Great 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 . Books also by

Compactifications of Symmetric Spaces by Yves Guivarc’h, Lizhen Ji, and John C. Taylor, Birkhäuser, 1998 Compactifications of Symmetric and Locally Symmetric Spaces by 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, , 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 Great Mathematics Books of the Twentieth Century

A Personal Journey

Lizhen Ji Department of Mathematics University of Michigan

International Press www.intlpress.com Great Mathematics Books of the Twentieth Century: A Personal Journal by Lizhen Ji (Department of Mathematics, University of Michigan)

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A Aleksandrov, Kolmogorov, Lavrent’ev Mathematics: Its Content, Methods, and Abikoff Meaning, 12 The Real Analytic Theory of Teichm¨uller Alexandroff Space, 136 Elementary Concepts of Topology, 38 Abraham, Marsden Alexandroff, Hopf Foundations of Mechanics, 512 Topologie I, 316 Abramenko, Brown Alexandrov (or Alexandroff) Buildings. Theory and Applications, 455 Combinatorial Topology, 317 Acton Alfsen Numerical Methods that Work, 611 Compact Convex Sets and Boundary Adams, J. Integrals, 312 Stable Homotopy and Generalised Alligood, Sauer, Yorke Homology, 332 Chaos. An Introduction to Dynamical Adams, R., Fournier Systems, 521 Sobolev Spaces, 427 Alon, Spencer Adem, Milgram The Probabilistic Method, 576 Cohomology of Finite Groups, 336 Ambrosio, Fusco, Pallara Agmon Functions of Bounded Variation and Free Lectures on Elliptic Boundary Value Discontinuity Problems, 432 Problems, 422 Anderson, Fuller Ahlfors Rings and Categories of Modules, 216 Complex Analysis, 115 Anderson, Guionnet, Zeitouni Conformal Invariants: Topics in Geometric An Introduction to Random Matrices, 581 Function Theory, 133 Andrews Lectures on Quasiconformal Mappings, 132 The Theory of Partitions, 406 Aigner Apostol Combinatorial Theory, 544 Calculus, 84 Aigner, Ziegler Introduction to Analytic Number Theory, 377 Proofs from The Book, 107 Arbarello, Cornalba, Griffiths Ainsworth, Oden Geometry of Algebraic Curves, II, 298 A Posteriori Error Estimation in Finite Arbarello, Cornalba, Griffiths, Harris Element Analysis, 620 Geometry of Algebraic Curves, I, 297 Akhiezer, Glazman Arnold, L. Theory of Linear Operators in Hilbert Random Dynamical Systems, 523 Space, 170 Arnold, V. Akivis, Rosenfeld Geometrical Methods in the Theory of Elie´ Cartan (1869–1951), 75 Ordinary Differential Equations, 410

643 644 INDEX

Mathematical Methods of Classical Banach Mechanics, 512 Theory of Linear Operations, 163 Ordinary Differential Equations, 410 Bannai, Ito Artin, E. Algebraic Combinatorics. I. Association Schemes, Galois Theory, 364 539 Geometric Algebra, 452 Bardi, Capuzzo-Dolcetta Artin, M. Optimal Control and Viscosity Solutions of Algebra, 199 Hamilton-Jacobi-Bellman Equations, 434 Ash, Gross Barth, Hulek, Peters, Ven Fearless Symmetry. Exposing the Hidden Compact Complex Surfaces, 299 Patterns of Numbers, 33 Bass Astala, Iwaniec, Martin Algebraic K-theory, 335 Elliptic Partial Differential Equations and Baxter Quasiconformal Mappings in the Exactly Solved Models in Statistical Plane, 134 Mechanics, 511 Atiyah Beardon K -theory, 333 Iteration of Rational Functions, 531 Atiyah, MacDonald The Geometry of Discrete Groups, 468 Introduction to Commutative Algebra, 219 Beauville Attouch Surfaces Algebriques Complexes, 300 Variational Convergence for Functions and Beckenbach, Bellman Operators, 269 Inequalities, 111 Aubin Becker, Weispfenning Nonlinear Analysis on Manifolds. Monge Gr¨obner Bases. A Computational Approach Amp´ere Equations, 260 to Commutative Algebra, 542 Some Nonlinear Problems in Riemannian Bell Geometry, 260 Men of Mathematics, 42 Aubin, Cellina Benedetti, Petronio Differential Inclusions, 311 Lectures on Hyperbolic Geometry, 348 Aubin, Ekeland Bennett, Sharpley Applied Nonlinear Analysis, 102 Interpolation of Operators, 157 Aubin, Frankowska Benson Set-valued Analysis, 102 Representations and Cohomology, 336 Auslander, Reiten, Smalo of Artin Bensoussan, Lions, Papanicolaou Algebras, 492 Asymptotic Analysis for Periodic Structures, Axler 417 Linear Algebra Done Right, 190 Berge Graphs, 549 B Bergh, L¨ofstr¨om Interpolation Spaces. An Introduction, 156 Babin, Vishik Berlekamp, Conway, Guy Attractors of Evolution Equations, 527 Winning Ways for Your Mathematical Plays, Baker 608 Principles of Geometry, 283 Berline, Getzler, Vergne Transcendental Number Theory, 382 Heat Kernels and Dirac Operators, 262 Ballmann, Gromov, Schroeder Berman, Plemmons Manifolds of Nonpositive Curvature, 253 Nonnegative Matrices in the Mathematical INDEX 645

