great mathematics books of the twentieth century · international press great mathematics books of...

Great Mathematics Books of the Twentieth Century

These two pages are from a papyrus manuscript dated in

early second century A.D. They contain tables of fractions

with prime denominators, followed by arithmetical problems

concerning conversions between silver and copper money and

between wheat standards, as well as calculations of carriage

charges and of interests. They are in the special collection of

University of Michigan.

Books also by Lizhen Ji

Compactifications of Symmetric Spaces by Yves Guivarc’h, Lizhen Ji, and John C. Taylor, Birkhäuser, 1998

Compactifications of Symmetric and Locally Symmetric Spaces by Armand Borel and Lizhen Ji, Birkhäuser, 2005

Lie Groups and Automorphic Forms by Lizhen Ji, Jian-Shu Li, H.W. Xu, and Shing-Tung Yau (Ed.), AMS & IP, 2006

Proceedings of The 4th International Congress of Chinese Mathematicians by Lizhen Ji, Kefeng Liu, Lo Yang, and Shing-Tung Yau (Ed.), HEP & IP, 2007

Arithmetic Groups and Their Generalizations: what, why, how? by Lizhen Ji, AMS & IP, 2008

Geometry, Analysis and Topology of Discrete Groups by Lizhen Ji, Kefeng Liu, Lo Yang, and Shing-Tung Yau (Ed.), HEP & IP, 2008

Handbook of Geometric Analysis Vol. I by Lizhen Ji, Peter Li, Richard Schoen, and Leon Simon (Ed.), HEP & IP, 2008

Automorphic Forms and the Langlands Program by Lizhen Ji, Kefeng Liu, and Shing-Tung Yau (Ed.), HEP & IP, 2009

Cohomology of Groups and Algebraic K-theory by Lizhen Ji, Kefeng Liu, and Shing-Tung Yau (Ed.), HEP & IP, 2009

Handbook of Geometric Analysis Vol. II, III by Lizhen Ji, Peter Li, Richard Schoen, and Leon Simon (Ed.), HEP & IP, 2010

Transformation Groups and Moduli Spaces of Curves by Lizhen Ji and Shing-Tung Yau (Ed.), HEP & IP, 2010

Geometry and Analysis Vol. I, II by Lizhen Ji (Ed.), HEP & IP, 2010

Fourth International Congress of Chinese Mathematicians by Lizhen Ji, Kefeng Liu, Lo Yang, and Shing-Tung Yau (Ed.), AMS & IP, 2010

Geometry of Riemann Surfaces and Their Moduli Spaces by Lizhen Ji, Scott A. Wolpert, and Shing-Tung Yau (Ed.), AMS & IP, 2010

Frontiers of Mathematical Sciences by Huai-Dong Cao, Shiu-Yuen Cheng, Binglin Gu, Lizhen Ji, and Shing-Tung Yau (Ed.), IP, 2011

Fifth International Congress of Chinese Mathematicians by Lizhen Ji, Yat Sun Poon, Lo Yang, and Shing-Tung Yau (Ed.), AMS & IP, 2012

Open Problems and Surveys of Contemporary Math by Lizhen Ji, Yat Sun Poon, and Shing-Tung Yau (Ed.), HEP & IP, 2013

International Presswww.intlpress.com

Great Mathematics Books of the Twentieth Century

A Personal Journey

Lizhen Ji Department of Mathematics

University of Michigan

Copyright © 2014 by International Press, Somerville, Massachusetts, U.S.A., and by Higher Education Press, Beijing, China. This work is published and sold in China exclusively by Higher Education Press of China. All rights reserved. Individual readers of this publication, and non-profit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgement of the source is given. Republication, systematic copying, or mass reproduction of any material in this publication is permitted only under license from International Press. Excluded from these provisions is material in articles to which the author holds the copyright. (If the author holds copyright, notice of this will be given with the article.) In such cases, requests for permission to use or reprint should be addressed directly to the author. ISBN: 978-1-57146-283-1 Printed in the United States of America. 18 17 16 15 14 1 2 3 4 5 6 7 8 9

Great Mathematics Books of the Twentieth Century: A Personal Journal by Lizhen Ji (Department of Mathematics, University of Michigan)

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Index

A

AbikoffThe Real Analytic Theory of Teichmuller

Space, 136Abraham, Marsden

Foundations of Mechanics, 512Abramenko, Brown

Buildings. Theory and Applications, 455Acton

Numerical Methods that Work, 611Adams, J.

Stable Homotopy and GeneralisedHomology, 332

Adams, R., FournierSobolev Spaces, 427

Adem, MilgramCohomology of Finite Groups, 336

AgmonLectures on Elliptic Boundary Value

Problems, 422Ahlfors

Complex Analysis, 115Conformal Invariants: Topics in Geometric

Function Theory, 133Lectures on Quasiconformal Mappings, 132

AignerCombinatorial Theory, 544

Aigner, ZieglerProofs from The Book, 107

Ainsworth, OdenA Posteriori Error Estimation in Finite

Element Analysis, 620Akhiezer, Glazman

Theory of Linear Operators in HilbertSpace, 170

Akivis, RosenfeldElie Cartan (1869–1951), 75

Aleksandrov, Kolmogorov, Lavrent’evMathematics: Its Content, Methods, and

Meaning, 12Alexandroff

Elementary Concepts of Topology, 38Alexandroff, Hopf

Topologie I, 316Alexandrov (or Alexandroff)

Combinatorial Topology, 317Alfsen

Compact Convex Sets and BoundaryIntegrals, 312

Alligood, Sauer, YorkeChaos. An Introduction to Dynamical

Systems, 521Alon, Spencer

The Probabilistic Method, 576Ambrosio, Fusco, Pallara

Functions of Bounded Variation and FreeDiscontinuity Problems, 432

Anderson, FullerRings and Categories of Modules, 216

Anderson, Guionnet, ZeitouniAn Introduction to Random Matrices, 581

AndrewsThe Theory of Partitions, 406

ApostolCalculus, 84Introduction to Analytic Number Theory, 377

Arbarello, Cornalba, GriffithsGeometry of Algebraic Curves, II, 298

Arbarello, Cornalba, Griffiths, HarrisGeometry of Algebraic Curves, I, 297

Arnold, L.Random Dynamical Systems, 523

Arnold, V.Geometrical Methods in the Theory of

Ordinary Differential Equations, 410

643

644 INDEX

Mathematical Methods of ClassicalMechanics, 512

Ordinary Differential Equations, 410Artin, E.

Galois Theory, 364Geometric Algebra, 452

Artin, M.Algebra, 199

Ash, GrossFearless Symmetry. Exposing the Hidden

Patterns of Numbers, 33Astala, Iwaniec, Martin

Elliptic Partial Differential Equations andQuasiconformal Mappings in thePlane, 134

