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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Great Mathematics Books of the Twentieth Century: A Personal
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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