Sciences, 193 Modern Graph Theory, 546 Bertoin Random Graphs, 552 L´evy Processes, 569 Bolza Besicovitch Lectures on the Calculus of Variations, 270 Almost Periodic Functions, 143 Bombieri, Gubler Besse Heights in Diophantine Geometry, 390 Einstein Manifolds, 248 Bondy, Murty Manifolds all of Whose Geodesics are Graph Theory with Applications, 549 Closed, 248 Borel Bhatia Essays in the History of Lie Groups and Matrix Analysis, 193 Algebraic Groups, 74 Bhatia, Szeg¨o Introduction aux groupes arithm´etiques, 463 Stability Theory of Dynamical Linear Algebraic Groups, 445 Systems, 524 Borel, Casselman Biggs Automorphic Forms, Representations and Algebraic Graph Theory, 548 L-functions, 403 Billingsley Borel, Wallach Convergence of Probability Measures, 560 Continuous Cohomology, Discrete Subgroups, Probability and measure, 560 and Representations of Reductive Groups, Bingham, Goldie, Teugels 404 Regular variation, 94 Borevich, Shafarevich Birkhoff, Ga. Number Theory, 362 Lattice Theory, 200 Borwein, Erd´elyi Birkhoff, Ge. Polynomials and Polynomial Inequalities, 105 Dynamical Systems, 519 Bosch, G¨untzer, Remmert Birkhoff, Mac Lane Non-Archimedean Analysis. A Systematic Ap- A Survey of Modern Algebra, 196 proach to Rigid Analytic Geometry, 393 Birman Bosch, L¨utkebohmert, Raynaud Braids, Links, and Mapping N´eron Models, 393 Class Groups, 351 Bott, Tu Bishop, Crittenden Differential Forms in , 341 Geometry of Manifolds, 236 Bourbaki Bix Commutative Algebra, 220 Conics and Cubics, 289 Elements of the History of Mathematics, 63 Bjorck, Dahlquist Lie Groups and Lie Algebras, 442 Numerical Methods, 612 Bowen Blair Equilibrium States and the Ergodic Theory of Riemannian Geometry of Contact and Anosov Diffeomorphisms, 535 Symplectic Manifolds, 292 Boyd, El Ghaoui, Feron, Balakrishnan Bochnak, Coste, Roy Linear Matrix Inequalities in System and Real Algebraic Geometry, 290 Control Theory, 113 Bohner, Peterson Boyd, Vandenberghe Dynamic Equations on Time Scales, 525 Convex Optimization, 608 Bohr Boyer Almost Periodic Functions, 144 A History of Mathematics, 61 Bollob´as Bredon Graph Theory. An Introductory Course, 546 Introduction to Compact Transformation 646 INDEX

Groups, 475 Busemann Topology and Geometry, 327 The Geometry of Geodesics, 240 Breiman Buser Probability, 557 Geometry and Spectra of Compact Riemann Brenner, Scott Surfaces, 139 The Mathematical Theory of Finite Element Byron, Fuller Methods, 617 Mathematics of Classical and Quantum Physics, Brezis 498 Analyse Fonctionnelle. Th´eorie et Applications, 184 C Functional Analysis, Sobolev Spaces and Partial Differential Equations, 184 Caffarelli, Cabr´e Operateurs Maximaux Monotones et Fully Nonlinear Elliptic Equations, 429 Semi-groupes de Contractions dans les Canary, Epstein, Green espaces de Hilbert, 185 Notes on notes of Thurston, 346 Brezzi, Fortin Canuto, Hussaini, Quarteroni, Zang Mixed and Hybrid Finite Element Methods, Spectral Methods in Fluid Dynamics, 432 617 Carleson, Gamelin Complex Dynamics, 531 Bridson, Haefliger Carslaw, Jaeger Metric Spaces of Non-positive Curvature, 255 Conduction of Heat in Solids, 426 Brieskorn, Kn¨orrer Cartan Plane Algebraic Curves, 298 Elementary Theory of Analytic Functions of Brocker, tom Dieck One or Several Complex Variables, 115 Representations of Compact Lie Groups, 492 Cartan, Eilenberg Brouwer, Cohen, Neumaier Homological Algebra, 226 Distance-regular Graphs, 550 Carter Browder Finite Groups of Lie Type. Conjugacy Classes Surgery on Simply-connected Manifolds, 352 and Complex Characters, 206 Brown Simple Groups of Lie Type, 205 Buildings, 454 Cassels Cohomology of Groups, 335 An Introduction to Diophantine Bruns, Herzog Approximation, 383 Cohen-Macaulay Rings, 223 An Introduction to the Geometry of Numbers, Buhler 373 Gauss. A Biographical Study, 53 Local Fields, 371 Bump Rational Quadratic Forms, 393 Automorphic Forms and Representations, 404 Cassels, Fr¨ohlich Burago, D., Burago, Y., Ivanov Algebraic Number Theory, 367 A Course in Metric Geometry, 254 Casson, Bleiler Burago, Zalgaller Automorphisms of Surfaces after Nielsen and Geometric Inequalities, 112 Thurston, 347 Burde, Zieschang Castaing, Valadier Knots, 329 Convex Analysis and Measurable Burnside Multifunctions, 310 Theory of Groups of Finite Order, 207 Cercignani Burris, Sankappanavar The Boltzmann Equation and Its Applications, A Course in Universal Algebra, 203 510 INDEX 647