AtiyahK-theory, 333

Atiyah, MacDonaldIntroduction to Commutative Algebra, 219

AttouchVariational Convergence for Functions and

Operators, 269Aubin

Nonlinear Analysis on Manifolds. MongeAmpere Equations, 260

Some Nonlinear Problems in RiemannianGeometry, 260

Aubin, CellinaDifferential Inclusions, 311

Aubin, EkelandApplied Nonlinear Analysis, 102

Aubin, FrankowskaSet-valued Analysis, 102

Auslander, Reiten, SmaloRepresentation Theory of Artin

Algebras, 492Axler

Linear Algebra Done Right, 190

B

Babin, VishikAttractors of Evolution Equations, 527

BakerPrinciples of Geometry, 283Transcendental Number Theory, 382

Ballmann, Gromov, SchroederManifolds of Nonpositive Curvature, 253

BanachTheory of Linear Operations, 163

Bannai, Ito

Algebraic Combinatorics. I. Association Schemes,539

Bardi, Capuzzo-Dolcetta

Optimal Control and Viscosity Solutions ofHamilton-Jacobi-Bellman Equations, 434

Barth, Hulek, Peters, VenCompact Complex Surfaces, 299

BassAlgebraic K-theory, 335

Baxter

Exactly Solved Models in StatisticalMechanics, 511

BeardonIteration of Rational Functions, 531

The Geometry of Discrete Groups, 468Beauville

Surfaces Algebriques Complexes, 300

Beckenbach, BellmanInequalities, 111

Becker, WeispfenningGrobner Bases. A Computational Approach

to Commutative Algebra, 542Bell

Men of Mathematics, 42Benedetti, Petronio

Lectures on Hyperbolic Geometry, 348Bennett, Sharpley

Interpolation of Operators, 157

BensonRepresentations and Cohomology, 336

Bensoussan, Lions, PapanicolaouAsymptotic Analysis for Periodic Structures,

417Berge

Graphs, 549Bergh, Lofstrom

Interpolation Spaces. An Introduction, 156Berlekamp, Conway, Guy

Winning Ways for Your Mathematical Plays,608

Berline, Getzler, VergneHeat Kernels and Dirac Operators, 262

Berman, Plemmons

Nonnegative Matrices in the Mathematical

INDEX 645

Sciences, 193Bertoin

Levy Processes, 569Besicovitch

Almost Periodic Functions, 143Besse

Einstein Manifolds, 248Manifolds all of Whose Geodesics are

Closed, 248Bhatia

Matrix Analysis, 193Bhatia, Szego

Stability Theory of DynamicalSystems, 524

BiggsAlgebraic Graph Theory, 548

BillingsleyConvergence of Probability Measures, 560Probability and measure, 560

Bingham, Goldie, TeugelsRegular variation, 94

Birkhoff, Ga.Lattice Theory, 200

Birkhoff, Ge.Dynamical Systems, 519

Birkhoff, Mac LaneA Survey of Modern Algebra, 196

BirmanBraids, Links, and Mapping

Class Groups, 351Bishop, Crittenden

Geometry of Manifolds, 236Bix

Conics and Cubics, 289Bjorck, Dahlquist

Numerical Methods, 612Blair

Riemannian Geometry of Contact andSymplectic Manifolds, 292

Bochnak, Coste, Roy

Real Algebraic Geometry, 290Bohner, Peterson

Dynamic Equations on Time Scales, 525Bohr

Almost Periodic Functions, 144

BollobasGraph Theory. An Introductory Course, 546

Modern Graph Theory, 546Random Graphs, 552

BolzaLectures on the Calculus of Variations, 270

Bombieri, Gubler

Heights in Diophantine Geometry, 390Bondy, Murty

Graph Theory with Applications, 549Borel

Essays in the History of Lie Groups andAlgebraic Groups, 74

Introduction aux groupes arithmetiques, 463

Linear Algebraic Groups, 445Borel, Casselman

Automorphic Forms, Representations andL-functions, 403

Borel, WallachContinuous Cohomology, Discrete Subgroups,

and Representations of Reductive Groups,404

Borevich, Shafarevich

Number Theory, 362Borwein, Erdelyi

Polynomials and Polynomial Inequalities, 105

Bosch, Guntzer, RemmertNon-Archimedean Analysis. A Systematic Ap-

proach to Rigid Analytic Geometry, 393

Bosch, Lutkebohmert, RaynaudNeron Models, 393

Bott, Tu

Differential Forms in Algebraic Topology, 341Bourbaki

Commutative Algebra, 220

Elements of the History of Mathematics, 63Lie Groups and Lie Algebras, 442

BowenEquilibrium States and the Ergodic Theory of

Anosov Diffeomorphisms, 535Boyd, El Ghaoui, Feron, Balakrishnan

Linear Matrix Inequalities in System andControl Theory, 113

Boyd, VandenbergheConvex Optimization, 608

BoyerA History of Mathematics, 61

Bredon

Introduction to Compact Transformation

646 INDEX

Groups, 475Topology and Geometry, 327

Breiman

Probability, 557Brenner, Scott

The Mathematical Theory of Finite ElementMethods, 617

BrezisAnalyse Fonctionnelle. Theorie

et Applications, 184

Functional Analysis, Sobolev Spaces andPartial Differential Equations, 184

Operateurs Maximaux Monotones etSemi-groupes de Contractions dans lesespaces de Hilbert, 185

Brezzi, Fortin

Mixed and Hybrid Finite Element Methods,617

Bridson, HaefligerMetric Spaces of Non-positive Curvature, 255

Brieskorn, KnorrerPlane Algebraic Curves, 298

Brocker, tom DieckRepresentations of Compact Lie Groups, 492

Brouwer, Cohen, NeumaierDistance-regular Graphs, 550

Browder

Surgery on Simply-connected Manifolds, 352Brown

Buildings, 454Cohomology of Groups, 335

Bruns, HerzogCohen-Macaulay Rings, 223

BuhlerGauss. A Biographical Study, 53

BumpAutomorphic Forms and Representations, 404

Burago, D., Burago, Y., Ivanov

A Course in Metric Geometry, 254Burago, Zalgaller

Geometric Inequalities, 112Burde, Zieschang

Knots, 329Burnside

Theory of Groups of Finite Order, 207Burris, Sankappanavar

A Course in Universal Algebra, 203

BusemannThe Geometry of Geodesics, 240

BuserGeometry and Spectra of Compact Riemann

Surfaces, 139Byron, Fuller

Mathematics of Classical and Quantum Physics,498

C

Caffarelli, CabreFully Nonlinear Elliptic Equations, 429

Canary, Epstein, GreenNotes on notes of Thurston, 346

Canuto, Hussaini, Quarteroni, ZangSpectral Methods in Fluid Dynamics, 432

Carleson, GamelinComplex Dynamics, 531

Carslaw, JaegerConduction of Heat in Solids, 426

CartanElementary Theory of Analytic Functions of

One or Several Complex Variables, 115Cartan, Eilenberg

Homological Algebra, 226Carter

Finite Groups of Lie Type. Conjugacy Classesand Complex Characters, 206

Simple Groups of Lie Type, 205Cassels

An Introduction to DiophantineApproximation, 383

An Introduction to the Geometry of Numbers,373

Local Fields, 371Rational Quadratic Forms, 393

Cassels, FrohlichAlgebraic Number Theory, 367

Casson, BleilerAutomorphisms of Surfaces after Nielsen and

Thurston, 347Castaing, Valadier

Convex Analysis and MeasurableMultifunctions, 310

CercignaniThe Boltzmann Equation and Its Applications,

510

INDEX 647

Cercignani, Illner, PulvirentiThe Mathematical Theory of Dilute Gases, 510

Cesari

Optimization—Theory and Applications.Problems with Ordinary DifferentialEquations, 610

symptotic Behavior and Stability Problems inOrdinary Differential Equations, 409

ChangInfinite-dimensional Morse Theory and

Multiple Solution Problems, 420Chang, Keisler

Model Theory, 591Chavel

Eigenvalues in Riemannian Geometry, 261Riemannian Geometry–A Modern

Introduction, 237Cheeger, Ebin

Comparison Theorems in RiemannianGeometry, 241

Chen, ShawPartial Differential Equations in Several

Complex Variables, 125

Chern

Complex Manifolds Without PotentialTheory, 273

Chevalley

Theory of Lie Groups. I. , 440Chihara

An Introduction to OrthogonalPolynomials, 106

Chow, HaleMethods of Bifurcation Theory, 411

Chriss, Ginzburg

Representation Theory and ComplexGeometry, 491

Chung

A Course in Probability Theory, 556

Spectral Graph Theory, 551Church

Introduction to Mathematical Logic, 584Ciarlet

The Finite Element Method for EllipticProblems, 620

ClarkeOptimization and Nonsmooth Analysis, 103

Clemens

A Scrapbook of Complex Curve Theory, 298Clifford, Preston

The Algebraic Theory of Semigroups, 203Coddington, Levinson

Theory of Ordinary Differential Equations, 408Cohen, H.

A Course in Computational Algebraic NumberTheory, 370

Advanced Topics in Computational NumberTheory, 370

Cohen, P.

