorization Calculus and Geometric Probability

[33] Factorization Calculus and Geometric Probability

[22] Field Extensions and Galois Theory

[22] Field Extensions and Galois Theory

[20] Finite Fields

Volume 0, Part 0, 2nd Edition

[20] Finite Fields

Volume 0, Part 0, 2nd Edition

[144] Finite Ordered Sets

Concepts, Results and Uses

[133] Finite Precision Number Systems and Arithmetic

Volume 0, Part 0,

[31] Functional Equations in Several Variables

[31] Functional Equations in Several Variables

[43] General Orthogonal Polynomials

Volume 0, Part 0,

[43] General Orthogonal Polynomials

Volume 0, Part 0,

[61] Geometric Applications of Fourier Series and Spherical Harmonics

[61] Geometric Applications of Fourier Series and Spherical Harmonics

[58] Geometric Tomography

Volume 0, Part 0, 2nd Edition

[58] Geometric Tomography

Volume 0, Part 0, 2nd Edition

[84] Geometries on Surfaces

[119] Geometry of Chemical Graphs

Polycycles and Two-faced Maps

[91] Geometry of Sporadic Groups

Volume 2, Representations and Amalgams

[76] Geometry of Sporadic Groups

Volume 1, Petersen and Tilde Geometries

[76] Geometry of Sporadic Groups

Volume 1, Petersen and Tilde Geometries

[138] Graph Structure and Monadic Second-Order Logic

A Language-Theoretic Approach

[141] Hadamard Expansions and Hyperasymptotic Evaluation

An Extension of the Method of Steepest Descents

[52] Handbook of Categorical Algebra

Volume 3, Sheaf Theory

[52] Handbook of Categorical Algebra

Volume 3, Sheaf Theory

[51] Handbook of Categorical Algebra

Volume 2, Categories and Structures

[51] Handbook of Categorical Algebra

Volume 2, Categories and Structures

[50] Handbook of Categorical Algebra

Volume 1, Basic Category Theory

[50] Handbook of Categorical Algebra

Volume 1, Basic Category Theory

[125] Hilbert Transforms

Volume 2,

[124] Hilbert Transforms

Volume 1,

Hilbert Transforms 2 Volume Hardback Set

[62] Infinite Dimensional Optimization and Control Theory

[62] Infinite Dimensional Optimization and Control Theory

[37] Interval Methods for Systems of Equations

[37] Interval Methods for Systems of Equations

Introduction to Radon Transforms

With Elements of Fractional Calculus and Harmonic Analysis
Volume 0, Part 0,

[54] Introduction to the Modern Theory of Dynamical Systems

[54] Introduction to the Modern Theory of Dynamical Systems

[148] Introduction to the Network Approximation Method for Materials Modeling

Volume 0, Part 0,

[161] Isolated Singularities in Partial Differential Inequalities

Volume 0, Part 0,

[32] Iterative Functional Equations

[32] Iterative Functional Equations

[116] J-Contractive Matrix Valued Functions and Related Topics

Volume 0, Part 0,

[100] Large Deviations and Metastability

[150] Lattice Sums Then and Now

Volume 0, Part 0,

  • J. M. Borwein, M. L. Glasser, R. C. McPhedran, J. G. Wan, I. J. Zucker
  • Hardback | Published September 2013
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[80] Lie's Structural Approach to PDE Systems

Volume 0, Part 0,

[80] Lie's Structural Approach to PDE Systems

Volume 0, Part 0,

[94] Mathematical Constants

Volume 0, Part 0,

[169] Mathematical Constants II

Volume 0, Part 0,

[12] Mathematical Theory of Entropy

[12] Mathematical Theory of Entropy

[139] Matrices and Graphs in Geometry

[40] Matroid Applications

[40] Matroid Applications

[7] Measurement Theory

With Applications to Decisionmaking, Utility, and the Social Sciences
Volume 7,

[63] Minkowski Geometry

[42] Model Theory

[42] Model Theory

[130] Modules over Endomorphism Rings

[153] Monoidal Topology

A Categorical Approach to Order, Metric, and Topology
Volume 0, Part 0,

[107] Multiple Scattering

Interaction of Time-Harmonic Waves with N Obstacles

[83] Navier-Stokes Equations and Turbulence

Volume 0, Part 0,

[83] Navier-Stokes Equations and Turbulence

Volume 0, Part 0,

[167] Non-Associative Normed Algebras

Volume 2, Representation Theory and the Zel'manov Approach
Part 0,

[154] Non-Associative Normed Algebras

Volume 1, The Vidav–Palmer and Gelfand–Naimark Theorems
Part 0,

Non-Associative Normed Algebras 2 Volume Hardback Set

Volume 0, Part 0,

[137] Noncommutative Rational Series with Applications

[64] Nonnegative Matrices and Applications

[64] Nonnegative Matrices and Applications

[115] Nonuniform Hyperbolicity

Dynamics of Systems with Nonzero Lyapunov Exponents
Volume 0, Part 0,

[41] Operator Algebras in Dynamical Systems

Volume 0, Part 0,

[41] Operator Algebras in Dynamical Systems

Volume 0, Part 0,

[46] Oriented Matroids

Volume 0, Part 0, 2nd Edition

  • Anders Björner, Michel Las Vergnas, Bernd Sturmfels, Neil White, Gunter M. Ziegler
  • Paperback | Published November 1999
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[122] Orthogonal Polynomials and Continued Fractions