Cercignani, Illner, Pulvirenti A Scrapbook of Complex Curve Theory, 298 The Mathematical Theory of Dilute Gases, 510 Clifford, Preston Cesari The Algebraic Theory of Semigroups, 203 Optimization—Theory and Applications. Coddington, Levinson Problems with Ordinary Differential Theory of Ordinary Differential Equations, 408 Equations, 610 Cohen, H. symptotic Behavior and Stability Problems in A Course in Computational Algebraic Number Ordinary Differential Equations, 409 Theory, 370 Chang Advanced Topics in Computational Number Infinite-dimensional Morse Theory and Theory, 370 Multiple Solution Problems, 420 Cohen, P. Chang, Keisler Set Theory and the Continuum Hypothesis, Model Theory, 591 589 Chavel Cohn Eigenvalues in Riemannian Geometry, 261 Measure Theory, 98 Riemannian Geometry–A Modern Collet, Eckmann Introduction, 237 Iterated Maps on the Interval as Dynamical Cheeger, Ebin Systems, 522 Comparison Theorems in Riemannian Colton, Kress Geometry, 241 Integral Equation Methods in Scattering Chen, Shaw Theory, 517 Partial Differential Equations in Several Inverse Acoustic and Electromagnetic Complex Variables, 125 Scattering Theory, 419 Chern Comtet Complex Manifolds Without Potential Advanced Combinatorics. The Art of Finite Theory, 273 and Infinite Expansions, 539 Chevalley Conley Theory of Lie Groups. I. , 440 Isolated Invariant Sets and the Morse Index, Chihara 412 An Introduction to Orthogonal Connes Polynomials, 106 Noncommutative Geometry, 178 Chow, Hale Constantin, Foias Methods of Bifurcation Theory, 411 Navier-Stokes Equations, 434 Chriss, Ginzburg Conway, J.B. Representation Theory and Complex A Course in Functional Analysis, 167 Geometry, 491 Conway, J.H. Chung On Numbers and Games, 607 A Course in Probability Theory, 556 Conway, J.H., Burgiel, Goodman-Strauss Spectral Graph Theory, 551 The Symmetries of Things, 30 Church Conway, J.H., Curtis, Norton, Parker, Wilson Introduction to Mathematical Logic, 584 Atlas of Finite Groups. Maximal Subgroups Ciarlet and Ordinary Characters for Simple The Finite Element Method for Elliptic Groups, 212 Problems, 620 Conway, Sloane Clarke Sphere Packings, Lattices and Groups, 545 Optimization and Nonsmooth Analysis, 103 Cormen, Leiserson, Rivest Clemens Introduction to Algorithms, 603 648 INDEX

Cornfeld, Fomin, Sinai Systems Theory, 528 Ergodic Theory, 534 Curtis Corwin, Greenleaf Pioneers of Representation Theory: Frobenius, Representations of Nilpotent Lie Groups and Burnside, Schur, and Brauer, 68 Their Applications. Part I. Basic Theory Curtis, Reiner and Examples, 492 Methods of Representation Theory, 215 Courant, Friedrichs Curtis, Reiner Supersonic Flow and Shock Waves, 433 Representation Theory of Finite Groups and Courant, Hilbert Associative Algebras, 214 Methods of Mathematical Physics. Vol. I., Cvetkovi´c, Doob, Sachs Vol. II., 496 Spectra of Graphs, 551 Courant, John Introduction to Calculus and Analysis, 83 D Courant, Robbins What Is Mathematics?, 6 Da Prato, Zabczyk Stochastic Equations in Infinite Dimensions, Cover, Thomas 572 Elements of Information Theory, 596 Dacorogna Cowen, MacCluer Direct Methods in the Calculus of Variations, Composition Operators on Spaces of Analytic 268 Functions, 155 Dafermos Cox Hyperbolic Conservation Laws in Continuum Primes of the Form x2 + ny2.Fermat,Class Physics, 436 Field Theory and Complex Multiplication, Dal Maso 58 An Introduction to Γ-convergence, 269 Cox, Little, O’Shea Daubechies Ideals, Varieties, and Algorithms, 224 Ten Lectures on Wavelets, 160 Using Algebraic Geometry, 541 Dauben Coxeter Georg Cantor, 50 Introduction to Geometry, 39 Davenport Projective Geometry, 40 Multiplicative Number Theory, 381 Regular Polytopes, 41 The Higher Arithmetic. An Introduction to Coxeter, Greitzer the Theory of Numbers, 361 Geometry Revisited, 40 David, Semmes Coxeter, Moser Analysis of and on Uniformly Rectifiable Sets, Generators and Relations for Discrete Groups, 101 470 Davies Crilly Heat Kernels and Spectral Theory, 262 Arthur Cayley, 54 Davis Croft, Falconer, Guy Circulant Matrices, 194 Unsolved Problems in Geometry, 110 The Geometry and Topology of Coxeter Groups, Crowell, Fox 475 Introduction to Knot Theory, 330 Davis, Rabinowitz Csisz´ar, K¨orner Methods of Numerical Integration, 614 Information Theory. Coding Theorems for de Azc´arraga, Izquierdo Discrete Memoryless Systems, 597 Lie Groups, Lie Algebras, Cohomology and Curtain, Zwart Some Applications in Physics, 483 An Introduction to Infinite-dimensional Linear de Boor INDEX 649