Set Theory and the Continuum Hypothesis,589

CohnMeasure Theory, 98

Collet, EckmannIterated Maps on the Interval as Dynamical

Systems, 522Colton, Kress

Integral Equation Methods in ScatteringTheory, 517

Inverse Acoustic and ElectromagneticScattering Theory, 419

Comtet

Advanced Combinatorics. The Art of Finiteand Infinite Expansions, 539

Conley

Isolated Invariant Sets and the Morse Index,412

ConnesNoncommutative Geometry, 178

Constantin, FoiasNavier-Stokes Equations, 434

Conway, J.B.A Course in Functional Analysis, 167

Conway, J.H.On Numbers and Games, 607

Conway, J.H., Burgiel, Goodman-StraussThe Symmetries of Things, 30

Conway, J.H., Curtis, Norton, Parker, WilsonAtlas of Finite Groups. Maximal Subgroups

and Ordinary Characters for SimpleGroups, 212

Conway, Sloane

Sphere Packings, Lattices and Groups, 545Cormen, Leiserson, Rivest

Introduction to Algorithms, 603

648 INDEX

Cornfeld, Fomin, SinaiErgodic Theory, 534

Corwin, GreenleafRepresentations of Nilpotent Lie Groups and

Their Applications. Part I. Basic Theoryand Examples, 492

Courant, FriedrichsSupersonic Flow and Shock Waves, 433

Courant, HilbertMethods of Mathematical Physics. Vol. I.,

Vol. II., 496Courant, John

Introduction to Calculus and Analysis, 83

Courant, RobbinsWhat Is Mathematics?, 6

Cover, Thomas

Elements of Information Theory, 596Cowen, MacCluer

Composition Operators on Spaces of AnalyticFunctions, 155

Cox

Primes of the Form x2 + ny2. Fermat, ClassField Theory and Complex Multiplication,58

Cox, Little, O’SheaIdeals, Varieties, and Algorithms, 224Using Algebraic Geometry, 541

CoxeterIntroduction to Geometry, 39Projective Geometry, 40

Regular Polytopes, 41Coxeter, Greitzer

Geometry Revisited, 40Coxeter, Moser

Generators and Relations for Discrete Groups,470

CrillyArthur Cayley, 54

Croft, Falconer, GuyUnsolved Problems in Geometry, 110

Crowell, FoxIntroduction to Knot Theory, 330

Csiszar, Korner

Information Theory. Coding Theorems forDiscrete Memoryless Systems, 597

Curtain, Zwart

An Introduction to Infinite-dimensional Linear

Systems Theory, 528Curtis

Pioneers of Representation Theory: Frobenius,Burnside, Schur, and Brauer, 68

Curtis, ReinerMethods of Representation Theory, 215

Curtis, ReinerRepresentation Theory of Finite Groups and

Associative Algebras, 214Cvetkovic, Doob, Sachs

Spectra of Graphs, 551

D

Da Prato, ZabczykStochastic Equations in Infinite Dimensions,

572Dacorogna

Direct Methods in the Calculus of Variations,268

DafermosHyperbolic Conservation Laws in Continuum

Physics, 436Dal Maso

An Introduction to Γ-convergence, 269Daubechies

Ten Lectures on Wavelets, 160Dauben

Georg Cantor, 50Davenport

Multiplicative Number Theory, 381The Higher Arithmetic. An Introduction to

the Theory of Numbers, 361David, Semmes

Analysis of and on Uniformly Rectifiable Sets,101

DaviesHeat Kernels and Spectral Theory, 262

DavisCirculant Matrices, 194The Geometry and Topology of Coxeter Groups,

475Davis, Rabinowitz

Methods of Numerical Integration, 614de Azcarraga, Izquierdo

Lie Groups, Lie Algebras, Cohomology andSome Applications in Physics, 483

de Boor

INDEX 649

A Practical Guide to Splines, 622de la Harpe

Topics in Geometric Group Theory, 470de Melo, van Strien

One-dimensional Dynamics, 522

DeiftOrthogonal Polynomials and Random Matri-

ces: a Riemann-Hilbert Approach, 581

DeimlingNonlinear Functional Analysis, 185

DeligneCohomologie etale, 391

Demazure, Gabriel

Groupes algebriques. Tome I: Geometriealgebrique, generalites, groupescommutatifs, 447

Introduction to Algebraic Geometry andAlgebraic Groups, 447

Dembo, Zeitouni

Large Deviations Techniques and Applications,574

DembowskiFinite Geometries, 457

Demidovich

Problems in Mathematical Analysis, 108Derezinski, Gerard

Scattering Theory of Classical and QuantumN-particle Systems, 515

Derksen, KemperComputational Invariant Theory, 451

Deuschel, StroockLarge Deviations, 574

DevaneyAn Introduction to Chaotic Dynamical

Systems, 521

DeVore, LorentzConstructive Approximation, 621

Dickson

History of the Theory of Numbers. I, II, III,70

Diestel

Graph Theory, 547Diestel, Jarchow, Tonge

Absolutely Summing Operators, 168Diestel, Uhl

Vector Measures, 100

Dieudonne

A History of Algebraic and DifferentialTopology 1900–1960, 72

Foundations of Modern Analysis, 91

DiracGeneral Theory of Relativity, 504

DixmierC∗-algebras, 181

von Neumann Algebras, 180Dixon, Mortimer

Permutation Groups, 210do Carmo

Differential Geometry of Curves and Surfaces,237

Riemannian Geometry, 237Dolgachev

Lectures on Invariant Theory, 294

Donaldson, KronheimerThe Geometry of Four-manifolds, 350

DoobClassical Potential Theory and Its

Probabilistic Counterpart, 565Stochastic Processes, 565

Doyle, SnellRandom Walks and Electric Networks, 563

Drake, SinghIntermediate Set Theory, 587

Du SautoySymmetry: A Journey into the Patterns of

Nature, 28Dubrovin, Fomenko, Novikov

Modern Geometry—Methods and Applications,238

DudleyReal Analysis and Probability, 560

DugundjiTopology, 320

Dunford, Schwartz

Linear Operators, 175Dunham

Euler: the Master of Us All, 54Duoandikoetxea

Fourier Analysis, 142Duren

Theory of Hp Spaces, 153Durrett

Probability: Theory and Examples, 558

Duvaut, Lions

650 INDEX

Inequalities in Mechanics and Physics, 114Dym, McKean

Fourier Series and Integrals, 143

E

EdwardsRiemann’s Zeta Function, 375

Eichler, ZagierThe Theory of Jacobi Forms, 405

EilenbergAutomata, Languages, and Machines, 603

Eilenberg, SteenrodFoundations of Algebraic Topology, 325

EinsteinThe Meaning of Relativity, 503

EisenbudCommutative Algebra. With a View

Toward Algebraic Geometry, 221Eisenhart

Riemannian Geometry, 239Ekeland, Temam

Convex Analysis and VariationalProblems, 310

EllisEntropy, Large Deviations, and Statistical

Mechanics, 574Engel, Nagel

One-parameter Semigroups for LinearEvolution Equations, 176

EngelkingGeneral Topology, 320

Engl, Hanke, NeubauerRegularization of Inverse Problems, 419

EnriquesLe Superficie Algebriche, 301

Epstein, Cannon, Holt, Levy, Paterson, ThurstonWord Processing in Groups, 471

Erdelyi, Magnus, Oberhettinger, TricomiHigher Transcendental Functions, 86

Ethier, KurtzMarkov Processes, 571

EvansPartial Differential Equations, 413

Evans, GariepyMeasure Theory and Fine Properties of

Functions, 99Eves

An Introduction to the History ofMathematics, 62

F

Faddeev, TakhtajanHamiltonian Methods in the Theory of

Solitons, 517Falconer

Fractal Geometry. Mathematical Foundationsand Applications, 270

The Geometry of Fractal Sets, 271Faltings, Chai

Degeneration of Abelian Varieties, 387Faraut, Koranyi

Analysis on Symmetric Cones, 257Farkas, Kra

Riemann Surfaces, 131Federer

Geometric Measure Theory, 265Feit

The Representation Theory of Finite Groups,213

FellerAn Introduction to Probability Theory and its

Applications, 555Fenchel, Nielsen

Discontinuous Groups of Isometries in theHyperbolic Plane, 468

Feynman,Leighton,SandsThe Feynman Lectures on Physics, 502

Field, GolubitskySymmetry in Chaos. A Search for Pattern in

Mathematics, Art, and Nature, 31Fine

Basic Hypergeometric Series and Applications,406

Fleming, SonerControlled Markov Processes and Viscosity

Solutions, 566Fletcher, Markovic

Quasiconformal Maps and TeichmullerTheory, 138

FollandHarmonic Analysis in Phase Space, 160Real Analysis. Modern Techniques and Their