From Euler's Point of View
Volume 0, Part 0,

[155] Orthogonal Polynomials of Several Variables

Volume 0, Part 0, 2nd Edition

[70] Orthonormal Systems and Banach Space Geometry

[70] Orthonormal Systems and Banach Space Geometry

[59] Padé Approximants

Volume 0, Part 0, 2nd Edition

[59] Padé Approximants

Volume 0, Part 0, 2nd Edition

[6] Permanents

[6] Permanents

[77] Polynomials with Special Regard to Reducibility

[56] Probabilistic Methods in Combinatorial Analysis

[56] Probabilistic Methods in Combinatorial Analysis

[10] Product Integration with Application to Differential Equations

Volume 0, Part 0,

[10] Product Integration with Application to Differential Equations

Volume 0, Part 0,

[170] Proof Complexity

Volume 0, Part 0,

[121] Purity, Spectra and Localisation

[72] Quantum Field Theory for Mathematicians

[72] Quantum Field Theory for Mathematicians

[171] Quasi-Hopf Algebras

A Categorical Approach
Volume 0, Part 0,

  • Daniel Bulacu, Stefaan Caenepeel, Florin Panaite, Freddy Van Oystaeyen
  • Hardback | Published February 2019
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[53] Random Graphs

[53] Random Graphs

[28] Rational Approximation of Real Functions

[28] Rational Approximation of Real Functions

[140] Real Analysis through Modern Infinitesimals

[27] Regular Variation

[132] Relational Mathematics

[73] Semimodular Lattices

Theory and Applications

[73] Semimodular Lattices

Theory and Applications

[57] Skew Fields

Theory of General Division Rings

[57] Skew Fields

Theory of General Division Rings

[88] Solving Polynomial Equation Systems I

The Kronecker-Duval Philosophy
Volume 0, Part 0,

[99] Solving Polynomial Equation Systems II

Macaulay's Paradigm and Gröbner Technology

[157] Solving Polynomial Equation Systems III

Volume 3, Algebraic Solving
Part 0,

[158] Solving Polynomial Equation Systems IV

Volume 4, Buchberger Theory and Beyond
Part 0,

[71] Special Functions

[71] Special Functions

[65] Sperner Theory

[110] Spline Functions on Triangulations

Volume 0, Part 0,

[131] Stochastic Control and Mathematical Modeling

Applications in Economics

[152] Stochastic Equations in Infinite Dimensions

Volume 0, Part 0, 2nd Edition

[89] Stochastic Integration with Jumps

[89] Stochastic Integration with Jumps

[113] Stochastic Partial Differential Equations with Lévy Noise

An Evolution Equation Approach
Volume 0, Part 0,

[47] Stopping Times and Directed Processes

[47] Stopping Times and Directed Processes

[126] Sub-Riemannian Geometry

General Theory and Examples
Volume 0, Part 0,

[111] Symmetric Generation of Groups

With Applications to many of the Sporadic Finite Simple Groups

[4] Symmetry and Separation of Variables

[4] Symmetry and Separation of Variables

[163] The Banach–Tarski Paradox

Volume 0, Part 0, 2nd Edition

[18] The Cauchy Problem

[18] The Cauchy Problem

[112] The Classical Fields

Structural Features of the Real and Rational Numbers

[82] The Foundations of Mathematics in the Theory of Sets

[82] The Foundations of Mathematics in the Theory of Sets

[15] The Logic of Quantum Mechanics

Volume 15,

  • Enrico G. Beltrametti, Gianni Cassinelli, Edited by Gian-Carlo Rota, Foreword by Peter A. Carruthers
  • Paperback | Published December 2010
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[95] The Mountain Pass Theorem

Variants, Generalizations and Some Applications

[95] The Mountain Pass Theorem

Variants, Generalizations and Some Applications

[23] The One-Dimensional Heat Equation

[23] The One-Dimensional Heat Equation

[9] The Racah-Wigner Algebra in Quantum Theory

[16] The Representation Theory of the Symmetric Group

Volume 0, Part 0,

[86] The Theory of Information and Coding

Student Edition
Volume 0, Part 0,

[86] The Theory of Information and Coding

Volume 0, Part 0, 2nd Edition

[2] The Theory of Partitions

Volume 0, Part 0,

[26] Theory of Matroids

[102] Topics in Algebraic Graph Theory

Volume 0, Part 0,

  • Edited by Lowell W. Beineke, Robin J. Wilson, Peter J. Cameron
  • Hardback | Published December 2004
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[156] Topics in Chromatic Graph Theory

Volume 0, Part 0,

[147] Topics in Structural Graph Theory

Volume 0, Part 0,

  • Edited by Lowell W. Beineke, Robin J. Wilson, Edited in consultation with Ortrud R. Oellermann
  • Hardback | Published November 2012
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[128] Topics in Topological Graph Theory

  • Edited by Lowell W. Beineke, Robin J. Wilson, Edited in consultation with Jonathan L. Gross, Thomas W. Tucker
  • Hardback | Published July 2009
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[168] Ultrametric Pseudodifferential Equations and Applications

Volume 0, Part 0,

  • Andrei Yu. Khrennikov, Sergei V. Kozyrev, W. A. Zúñiga-Galindo
  • Hardback | Published April 2018
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[162] Variational Methods for Nonlocal Fractional Problems

Volume 0, Part 0,

  • Giovanni Molica Bisci, Vicentiu D. Radulescu, Raffaella Servadei
  • Hardback | Published March 2016
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[136] Variational Principles in Mathematical Physics, Geometry, and Economics

Qualitative Analysis of Nonlinear Equations and Unilateral Problems
Volume 0, Part 0,

[34] Volterra Integral and Functional Equations

[34] Volterra Integral and Functional Equations

[103] Well-Posed Linear Systems