A Practical Guide to Splines, 622 A History of Algebraic and Differential de la Harpe Topology 1900–1960, 72 Topics in Geometric Theory, 470 Foundations of Modern Analysis, 91 de Melo, van Strien Dirac One-dimensional Dynamics, 522 General Theory of Relativity, 504 Deift Dixmier Orthogonal Polynomials and Random Matri- C∗-algebras, 181 ces: a Riemann-Hilbert Approach, 581 von Neumann Algebras, 180 Deimling Dixon, Mortimer Nonlinear Functional Analysis, 185 Permutation Groups, 210 Deligne do Carmo Cohomologie ´etale, 391 Differential Geometry of Curves and Surfaces, Demazure, Gabriel 237 Groupes alg´ebriques. Tome I: G´eom´etrie Riemannian Geometry, 237 alg´ebrique, g´en´eralit´es, groupes Dolgachev commutatifs, 447 Lectures on , 294 Introduction to Algebraic Geometry and Donaldson, Kronheimer Algebraic Groups, 447 The Geometry of Four-manifolds, 350 Dembo, Zeitouni Doob Large Deviations Techniques and Applications, Classical Potential Theory and Its 574 Probabilistic Counterpart, 565 Dembowski Stochastic Processes, 565 Finite Geometries, 457 Doyle, Snell Demidovich Random Walks and Electric Networks, 563 Problems in Mathematical Analysis, 108 Drake, Singh Derezi´nski, G´erard Intermediate Set Theory, 587 Scattering Theory of Classical and Quantum Du Sautoy N-particle Systems, 515 Symmetry: A Journey into the Patterns of Derksen, Kemper Nature, 28 Computational Invariant Theory, 451 Dubrovin, Fomenko, Novikov Deuschel, Stroock Modern Geometry—Methods and Applications, Large Deviations, 574 238 Devaney Dudley An Introduction to Chaotic Dynamical Real Analysis and Probability, 560 Systems, 521 Dugundji DeVore, Lorentz Topology, 320 Constructive Approximation, 621 Dunford, Schwartz Dickson Linear Operators, 175 History of the Theory of Numbers. I, II, III, Dunham 70 Euler: the Master of Us All, 54 Diestel Duoandikoetxea Graph Theory, 547 Fourier Analysis, 142 Diestel, Jarchow, Tonge Duren Absolutely Summing Operators, 168 Theory of H p Spaces, 153 Diestel, Uhl Durrett Vector Measures, 100 Probability: Theory and Examples, 558 Dieudonn´e Duvaut, Lions 650 INDEX

Inequalities in Mechanics and Physics, 114 An Introduction to the History of Dym, McKean Mathematics, 62 Fourier Series and Integrals, 143 F E Faddeev, Takhtajan Edwards Hamiltonian Methods in the Theory of Riemann’s Zeta Function, 375 Solitons, 517 Eichler, Zagier Falconer The Theory of Jacobi Forms, 405 Fractal Geometry. Mathematical Foundations Eilenberg and Applications, 270 Automata, Languages, and Machines, 603 The Geometry of Fractal Sets, 271 Eilenberg, Steenrod Faltings, Chai Foundations of Algebraic Topology, 325 Degeneration of Abelian Varieties, 387 Einstein Faraut, Kor´anyi The Meaning of Relativity, 503 Analysis on Symmetric Cones, 257 Eisenbud Farkas, Kra Commutative Algebra. With a View Riemann Surfaces, 131 Toward Algebraic Geometry, 221 Federer Eisenhart Geometric Measure Theory, 265 Riemannian Geometry, 239 Feit Ekeland, T´emam The Representation Theory of Finite Groups, Convex Analysis and Variational 213 Problems, 310 Feller Ellis An Introduction to Probability Theory and its Entropy, Large Deviations, and Statistical Applications, 555 Mechanics, 574 Fenchel, Nielsen Engel, Nagel Discontinuous Groups of Isometries in the One-parameter Semigroups for Linear Hyperbolic Plane, 468 Evolution Equations, 176 Feynman,Leighton,Sands Engelking The Feynman Lectures on Physics, 502 General Topology, 320 Field, Golubitsky Engl, Hanke, Neubauer Symmetry in Chaos. A Search for Pattern in Regularization of Inverse Problems, 419 Mathematics, Art, and Nature, 31 Enriques Fine Le Superficie Algebriche, 301 Basic Hypergeometric Series and Applications, Epstein, Cannon, Holt, Levy, Paterson, Thurston 406 Word Processing in Groups, 471 Fleming, Soner Erd´elyi, Magnus, Oberhettinger, Tricomi Controlled Markov Processes and Viscosity Higher Transcendental Functions, 86 Solutions, 566 Ethier, Kurtz Fletcher, Markovic Markov Processes, 571 Quasiconformal Maps and Teichm¨uller Evans Theory, 138 Partial Differential Equations, 413 Folland Evans, Gariepy Harmonic Analysis in Phase Space, 160 Measure Theory and Fine Properties of Real Analysis. Modern Techniques and Their Functions, 99 Applications, 92 Eves Forster INDEX 651