Applications, 92Forster

INDEX 651

Lectures on Riemann Surfaces, 131Forsythe, Wasow

Finite-difference Methods for PartialDifferential Equations, 618

FraleighA First Course in Abstract Algebra, 200

FrankelThe Geometry of Physics, 239

Frenkel, Lepowsky, MeurmanVertex Operator Algebras and the

Monster, 481Fricke, Klein

Vorlesungen uber die Theorie derelliptischen Modulfunctionen, 397

Vorlesungen uber die Theorie derautomorphen Funktionen, 396

Fried, JardenField Arithmetic, 394

FriedmanPartial Differential Equations of Parabolic

Type, 426Fuchs

Infinite Abelian Groups, 473Fukushima, Oshima, Takeda

Dirichlet Forms and Symmetric MarkovProcesses, 561

FultonAlgebraic Curves. An Introduction to

Algebraic Geometry, 288Intersection Theory, 302Introduction to Intersection Theory in

Algebraic Geometry, 304Introduction to Toric Varieties, 307Young Tableaux, 486

Fulton, HarrisRepresentation Theory. A first Course, 489

FurstenbergRecurrence in Ergodic Theory and

Combinatorial Number Theory, 536

G

GaldiAn Introduction to the Mathematical Theory

of the Navier-Stokes Equations, 434Gallot, Hulin, Lafontaine

Riemannian Geometry, 238Gantmacher

The Theory of Matrices, 192Garcia-Cuerva, Rubio de Francia

Weighted Norm Inequalities and RelatedTopics, 113

GardinerTeichmuller Theory and Quadratic

Differentials, 137

Gardiner, LakicQuasiconformal Teichmuller Theory, 138

GardnerGeometric Tomography, 312

Garey, JohnsonComputers and Intractability, 602

GarnettBounded Analytic Functions, 152

Garnett, Marshall

Harmonic Measure, 153Garrett

Buildings and Classical Groups, 455Gasper, Rahman

Basic Hypergeometric Series, 405Geck

An Introduction to Algebraic Geometry andAlgebraic Groups, 449

GelbartAutomorphic Forms on Adele Groups, 401

Gelbaum, OlmstedCounterexamples in Analysis, 96

Gelfand

Lectures on Linear Algebra, 188Gelfand, Fomin

Calculus of Variations, 268Gelfand, Graev, Pyatetskii-Shapiro

Representation Theory and AutomorphicFunctions, 172, 399

Gelfand, Kapranov, ZelevinskyDiscriminants, Resultants, and

Multidimensional Determinants, 308Gelfand, Manin

Methods of Homological Algebra, 229Gelfand, Shilov, Vilenkin, Graev

Generalized Functions, 172Gelfond

Transcendental and Algebraic Numbers, 383George, Askey, Roy

Special Functions, 87

Georgii

652 INDEX

Gibbs Measures and Phase Transitions, 510Giaquinta

Multiple Integrals in the Calculus of Variationsand Nonlinear Elliptic Systems, 269

Gilbarg, TrudingerElliptic Partial Differential Equations of

Second Order, 421Gilkey

Invariance Theory, the Heat Equation, and theAtiyah-Singer Index Theorem, 263

Gillman, Jerison

Rings of Continuous Functions, 183Girault, Raviart

Finite Element Methods for Navier-StokesEquations, 619

GiustiMinimal Surfaces and Functions of

Bounded Variation, 252

Glimm, JaffeQuantum Physics. A Functional Integral

Point of View, 511Godel

The Consistency of the ContinuumHypothesis, 589

Godement

Topologie algebrique et theorie des faisceaux,127

Godsil, RoyleAlgebraic Graph Theory, 550

Goebel, KirkTopics in Metric Fixed Point Theory, 321

Gohberg, KreinIntroduction to the Theory of Linear

Nonselfadjoint Operators, 170Goldman

Complex Hyperbolic Geometry, 468Goldstein, Poole, Safko

Classical Mechanics, 513

Golub, Van LoanMatrix Computations, 613

Golubitsky, GuilleminStable Mappings and Their Singularities, 341

GolumbicAlgorithmic Graph Theory and Perfect

Graphs, 551Goluzin

Geometric Theory of Functions of a

Complex Variable, 121Gompf, Stipsicz

4-manifolds and Kirby Calculus, 350

Goodman, WallachRepresentations and Invariants of the

Classical Groups, 488

Symmetry, Representations, and Invariants, 489Gorenstein

Finite Groups, 208Gorenstein, Lyons, Solomon

The Classification of the Finite SimpleGroups, 211

Goresky, MacPherson

Stratified Morse theory, 343Goursat

A Course in Mathematical Analysis, 81Gowers, Barrow-Green, Leader

The Princeton Companion to Mathematics, 14Graham, Knuth, Patashnik

Concrete Mathematics. A Foundation forComputer Science, 595

Granas, DugundjiFixed Point Theory, 321

Gratzer

General Lattice Theory, 201Grauert, Remmert

Coherent Analytic Sheaves, 126Greenleaf

Invariant Means on Topological Groups andTheir Applications, 536

Griffiths, Harris

Principles of Algebraic Geometry, 286Grimmett

Percolation, 577Grisvard

Elliptic Problems in Nonsmooth Domains, 422Grochenig

Foundations of Time-frequency Analysis, 144Gromov

Metric Structures for Riemannian andNon-Riemannian Spaces, 253

Asymptotic Invariants of Infinite Groups.Geometric Group Theory, 471

Partial Differential Relations, 264Grothendieck

The Elements de geometrie algebrique, 279

Grotschel, Lovasz, Schrijver

INDEX 653

Geometric Algorithms and CombinatorialOptimization, 609

GruberConvex and Discrete Geometry, 311

Gruber, LekkerkerkerGeometry of Numbers, 373

GrunbaumConvex Polytopes, 540

Grunbaum, ShephardTilings and Patterns, 31Tilings and Patterns. An Introduction, 32

Guckenheimer, HolmesNonlinear Oscillations, Dynamical Systems,

and Bifurcations of Vector Fields, 524Guillemin, Pollack

Differential Topology, 341Guillemin, Sternberg

Geometric Asymptotics, 416Symplectic Techniques in Physics, 290

GunningIntroduction to Holomorphic Functions of

Several Variables, 124Gunning, Rossi

Analytic Functions of Several ComplexVariables, 123

GuyUnsolved Problems in Number Theory, 109

H

Hairer, Norsett, WannerSolving Ordinary Differential Equations, 615

Halberstam, RichertSieve Methods, 379

HaleAsymptotic Behavior of Dissipative Systems,

526Theory of Functional Differential Equations,

530Hale, Verduyn Lunel

Introduction to Functional-differentialEquations, 530

HallThe Theory of Groups, 209

Hall, HeydeMartingale Limit Theory and its Application,

569Halmos

A Hilbert Space Problem Book, 169Finite-dimensional Vector Spaces, 189I Want to Be a Mathematician. An

Automathography in Three Parts, 22Measure Theory, 97Naive Set Theory, 587

Harary

Graph Theory, 548Hardy

A Course of Pure Mathematics, 80A Mathematician’s Apology, 19Divergent Series, 94

Hardy, Littlewood, PolyaInequalities, 110

Hardy, WrightAn Introduction to the Theory of Numbers,

356Hargittai, I., Hargittai, M.