Lectures on Riemann Surfaces, 131 The Theory of Matrices, 192 Forsythe, Wasow Garcia-Cuerva, Rubio de Francia Finite-difference Methods for Partial Weighted Norm Inequalities and Related Differential Equations, 618 Topics, 113 Fraleigh Gardiner A First Course in Abstract Algebra, 200 Teichm¨uller Theory and Quadratic Frankel Differentials, 137 The Geometry of Physics, 239 Gardiner, Lakic Frenkel, Lepowsky, Meurman Quasiconformal Teichm¨uller Theory, 138 Vertex Operator Algebras and the Gardner Monster, 481 Geometric Tomography, 312 Fricke, Klein Garey, Johnson Vorlesungenuber ¨ die Theorie der Computers and Intractability, 602 elliptischen Modulfunctionen, 397 Garnett Vorlesungen uber die Theorie der Bounded Analytic Functions, 152 automorphen Funktionen, 396 Garnett, Marshall Fried, Jarden Harmonic Measure, 153 Field Arithmetic, 394 Garrett Friedman Buildings and Classical Groups, 455 Partial Differential Equations of Parabolic Gasper, Rahman Type, 426 Basic Hypergeometric Series, 405 Fuchs Geck Infinite Abelian Groups, 473 An Introduction to Algebraic Geometry and Fukushima, Oshima, Takeda Algebraic Groups, 449 Dirichlet Forms and Symmetric Markov Gelbart Processes, 561 Automorphic Forms on Ad´ele Groups, 401 Fulton Gelbaum, Olmsted Algebraic Curves. An Introduction to Counterexamples in Analysis, 96 Algebraic Geometry, 288 Gelfand Intersection Theory, 302 Lectures on Linear Algebra, 188 Introduction to Intersection Theory in Gelfand, Fomin Algebraic Geometry, 304 Calculus of Variations, 268 Introduction to Toric Varieties, 307 Gelfand, Graev, Pyatetskii-Shapiro Young Tableaux, 486 Fulton, Harris Representation Theory and Automorphic Representation Theory. A first Course, 489 Functions, 172, 399 Furstenberg Gelfand, Kapranov, Zelevinsky Recurrence in Ergodic Theory and Discriminants, Resultants, and Combinatorial Number Theory, 536 Multidimensional Determinants, 308 Gelfand, Manin G Methods of Homological Algebra, 229 Gelfand, Shilov, Vilenkin, Graev Galdi Generalized Functions, 172 An Introduction to the Mathematical Theory Gelfond of the Navier-Stokes Equations, 434 Transcendental and Algebraic Numbers, 383 Gallot, Hulin, Lafontaine George, Askey, Roy Riemannian Geometry, 238 Special Functions, 87 Gantmacher Georgii 652 INDEX

Gibbs Measures and Phase Transitions, 510 Complex Variable, 121 Giaquinta Gompf, Stipsicz Multiple Integrals in the Calculus of Variations 4-manifolds and Kirby Calculus, 350 and Nonlinear Elliptic Systems, 269 Goodman, Wallach Gilbarg, Trudinger Representations and Invariants of the Elliptic Partial Differential Equations of Classical Groups, 488 Second Order, 421 Symmetry, Representations, and Invariants, 489 Gilkey Gorenstein Invariance Theory, the Heat Equation, and the Finite Groups, 208 Atiyah-Singer Index Theorem, 263 Gorenstein, Lyons, Solomon Gillman, Jerison The Classification of the Finite Simple Rings of Continuous Functions, 183 Groups, 211 Girault, Raviart Goresky, MacPherson Finite Element Methods for Navier-Stokes Stratified Morse theory, 343 Equations, 619 Goursat Giusti A Course in Mathematical Analysis, 81 Minimal Surfaces and Functions of Gowers, Barrow-Green, Leader Bounded Variation, 252 The Princeton Companion to Mathematics, 14 Glimm, Jaffe Graham, Knuth, Patashnik Quantum Physics. A Functional Integral Concrete Mathematics. A Foundation for Point of View, 511 Computer Science, 595 Godel Granas, Dugundji The Consistency of the Continuum Fixed Point Theory, 321 Hypothesis, 589 Gratzer Godement General Lattice Theory, 201 Topologie alg´ebrique et th´eorie des faisceaux, Grauert, Remmert 127 Coherent Analytic Sheaves, 126 Godsil, Royle Greenleaf Algebraic Graph Theory, 550 Invariant Means on Topological Groups and Goebel, Kirk Their Applications, 536 Topics in Metric Fixed Point Theory, 321 Griffiths, Harris Gohberg, Krein Principles of Algebraic Geometry, 286 Introduction to the Theory of Linear Grimmett Nonselfadjoint Operators, 170 Percolation, 577 Goldman Grisvard Complex Hyperbolic Geometry, 468 Elliptic Problems in Nonsmooth Domains, 422 Goldstein, Poole, Safko Grochenig Classical Mechanics, 513 Foundations of Time-frequency Analysis, 144 Golub, Van Loan Gromov Matrix Computations, 613 Metric Structures for Riemannian and Golubitsky, Guillemin Non-Riemannian Spaces, 253 Stable Mappings and Their Singularities, 341 Asymptotic Invariants of Infinite Groups. Golumbic Geometric , 471 Algorithmic Graph Theory and Perfect Partial Differential Relations, 264 Graphs, 551 Grothendieck Goluzin The El´´ ements de g´eom´etrie alg´ebrique, 279 Geometric Theory of Functions of a Grotschel, Lov´asz, Schrijver INDEX 653

Geometric Algorithms and Combinatorial A Hilbert Space Problem Book, 169 Optimization, 609 Finite-dimensional Vector Spaces, 189 Gruber I Want to Be a Mathematician. An Convex and Discrete Geometry, 311 Automathography in Three Parts, 22 Gruber, Lekkerkerker Measure Theory, 97 Geometry of Numbers, 373 Naive Set Theory, 587 Grunbaum Harary Convex Polytopes, 540 Graph Theory, 548 Grunbaum, Shephard Hardy Tilings and Patterns, 31 A Course of Pure Mathematics, 80 Tilings and Patterns. An Introduction, 32 A Mathematician’s Apology, 19 Guckenheimer, Holmes Divergent Series, 94 Nonlinear Oscillations, Dynamical Systems, Hardy, Littlewood, P´olya and Bifurcations of Vector Fields, 524 Inequalities, 110 Guillemin, Pollack Hardy, Wright Differential Topology, 341 An Introduction to the Theory of Numbers, Guillemin, Sternberg 356 Geometric Asymptotics, 416 Hargittai, I., Hargittai, M. Symplectic Techniques in Physics, 290 Symmetry Through the Eyes of a Chemist, 35 Gunning Symmetry: A Unifying Concept, 36 Introduction to Holomorphic Functions of Harris Several Variables, 124 Algebraic Geometry. A First Course, 287 Gunning, Rossi Harris, Morrison Analytic Functions of Several Complex Moduli of Curves, 296 Variables, 123 Hartman Guy Ordinary Differential Equations, 409 Unsolved Problems in Number Theory, 109 Hartshorne H Algebraic Geometry, 285 Hasse Hairer, Norsett, Wanner Number Theory, 362 Solving Ordinary Differential Equations, 615 Hatcher Halberstam, Richert Algebraic Topology, 326 Sieve Methods, 379 Hawking, Ellis Hale The Large Scale Structure of Space-time, 506 Asymptotic Behavior of Dissipative Systems, Hawkins 526 Emergence of the Theory of Lie Groups. An Theory of Functional Differential Equations, Essay in the History of Mathematics 1869– 530 1926, 73 Hale, Verduyn Lunel Hayman Introduction to Functional-differential Meromorphic Functions, 122 Equations, 530 Haynes, Hedetniemi, Slater Hall Fundamentals of Domination in Graphs, 550 The Theory of Groups, 209 Hecke Hall, Heyde Lectures on the Theory of Algebraic Numbers, Martingale Limit Theory and its Application, 366 569 Heinonen Halmos Lectures on Analysis on Metric Spaces, 100 654 INDEX

Heinonen, Kilpel¨ainen, Martio Hodge Nonlinear Potential Theory of Degenerate The Theory and Applications of Harmonic Elliptic Equations, 151 Integrals, 342 Helgason Hodge, Pedoe Differential Geometry and Symmetric Spaces, Methods of Algebraic Geometry, 282 256 Hodges A. Differential Geometry, Lie Groups, and Alan Turing: the Enigma, 47 Symmetric Spaces, 256 Hodges W. Geometric Analysis on Symmetric Spaces, 257 Model Theory, 592 Hempel Hofer, Zehnder 3-manifolds, 349 Symplectic Invariants and Hamiltonian Henrici Dynamics, 292 Applied and Computational Complex Hoffman P. Analysis, 119 The Man Who Loved Only Numbers, 49 Henry Hoffman, K. Geometric Theory of Semilinear Parabolic Banach Spaces of Analytic Functions, 154 Equations, 425 Hofstadter Herstein G¨odel, Escher, Bach: an Eternal Golden Braid, Topics in Algebra, 200 585 Hewitt, Ross Hopcroft, Ullman Abstract Harmonic Analysis, 145 Introduction to Automata Theory, Hilbert Languages, and Computation, 603 The Theory of Algebraic Number Fields, 365 Hopf Theory of Algebraic Invariants, 450 Differential Geometry in the Large, 234 Hilbert, Cohn-Vossen H¨ormander Geometry and the Imagination, 37 An Introduction to Complex Analysis in Hille, Phillips Several Variables, 272 Functional Analysis and Semi-groups, 177 Lectures on Nonlinear Hyperbolic Differential Hiller Equations, 415 Geometry of Coxeter Groups, 474 Linear Partial Differential Operators, 414 Hindry, Silverman Notions of Convexity, 415 Diophantine Geometry. An Introduction, 389 The Analysis of Linear Partial Differential Hiriart-Urruty, Lemar´echal Operators. I-IV, 414 Convex Analysis and Minimization Horn, Johnson Algorithms, 607 Matrix Analysis, 191 Hirsch Topics in Matrix Analysis, 192 Differential Topology, 340 Householder Hirsch, Smale The Theory of Matrices in Numerical Analysis, Differential Equations, Dynamical Systems, 613 and Linear Algebra, 411 Hovey Hirschfeld Model Categories, 337 Projective Geometries Over Finite Fields, 456 Howie Hirschfeld, Thas Fundamentals of Semigroup Theory, 204 General Galois Geometries, 456 Hsiang Hirzebruch Cohomology Theory of Topological Topological Methods in Algebraic Geometry, Transformation Groups, 476 289 Hua INDEX 655