Symmetry Through the Eyes of a Chemist, 35Symmetry: A Unifying Concept, 36

HarrisAlgebraic Geometry. A First Course, 287

Harris, MorrisonModuli of Curves, 296

Hartman

Ordinary Differential Equations, 409Hartshorne

Algebraic Geometry, 285Hasse

Number Theory, 362Hatcher

Algebraic Topology, 326Hawking, Ellis

The Large Scale Structure of Space-time, 506

HawkinsEmergence of the Theory of Lie Groups. An

Essay in the History of Mathematics 1869–1926, 73

HaymanMeromorphic Functions, 122

Haynes, Hedetniemi, SlaterFundamentals of Domination in Graphs, 550

HeckeLectures on the Theory of Algebraic Numbers,

366Heinonen

Lectures on Analysis on Metric Spaces, 100

654 INDEX

Heinonen, Kilpelainen, MartioNonlinear Potential Theory of Degenerate

Elliptic Equations, 151Helgason

Differential Geometry and Symmetric Spaces,256

Differential Geometry, Lie Groups, andSymmetric Spaces, 256

Geometric Analysis on Symmetric Spaces, 257Hempel

3-manifolds, 349Henrici

Applied and Computational ComplexAnalysis, 119

HenryGeometric Theory of Semilinear Parabolic

Equations, 425Herstein

Topics in Algebra, 200

Hewitt, RossAbstract Harmonic Analysis, 145

HilbertThe Theory of Algebraic Number Fields, 365Theory of Algebraic Invariants, 450

Hilbert, Cohn-VossenGeometry and the Imagination, 37

Hille, Phillips

Functional Analysis and Semi-groups, 177Hiller

Geometry of Coxeter Groups, 474Hindry, Silverman

Diophantine Geometry. An Introduction, 389

Hiriart-Urruty, LemarechalConvex Analysis and Minimization

Algorithms, 607

HirschDifferential Topology, 340

Hirsch, Smale

Differential Equations, Dynamical Systems,and Linear Algebra, 411

HirschfeldProjective Geometries Over Finite Fields, 456

Hirschfeld, Thas

General Galois Geometries, 456Hirzebruch

Topological Methods in Algebraic Geometry,289

HodgeThe Theory and Applications of Harmonic

Integrals, 342Hodge, Pedoe

Methods of Algebraic Geometry, 282Hodges A.

Alan Turing: the Enigma, 47

Hodges W.Model Theory, 592

Hofer, ZehnderSymplectic Invariants and Hamiltonian

Dynamics, 292

Hoffman P.The Man Who Loved Only Numbers, 49

Hoffman, K.Banach Spaces of Analytic Functions, 154

HofstadterGodel, Escher, Bach: an Eternal Golden Braid,

585

Hopcroft, UllmanIntroduction to Automata Theory,

Languages, and Computation, 603Hopf

Differential Geometry in the Large, 234

HormanderAn Introduction to Complex Analysis in

Several Variables, 272Lectures on Nonlinear Hyperbolic Differential

Equations, 415

Linear Partial Differential Operators, 414Notions of Convexity, 415

The Analysis of Linear Partial DifferentialOperators. I-IV, 414

Horn, Johnson

Matrix Analysis, 191Topics in Matrix Analysis, 192

HouseholderThe Theory of Matrices in Numerical Analysis,

613

HoveyModel Categories, 337

HowieFundamentals of Semigroup Theory, 204

HsiangCohomology Theory of Topological

Transformation Groups, 476

Hua

INDEX 655

Additive Theory of Prime Numbers, 380Introduction to Number Theory, 358

HubbardTeichmuller Theory and Applications to

Geometry, Topology, and Dynamics, 137Hughes

Random Walks and Random Environments,577

HumphreysIntroduction to Lie Algebras and

Representation Theory, 443Linear Algebraic Groups, 446Reflection Groups and Coxeter Groups, 474

HuppertEndliche Gruppen. I., 210

Huppert, BlackburnFinite groups. II, III, 210

Hurewicz, WallmanDimension Theory, 322

HuybrechtsComplex Geometry. An Introduction, 274

Huybrechts, LehnThe Geometry of Moduli Spaces of Sheaves,

295

I

Ikeda, WatanabeStochastic Differential Equations and Diffusion

Processes, 572Imayoshi, Taniguchi

An Introduction to Teichmuller Spaces, 136Ince

Ordinary Differential Equations, 410Ireland, Rosen

A Classical Introduction to Modern NumberTheory, 359

IsaacsCharacter Theory of Finite Groups, 214

IsakovInverse Problems for Partial Differential

Equations, 418Ito, McKean

Diffusion Processes and their Sample Paths,567

IvicThe Riemann Zeta-function, 375

Iwaniec

Topics in Classical Automorphic Forms, 402Iwaniec, Kowalski

Analytic Number Theory, 378

J

JacoLectures on Three-manifold Topology, 349

JacobsonBasic Algebra, 198Lie Algebras, 445

Jacod, ShiryaevLimit Theorems for Stochastic Processes, 568

Jacquet, LanglandsAutomorphic Forms on GL(2), 400

James, KerberThe Representation Theory of the Symmetric

Group, 486Janson, Svante, Luczak, Rucinski

Random Graphs, 552Jantzen

Representations of Algebraic Groups, 452Jech

Set Theory, 588Jikov, Kozlov, Oleinik

Homogenization of Differential Operators andIntegral Functionals, 579

JohnPartial Differential Equations, 416

JostRiemannian Geometry and Geometric

Analysis, 260Joyce

Compact Manifolds with Special Holonomy, 249Jurdjevic

Geometric Control Theory, 431

K

Kac, M.Enigmas of Chance, 25Statistical Independence in Probability,

Analysis and Number Theory, 557Kac, M., Ulam

Mathematics and Logic, 10Kac, V.

Infinite-dimensional Lie Algebras, 479Kadison, Ringrose

656 INDEX

Fundamentals of the Theory of OperatorAlgebras, 182

Kahane

Some Random Series of Functions, 577Kailath

Linear Systems, 528Kallenberg

Foundations of Modern Probability, 558Kanigel

The Man Who Knew Infinity. A Life of theGenius Ramanujan, 49

KapovichHyperbolic Manifolds and Discrete Groups, 348

Karatsuba, VoroninThe Riemann Zeta-function, 376

Karatzas, Shreve

Brownian Motion and Stochastic Calculus, 572Methods of Mathematical Finance, 573

KaroubiK-theory. An Introduction, 334

Kashiwara, SchapiraSheaves on Manifolds, 127

KasselQuantum Groups, 480

Kato

Perturbation Theory for Linear Operators, 428Katok, Hasselblatt

Introduction to the Modern Theory ofDynamical Systems, 520

KatzA History of Mathematics. An Introduction,

60Katz, Sarnak

Random Matrices, Frobenius Eigenvalues, andMonodromy, 581

KatznelsonAn Introduction to Harmonic Analysis, 141

KechrisClassical Descriptive Set Theory, 588

KelleyGeneral Topology, 319

Kempf, Knudsen, Mumford, Saint-DonatToroidal Embeddings. I, 307

KhinchinContinued Fractions, 364Three Pearls of Number Theory, 363

Kinderlehrer, Stampacchia

An Introduction to Variational Inequalities andTheir Applications, 417

Kirby, SiebenmannFoundational Essays on Topological Manifolds,

Smoothings, and Triangulations, 353Klee, Wagon

Old and New Unsolved Problems in PlaneGeometry and Number Theory, 18

Kleene

Mathematical Logic, 590Klein

Development of Mathematics in the 19thCentury, 76

Lectures on Mathematics, 77Lectures on the Icosahedron and the Solution

of Equations of the Fifth Degree, 398Klimek

Pluripotential Theory, 150

KlineMathematical Thought from Ancient to

Modern Times, 65

Klingenberg

Riemannian Geometry, 242Kloeden, Platen

Numerical Solution of Stochastic DifferentialEquations, 616

KnappLie Groups Beyond an Introduction, 444

Representation Theory of Semisimple Groups.An Overview Based on Examples, 490

Knopp

Theory of Functions, 118Knuth

The Art of Computer Programming, 595Kobayashi

Differential Geometry of Complex VectorBundles, 249

Hyperbolic Complex Spaces, 275

Hyperbolic Manifolds and HolomorphicMappings, 275

Transformation Groups in DifferentialGeometry, 476

Kobayashi, NomizuFoundations of Differential Geometry, 245

Koblitzp-adic Numbers, p-adic Analysis, and

Zeta-functions, 360

INDEX 657

KodairaComplex Manifolds and Deformation of

Complex Structures, 273Kolchin

Differential Algebra and Algebraic Groups, 460Kollar

Rational Curves on Algebraic Varieties, 296Kollar, Mori

Birational Geometry of Algebraic Varieties, 297Kolmogorov

Foundations of the Theory of Probability, 554Kolmogorov, Fomin

Elements of the Theory of Functions andFunctional Analysis, 164

KomornikExact Controllability and Stabilization, 528

KornerFourier Analysis, 11The Pleasures of Counting, 10

Kosmann-SchwarzbachThe Noether Theorems. Invariance and

Conservation Laws in the TwentiethCentury, 35

KrantzFunction Theory of Several Complex Variables,

125Kuang

Delay Differential Equations with Applicationsin Population Dynamics, 525

Kuipers, NiederreiterUniform Distribution of Sequences, 561

KunenSet Theory. An Introduction to Independence

Proofs, 590Kunita

Stochastic Flows and Stochastic DifferentialEquations, 573

KuratowskiTopology, 318

KuroshThe Theory of Groups, 209

L

Ladyenskaja, Solonnikov, UralcevaLinear and Quasilinear Equations of Parabolic

Type, 426Ladyzhenskaya

The Mathematical Theory of ViscousIncompressible Flow, 435

Ladyzhenskaya, Uraltseva

Linear and Quasilinear Elliptic Equations, 423Lakshmikantham, Bainov, Simeonov

Theory of Impulsive Differential Equations, 417Lam

Introduction to Quadratic Forms Over Fields,391

LambHydrodynamics, 437

Lancaster, TismenetskyThe Theory of Matrices, 193

Landau, LifshitzCourse of Theoretical Physics, 499

Landkof

Foundations of Modern Potential Theory, 149Lang

Algebra, 197Algebraic Number Theory, 368

Cyclotomic Fields, 369Elliptic Functions, 386Fundamentals of Diophantine Geometry, 389Introduction to Modular Forms, 401