Additive Theory of Prime Numbers, 380 Topics in Classical Automorphic Forms, 402 Introduction to Number Theory, 358 Iwaniec, Kowalski Hubbard Analytic Number Theory, 378 Teichm¨uller Theory and Applications to Geometry, Topology, and Dynamics, 137 J Hughes Random Walks and Random Environments, Jaco 577 Lectures on Three-manifold Topology, 349 Humphreys Jacobson Introduction to Lie Algebras and Basic Algebra, 198 Representation Theory, 443 Lie Algebras, 445 Linear Algebraic Groups, 446 Jacod, Shiryaev Reflection Groups and Coxeter Groups, 474 Limit Theorems for Stochastic Processes, 568 Huppert Jacquet, Langlands Endliche Gruppen. I., 210 Automorphic Forms on GL(2), 400 Huppert, Blackburn James, Kerber Finite groups. II, III, 210 The Representation Theory of the Symmetric Hurewicz, Wallman Group, 486 Dimension Theory, 322 Janson, Svante, Luczak, Rucinski Huybrechts Random Graphs, 552 Complex Geometry. An Introduction, 274 Jantzen Huybrechts, Lehn Representations of Algebraic Groups, 452 The Geometry of Moduli Spaces of Sheaves, Jech 295 Set Theory, 588 Jikov, Kozlov, Oleinik I Homogenization of Differential Operators and Integral Functionals, 579 Ikeda, Watanabe John Stochastic Differential Equations and Diffusion Partial Differential Equations, 416 Processes, 572 Jost Imayoshi, Taniguchi Riemannian Geometry and Geometric An Introduction to Teichm¨uller Spaces, 136 Analysis, 260 Ince Joyce Ordinary Differential Equations, 410 Compact Manifolds with Special , 249 Ireland, Rosen Jurdjevic A Classical Introduction to Modern Number Geometric Control Theory, 431 Theory, 359 Isaacs K Character Theory of Finite Groups, 214 Isakov Kac, M. Inverse Problems for Partial Differential Enigmas of Chance, 25 Equations, 418 Statistical Independence in Probability, Ito, McKean Analysis and Number Theory, 557 Diffusion Processes and their Sample Paths, Kac, M., Ulam 567 Mathematics and Logic, 10 Ivic Kac, V. The Riemann Zeta-function, 375 Infinite-dimensional Lie Algebras, 479 Iwaniec Kadison, Ringrose 656 INDEX

Fundamentals of the Theory of Operator An Introduction to Variational Inequalities and Algebras, 182 Their Applications, 417 Kahane Kirby, Siebenmann Some Random Series of Functions, 577 Foundational Essays on Topological Manifolds, Kailath Smoothings, and Triangulations, 353 Linear Systems, 528 Klee, Wagon Kallenberg Old and New Unsolved Problems in Plane Foundations of Modern Probability, 558 Geometry and Number Theory, 18 Kanigel Kleene The Man Who Knew Infinity. A Life of the Mathematical Logic, 590 Genius Ramanujan, 49 Klein Kapovich Development of Mathematics in the 19th Hyperbolic Manifolds and Discrete Groups, 348 Century, 76 Karatsuba, Voronin Lectures on Mathematics, 77 The Riemann Zeta-function, 376 Lectures on the Icosahedron and the Solution Karatzas, Shreve of Equations of the Fifth Degree, 398 Brownian Motion and Stochastic Calculus, 572 Klimek Methods of Mathematical Finance, 573 Pluripotential Theory, 150 Karoubi Kline K-theory. An Introduction, 334 Mathematical Thought from Ancient to Kashiwara, Schapira Modern Times, 65 Sheaves on Manifolds, 127 Klingenberg Kassel Riemannian Geometry, 242 Quantum Groups, 480 Kloeden, Platen Kato Numerical Solution of Stochastic Differential Perturbation Theory for Linear Operators, 428 Equations, 616 Katok, Hasselblatt Knapp Introduction to the Modern Theory of Lie Groups Beyond an Introduction, 444 Dynamical Systems, 520 Representation Theory of Semisimple Groups. Katz An Overview Based on Examples, 490 A History of Mathematics. An Introduction, Knopp 60 Theory of Functions, 118 Katz, Sarnak Knuth Random Matrices, Frobenius Eigenvalues, and The Art of Computer Programming, 595 Monodromy, 581 Kobayashi Katznelson Differential Geometry of Complex Vector An Introduction to Harmonic Analysis, 141 Bundles, 249 Kechris Hyperbolic Complex Spaces, 275 Classical Descriptive Set Theory, 588 Hyperbolic Manifolds and Holomorphic Kelley Mappings, 275 General Topology, 319 Transformation Groups in Differential Kempf, Knudsen, Mumford, Saint-Donat Geometry, 476 Toroidal Embeddings. I, 307 Kobayashi, Nomizu Khinchin Foundations of Differential Geometry, 245 Continued Fractions, 364 Koblitz Three Pearls of Number Theory, 363 p-adic Numbers, p-adic Analysis, and Kinderlehrer, Stampacchia Zeta-functions, 360 INDEX 657