Lange, Birkenhake

Complex Abelian Varieties, 388Langlands

Base Change for GL(2), 403On the Functional Equations Satisfied by

Eisenstein Series, 402Lawler

Intersections of Random Walks, 564Lawson, Michelsohn

Spin Geometry, 247Lax

Functional analysis, 165Hyperbolic Systems of Conservation Laws and

the Mathematical Theory of ShockWaves,433

LazarsfeldPositivity in Algebraic Geometry, 305

LebedevSpecial Functions and Their Applications, 89

Lederman, HillSymmetry and the Beautiful Universe, 34

Ledoux, Talagrand

Probability in Banach Spaces. Isoperimetry

658 INDEX

and Processes, 562Lee

Riemannian Manifolds. An Introduction toCurvature, 236

Lefschetz

Algebraic Topology, 319Lehner

Discontinuous Groups and AutomorphicFunctions, 398

Lehto

Univalent Functions and Teichmuller Spaces,135

Lehto, Virtanen

Quasiconformal Mappings in the Plane, 133Lickorish

An Introduction to Knot Theory, 330

Lidl, NiederreiterFinite Fields, 359

Lieb, Loss

Analysis, 93Lifshitz,Pitaevskii

Course of Theoretical Physics, 501Liggett

Interacting Particle Systems, 579

Stochastic Interacting Systems: Contact, Voterand Exclusion Processes, 579

Lind, Marcus

An Introduction to Symbolic Dynamics andCoding, 523

Lindenstrauss, TzafririClassical Banach Spaces, 167

Lions

Mathematical Topics in Fluid Mechanics, 435Quelques methodes de resolution des

problemes aux limites non lineaires, 430

LittlewoodLittlewood’s Miscellany, 21

Loeve

Probability Theory, 556Loday

Cyclic Homology, 231Lojasiewicz

Introduction to Complex Analytic Geometry,126

Lorentz, Golitschek, MakovozConstructive Approximation. Advanced

Problems, 621

LovaszCombinatorial Problems and Exercises, 544

LubotzkyDiscrete Groups, Expanding Graphs and

Invariant Measures, 467Lueck

L2-invariants: Theory and Applications toGeometry and K-theory, 478

LunardiAnalytic Semigroups and Optimal Regularity

in Parabolic Problems, 178Lusztig

Introduction to Quantum Groups, 480Lyndon, Schupp

Combinatorial Group Theory, 470

M

Mac LaneCategories for theWorking Mathematician, 230Homology, 227

MacdonaldSymmetric Functions and Hall Polynomials,

484Mackey

Unitary Group Representations in Physics,Probability, and Number Theory, 497

MacLane, BirkhoffAlgebra, 197

MacWilliams, SloaneThe Theory of Error-correcting Codes, 600

MagnusNoneuclidean Tesselations and Their Groups,

397Majid

Foundations of Quantum Group Theory, 480Malliavin

Stochastic Analysis, 575Mandelbrot

The Fractal Geometry of Nature, 271Mane

Ergodic Theory and Differentiable Dynamics,535

ManinA Course in Mathematical Logic, 590Cubic Forms. Algebra, Geometry, Arithmetic,

394Marchenko

INDEX 659

Sturm Liouville Operators and Applications,516

MarcusNumber Fields, 367

MardenOuter Circles. An Introduction to Hyperbolic

3-manifolds, 348Margulis

Discrete Subgroups of Semisimple Lie Groups,466

Marker

Model theory. An Introduction, 592Markushevich

Theory of Functions of a Complex Variable,120

Marsden, RatiuIntroduction to Mechanics and Symmetry. A

Basic Exposition of Classical MechanicalSystems, 501

Marshall, Olkin

Inequalities: Theory of Majorization and ItsApplications, 112

MaskitKleinian Groups, 469

Maslov, Fedoriuk

Semiclassical Approximation in QuantumMechanics, 416

MatousekLectures on Discrete Geometry, 540

MatsumuraCommutative Algebra, 221

Commutative Ring Theory, 222Mattila

Geometry of Sets and Measures in EuclideanSpaces. Fractals and Rectifiability, 266

Mawhin, WillemCritical Point Theory and Hamiltonian

Systems, 420

MaySimplicial Objects in Algebraic Topology, 328

Maz’jaSobolev Spaces, 427

McClearyUser’s Guide to Spectral Sequences, 230

McConnell, RobsonNoncommutative Noetherian Rings, 224

McDuff, Salamon

J-holomorphic Curves and SymplecticTopology, 291

Introduction to Symplectic Topology, 291McKean

Stochastic Integrals, 567

McMullenComplex Dynamics and Renormalization, 532Renormalization and 3-manifolds Which Fiber

Over the Circle, 532McWeeny

Symmetry: An Introduction to Group Theoryand Its Applications, 30

MehtaRandom Matrices, 580

Melrose

The Atiyah-Patodi-Singer Index Theorem, 424Meyer, Coifman

Wavelets and Operators, 161

Meyn, TweedieMarkov Chains and Stochastic Stability, 566

Milman, Schechtman

Asymptotic Theory of Finite-dimensionalNormed Spaces, 313

Milne

Etale Cohomology, 390Milnor

Dynamics in One Complex Variable.Introductory Lectures, 531

Introduction to Algebraic K-theory, 334Lectures on the h-cobordism Theorem, 339

Morse Theory, 339Singular Points of Complex Hypersurfaces, 289Topology from the Differentiable Viewpoint,

340Milnor, Stasheff

Characteristic Classes, 324Misner, Thorne, Wheeler

Gavitation, 507Mitrinovic

Analytic Inequalities, 111

MiyakeModular Forms, 401

Moeglin, Waldspurger

Spectral Decomposition and Eisenstein Series.Une paraphrase de l’Ecriture, 403

Monastyrsky

Riemann, Topology, and Physics, 52

660 INDEX

Montgomery, D., ZippinTopological Transformation Groups, 477

Montgomery, H.

Ten Lectures on the Interface BetweenAnalytic Number Theory and HarmonicAnalysis, 378

Montgomery, H., VaughanMultiplicative Number Theory. I. Classical

Theory, 381Montgomery, R.

A Tour of Subriemannian Geometries, TheirGeodesics and Applications, 247

Montgomery, S.Hopf Algebras and Their Actions on Rings,

481

Moore

Foundations of Point Set Theory, 319Morgan

Geometric Measure Theory, A Beginner’s Guide,267

MorreyMultiple Integrals in the Calculus of

Variations, 267

Morrow, Kodaira

Complex Manifolds, 274Morse

The Calculus of Variations in the Large, 339Moschovakis

Descriptive Set Theory, 588Moser

Stable and Random Motions in DynamicalSystems, 519

MostowStrong Rigidity of Locally Symmetric Spaces,

464Motohashi

Spectral Theory of the Riemann Zeta-function,376

MukaiAn Introduction to Invariants and Moduli, 295

MumfordAbelian Varieties, 387

Algebraic Geometry. I, 284Lectures on Curves on an Algebraic Surface,

302Tata Lectures on Theta, 387

The Red book of Varieties and Schemes, 283

Mumford, Fogarty, KirwanGeometric Invariant Theory, 293

Mumford, Series, WrightIndra’s Pearls, 36

MunkresElements of Algebraic Topology, 327Topology: A First Course, 327

MurrayMathematical Biology, 526

N

NadlerContinuum Theory. An Introduction, 320

NagThe Complex Analytic Theory of Teichmuller

Spaces, 135Nagata

Local Rings, 223Modern Dimension Theory, 322

NakajimaLectures on Hilbert Schemes of Points on

Surfaces, 294Nathanson

Additive Number Theory. Inverse Problemsand the Geometry of Sumsets, 380

NecasLes methodes directes en theorie des equations

elliptiques, 421Nehari

Conformal Mapping, 121Neugebauer

A History of Ancient MathematicalAstronomy, 70

NeukirchAlgebraic Number Theory, 369

Neukirch, Schmidt, WingbergCohomology of Number Fields, 372

NewmanThe World of Mathematics. Vols. I-IV, 66

NewsteadIntroduction to Moduli Problems and Orbit

Spaces, 293Nielsen, Chuang

Quantum Computation and QuantumInformation, 597

Nocedal, WrightNumerical Optimization, 609

INDEX 661

Novikov, Manakov, Pitaevskii, ZakharovTheory of Solitons. The Inverse Scattering

Method, 515Nualart

The Malliavin Calculus and Related Topics,575

O

O’MearaIntroduction to Quadratic Forms, 392

O’NeillSemi-Riemannian Geometry, 246

OdaConvex Bodies and Algebraic Geometry, 306

Olver, F.Asymptotics and Special Functions, 88

Olver, P.Applications of Lie Groups to Differential

Equations, 461Classical Invariant Theory, 451Equivalence, Invariants, and Symmetry, 462

Onishchik, VinbergLie Groups and Algebraic Groups, 443

Orlik, TeraoArrangements of Hyperplanes, 344

Ortega, RheinboldtIterative Solution of Nonlinear Equations in

Several Variables , 616Oxley

Matroid Theory, 542

P

Paley, WienerFourier Transforms in the Complex Domain,

143Papadimitriou

Computational Complexity, 604Parshall, Rowe

The Emergence of the American MathematicalResearch Community, 1876–1900, 71

PassmanThe Algebraic Structure of Group Rings, 217

Payne, ThasFinite Generalized Quadrangles, 456

Pazy

Semigroups of Linear Operators and Applica-tions to Partial Differential Equations, 176

PedersenC∗-algebras and Their Automorphism Groups,

182Penrose

The Road to Reality. A complete Guide to theLaws of the Universe, 508

Perko

Differential equations and dynamical systems,522

PesinDimension Theory in Dynamical Systems, 323

Petersen, K.Ergodic Theory, 534

Petersen, P.Riemannian Geometry, 241

Petkovsek, Wilf, ZeilbergerA = B, 599

PetrovskiOrdinary Differential Equations, 409

PhillipsScattering Theory for Automorphic Functions,

402

PierceAssociative Algebras, 215

PisierThe Volume of Convex Bodies and Banach Space

Geometry, 313Platonov, Rapinchuk

Algebraic Groups and Number Theory, 448Podlubny

Fractional Differential Equations, 95Polya

How to Solve it. A New Aspect ofMathematical Method, 15

Mathematical Discovery. On Understanding,Learning, and Teaching Problem Solving,17

Mathematics and Plausible Reasoning, 16

Polya,SzegoIsoperimetric Inequalities in Mathematical Physics,

263Problems and Theorems in Analysis, 104

PommerenkeBoundary Behaviour of Conformal Maps, 123

Pontryagin

662 INDEX

Topological Groups, 145Pressley, Segal

Loop Groups, 479Protter, Weinberger

Maximum Principles in Differential Equations,422

R

RabinowitzMinimax Methods in Critical Point Theory with

Applications to Differential Equations, 419Rademacher, Toeplitz

The Enjoyment of Mathematics; Selections fromMathematics for the Amateur, 8

RaghunathanDiscrete Subgroups of Lie Groups, 464

RansfordPotential Theory in the Complex Plane, 150

RatcliffeFoundations of Hyperbolic Manifolds, 348

RavenelComplex Cobordism and Stable Homotopy

Groups of Spheres, 332Reed, Simon

Methods of Modern Mathematical Physics, 514Reid

Julia. A Life in Mathematics, 45Courant in Gottingen and New York, 45Hilbert, 44Neyman–From Life, 45The Search for E.T. Bell, 45

ReinerMaximal Orders, 217

RemmertClassical Topics in Complex Function Theory,

117Theory of Complex Functions, 116

Revuz, YorContinuous Martingales and Brownian Motion,

568Richardson, Urbanke

Modern Coding Theory, 601Richtmyer, Morton

Difference Methods for Initial-value Problems,619

Riesz, Sz.-NagyFunctional Analysis, 164

RittDifferential Algebra, 460

Roberts, Varberg

Convex Functions, 311Robinson, A.

Non-standard Analysis, 593Robinson, D.

A Course in the Theory of Groups, 210

RockafellarConvex Analysis, 309

Rockafellar, WetsVariational analysis, 101

RogersHausdorff Measures, 99Packing and Covering, 373Theory of Recursive Functions and Effective

Computability, 594Rolfsen

Knots and Links, 328Ronan

Lectures on Buildings, 454

Symmetry and the Monster. One of theGreatest Quests of Mathematics, 32

Rosen, J.Symmetry Discovered: Concepts and

Applications in Nature and Science, 29Symmetry in Science. An Introduction to the

General Theory, 30

Symmetry Rules. How Science and Nature AreFounded on Symmetry, 30

Rosen, M.Number Theory in Function Fields, 359

RosenbergAlgebraic K-theory and Its Applications, 334

RossIntroduction to Probability Models, 559

Rotman

An Introduction to Homological Algebra, 228Rourke, Sanderson

Introduction to Piecewise-linear Topology, 351Rudin

Function Theory in the Unit Ball of Cn, 90Functional Analysis, 166Real and Complex Analysis, 90The Way I Remember It, 26

Ruelle

Statistical Mechanics: Rigorous Results, 509

INDEX 663

Thermodynamic Formalism. The Mathemat-ical Structures of Classical EquilibriumStatistical Mechanics, 510

RussellIntroduction to Mathematical Philosophy, 586

S

SaadIterative Methods for Sparse Linear Systems,

614Sachs, Wu

General Relativity for Mathematicians, 505Sagan

The Symmetric Group. Representations,Combinatorial Algorithms, and Symmet-ricFunctions, 487

SakaiC∗-algebras and W ∗-algebras, 181

SalsburgThe Lady Tasting Tea. How Statistics

Revolutionized Science in the TwentiethCentury, 45

Samko, Kilbas, MarichevFractional Integrals and Derivatives. Theory

and Applications, 95Samorodnitsky, Taqqu

Stable non-Gaussian Random Processes, 570Santalo

Integral Geometry and Geometric Probability,251

SarnakSome Applications of Modular Forms, 467

SatoLevy Processes and Infinitely Divisible

Distributions, 569Schaefer

Banach Lattices and Positive Operators, 202Topological Vector Spaces, 168

ScharlauQuadratic and Hermitian Forms, 392

Scharlau, OpolkaFrom Fermat to Minkowski. Lectures on the

Theory of Numbers and its HistoricalDevelopment, 59

Schechter

My Brain is Open. The MathematicalJourneys of Paul Erdos, 48

SchneiderConvex Bodies: the Brunn-Minkowski Theory,

312

Schoen, YauLectures on Differential Geometry, 259Lectures on Harmonic Maps, 259

SchrijverTheory of Linear and Integer Programming,

606Schroeder

Number Theory in Science andCommunication, 360

Schumaker

Spline Functions: Basic Theory, 622Schwartz

Theorie des Distributions, 171

Seifert, ThrelfallSeifert and Threlfall: A Textbook of Topology,

318

SerreA Course in Arithmetic, 385Complex Semisimple Lie Algebras, 441

Galois Cohomology, 372Linear Representations of Finite Groups, 484Local Algebra, 220

Local Fields, 371Trees, 466

Shafarevich

Basic Algebraic Geometry, 281Basic Notions of Algebra, 204

Shannon, Weaver

The Mathematical Theory of Communication,599

SharpeDifferential Geometry, 250

ShelahProper and Improper Forcing, 591

Shilov

Linear Algebra, 191Shimura

Introduction to the Arithmetic Theory ofAutomorphic Functions, 384

The Map of My Life, 24Shiryaev

Probability, 558

664 INDEX

ShoenfieldMathematical Logic, 584

Shohat, TamarkinThe Problem of Moments, 96

ShubinPseudodifferential Operators and Spectral

Theory, 424

SiegelTopics in Complex Function Theory, 276

Siegel, MoserLectures on Celestial Mechanics, 518

SilvermanAdvanced Topics in the Arithmetic of

Elliptic Curves, 386

The Arithmetic of Elliptic Curves, 385Smith

Monotone Dynamical Systems, 525Smith, Kahanpaa, Keklainen, Traves

An Invitation to Algebraic Geometry, 288

SmollerShock Waves and Reaction-diffusion

Equations, 433Soare

Recursively Enumerable Sets and Degrees.A Study of Computable Functions andComputably Generated Sets, 593

SpanierAlgebraic Topology, 326

Spicci

Beyond the Limit: The Dream of SofyaKovalevskaya, 47

SpitzerPrinciples of Random Walks, 562

Spivak

A Comprehensive Introduction to DifferentialGeometry, 243

Calculus, 82Calculus on Manifolds. A Modern Approach

to Classical Theorems of AdvancedCalculus, 82

Springer, G.

Introduction to Riemann Surfaces, 130Springer, T.

Linear Algebraic Groups, 447

StanleyEnumerative Combinatorics, 538

Steenrod

The Topology of Fibre Bundles, 325Stein

Harmonic Analysis: Real-variable Methods,Orthogonality, and OscillatoryIntegrals, 159

Singular Integrals and DifferentiabilityProperties of Functions, 157

Stein, Weiss

Introduction to Fourier Analysis on EuclideanSpaces, 158

Steinberg

Lectures on Chevalley Groups, 448Sternberg

Group Theory and Physics, 482Stewart

Introduction to Matrix Computations, 613

Why Beauty is Truth, 28Stichtenoth

Algebraic Function Fields and Codes, 601

StillwellMathematics and its History, 63

Strang, FixAn Analysis of the Finite Element Method,

618

StrebelQuadratic Differentials, 139

Stroock

Probability Theory, an Analytic View, 559Stroock, Varadhan

Multidimensional Diffusion Processes, 570Struik

A Concise History of Mathematics, 60

StruweVariational Methods. Applications to Non-

linear Partial Differential Equations andHamiltonian Systems, 431

StubhaugNiels Henrik Abel and His Times, 46

SturmfelsGrobner Bases and Convex Polytopes, 541

SweedlerHopf Algebras, 481

Switzer

Algebraic Topology—Homotopy andHomology, 327

Sz.-Nagy, Foias

Harmonic Analysis of Operators on Hilbert Space,

INDEX 665

146Szego

Orthogonal Polynomials, 106

T

TakesakiTheory of operator algebras, 180

Tauvel, YuLie Algebras and Algebraic Groups, 449

TaylorPartial Differential Equations, 423Pseudodifferential Operators, 424Pseudodifferential Operators and Nonlinear

PDE, 423Temam

Infinite-dimensional Dynamical Systems inMechanics and Physics, 526

Navier-Stokes Equations. Theory andNumerical Analysis, 615

TenenbaumIntroduction to Analytic and Probabilistic

Number Theory, 377Thirring

A Course in Mathematical Physics. Vol. I.Classical Dynamical Systems, 513

ThomStructural Stability and Morphogenesis. An

Outline of a General Theory of Models,529

ThurstonThe Geometry and Topology of Three

Manifolds, 345Three-dimensional Geometry and Topology,

Vol. 1, 346Titchmarsh

The Theory of Functions, 117The Theory of the Riemann Zeta-Function,

375Tits

Buildings of Spherical Type and FiniteBN-pairs, 453

tom DieckTransformation Groups, 476

TotikLogarithmic Potentials with External Fields,

151Triebel

Interpolation Theory, Function spaces,Differential Operators, 155

Theory of Function Spaces, 154Tsuji

Potential Theory in Modern Function Theory,149

TuraevQuantum Invariants of Knots and 3-manifolds,

331

U

UlamA Collection of Mathematical Problems, 108Adventures of a Mathematician, 23

V

van der Put, SingerGalois Theory of Linear Differential Equations,

461van der Vaart, Wellner

Weak Convergence and Empirical Processes.With Applications to Statistics, 571

van der WaerdenAlgebra, 194

van HeijenoortFrom Frege to Godel. A Source Book in

Mathematical Logic, 1879–1931, 585van Lint

Introduction to Coding Theory, 601Varadarajan

Lie Groups, Lie Algebras, and TheirRepresentations, 444

Varopoulos, Saloff-Coste, CoulhonAnalysis and Geometry on Groups, 147

VaughanThe Hardy-Littlewood Method, 379

VignerasArithmetique des algebres de quaternions, 384

VillaniOptimal Transport, Old and New, 430Topics in Optimal Transportation, 430

Voiculescu, Dykema, NicaFree Random Variables, 578

von NeumannMathematical Foundations of Quantum

Mechanics, 498

666 INDEX

The Computer and the Brain, 12von Neumann, Morgenstern

Theory of Games and Economic Behavior, 605

W

WaldschmidtDiophantine Approximation on Linear Alge-

braic Groups. Transcendence Propertiesof the Exponential Function in SeveralVariables, 383

WalkerAlgebraic Curves, 288

WallSurgery on Compact Manifolds, 351

WallachReal Reductive Groups, 491

WaltersAn Introduction to Ergodic Theory, 533

WarnerFoundations of Differentiable Manifolds and

Lie Groups, 235Washington

Introduction to Cyclotomic Fields, 369Watson

A Treatise on the Theory of Bessel Functions,86

WehrfritzInfinite Linear Groups. An Account of the

Group-Theoretic Properties of InfiniteGroups of Matrices, 472

WeibelAn Introduction to Homological Algebra, 228

WeilBasic Number Theory, 368Elliptic Functions According to Eisenstein and

Kronecker, 57Number theory. An Approach through His-

tory. From Hammurapi to Legendre, 55The Apprenticeship of a Mathematician, 22

WeinbergerThe Topological Classification of Stratified

Spaces, 344Wells

Differential Analysis on Complex Manifolds,275

WelshMatroid Theory, 543

WestIntroduction to Graph Theory, 547

WeylSpace, Time, Matter, 505Symmetry, 27The Classical Groups. Their Invariants and

Representations, 487The Concept of a Riemann Surface, 128The Theory of Groups and Quantum Mechan-

ics, 497Wheeden, Zygmund

Measure and Integral, 98Whitehead

Elements of Homotopy Theory, 337Whitham

Linear and Nonlinear Waves, 436Whittaker, Watson

A Course of Modern Analysis, 85Whyburn

Analytic Topology, 478Widder

The Laplace Transform, 145Wiener

I am a Mathematician. The later Life of aProdigy, 23

Cybernetics, or Control and Communicationin the Animal and the Machine, 597

Ex-prodigy. My Childhood and Youth, 23Extrapolation, Interpolation, and Smoothing

of Stationary Time Series, 598Wilkinson

The Algebraic Eigenvalue Problem, 612Willem

Minimax Theorems, 420Woess

RandomWalks on Infinite Graphs and Groups,563

WolfSpaces of Constant Curvature, 245

Y

YafaevMathematical Scattering Theory, 516

YaglomFelix Klein and Sophus Lie, 52

YosidaFunctional analysis, 174

INDEX 667

Z

ZariskiAlgebraic Surfaces, 301

Zariski, SamuelCommutative Algebra, 219

ZassenhausThe Theory of Groups, 207

ZeeFearful Symmetry. The Search for Beauty in

Modern Physics, 34Zeidler

Nonlinear Functional Analysis and ItsApplications, 186

ZhuOperator Theory in Function Spaces, 155

ZieglerLectures on Polytopes, 539

ZiemerWeakly Differentiable Functions. Sobolev Spaces

and Functions of Bounded Variation, 428Zimmer

Ergodic Theory and Semisimple Groups, 465Essential Results of Functional Analysis, 166

ZygmundTrigonometric Series, 147

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