Kodaira The Mathematical Theory of Viscous Complex Manifolds and Deformation of Incompressible Flow, 435 Complex Structures, 273 Ladyzhenskaya, Uraltseva Kolchin Linear and Quasilinear Elliptic Equations, 423 Differential Algebra and Algebraic Groups, 460 Lakshmikantham, Bainov, Simeonov Koll´ar Theory of Impulsive Differential Equations, 417 Rational Curves on Algebraic Varieties, 296 Lam Koll´ar, Mori Introduction to Quadratic Forms Over Fields, Birational Geometry of Algebraic Varieties, 297 391 Kolmogorov Lamb Foundations of the Theory of Probability, 554 Hydrodynamics, 437 Kolmogorov, Fomin Lancaster, Tismenetsky Elements of the Theory of Functions and The Theory of Matrices, 193 Functional Analysis, 164 Landau, Lifshitz Komornik Course of Theoretical Physics, 499 Exact Controllability and Stabilization, 528 Landkof Korner Foundations of Modern Potential Theory, 149 Fourier Analysis, 11 Lang The Pleasures of Counting, 10 Algebra, 197 Kosmann-Schwarzbach Algebraic Number Theory, 368 The Noether Theorems. Invariance and Cyclotomic Fields, 369 Conservation Laws in the Twentieth Elliptic Functions, 386 Century, 35 Fundamentals of Diophantine Geometry, 389 Krantz Introduction to Modular Forms, 401 Function Theory of Several Complex Variables, Lange, Birkenhake 125 Complex Abelian Varieties, 388 Kuang Langlands Delay Differential Equations with Applications Base Change for GL(2), 403 in Population Dynamics, 525 On the Functional Equations Satisfied by Kuipers, Niederreiter Eisenstein Series, 402 Uniform Distribution of Sequences, 561 Lawler Kunen Intersections of Random Walks, 564 Set Theory. An Introduction to Independence Lawson, Michelsohn Proofs, 590 Kunita Spin Geometry, 247 Stochastic Flows and Stochastic Differential Lax Equations, 573 Functional analysis, 165 Kuratowski Hyperbolic Systems of Conservation Laws and Topology, 318 the Mathematical Theory of Shock Waves, Kurosh 433 The Theory of Groups, 209 Lazarsfeld Positivity in Algebraic Geometry, 305 L Lebedev Special Functions and Their Applications, 89 Ladyenskaja, Solonnikov, Uralceva Lederman, Hill Linear and Quasilinear Equations of Parabolic Symmetry and the Beautiful Universe, 34 Type, 426 Ledoux, Talagrand Ladyzhenskaya Probability in Banach Spaces. Isoperimetry 658 INDEX

and Processes, 562 Lov´asz Lee Combinatorial Problems and Exercises, 544 Riemannian Manifolds. An Introduction to Lubotzky Curvature, 236 Discrete Groups, Expanding Graphs and Lefschetz Invariant Measures, 467 Algebraic Topology, 319 Lueck 2 Lehner L -invariants: Theory and Applications to Discontinuous Groups and Automorphic Geometry and K-theory, 478 Functions, 398 Lunardi Lehto Analytic Semigroups and Optimal Regularity Univalent Functions and Teichm¨uller Spaces, in Parabolic Problems, 178 135 Lusztig Lehto, Virtanen Introduction to Quantum Groups, 480 Quasiconformal Mappings in the Plane, 133 Lyndon, Schupp Lickorish Combinatorial Group Theory, 470 An Introduction to Knot Theory, 330 Lidl, Niederreiter M Finite Fields, 359 Mac Lane Lieb, Loss Categories for the Working Mathematician, 230 Analysis, 93 Homology, 227 Lifshitz,Pitaevskii Macdonald Course of Theoretical Physics, 501 Symmetric Functions and Hall Polynomials, Liggett 484 Interacting Particle Systems, 579 Mackey Stochastic Interacting Systems: Contact, Voter Representations in Physics, and Exclusion Processes, 579 Probability, and Number Theory, 497 Lind, Marcus MacLane, Birkhoff An Introduction to Symbolic Dynamics and Algebra, 197 Coding, 523 MacWilliams, Sloane Lindenstrauss, Tzafriri The Theory of Error-correcting Codes, 600 Classical Banach Spaces, 167 Magnus Lions Noneuclidean Tesselations and Their Groups, Mathematical Topics in Fluid Mechanics, 435 397 Quelques m´ethodes de r´esolution des Majid probl`emes aux limites non lin´eaires, 430 Foundations of Quantum Group Theory, 480 Littlewood Malliavin Littlewood’s Miscellany, 21 Stochastic Analysis, 575 Lo´eve Mandelbrot Probability Theory, 556 The Fractal Geometry of Nature, 271 Loday Mane Cyclic Homology, 231 Ergodic Theory and Differentiable Dynamics, Lojasiewicz 535 Introduction to Complex Analytic Geometry, Manin 126 A Course in Mathematical Logic, 590 Lorentz, Golitschek, Makovoz Cubic Forms. Algebra, Geometry, Arithmetic, Constructive Approximation. Advanced 394 Problems, 621 Marchenko INDEX 659

Sturm Liouville Operators and Applications, J-holomorphic Curves and Symplectic 516 Topology, 291 Marcus Introduction to Symplectic Topology, 291 Number Fields, 367 McKean Marden Stochastic Integrals, 567 Outer Circles. An Introduction to Hyperbolic McMullen 3-manifolds, 348 Complex Dynamics and Renormalization, 532 Margulis Renormalization and 3-manifolds Which Fiber Discrete Subgroups of Semisimple Lie Groups, Over the Circle, 532 466 McWeeny Marker Symmetry: An Introduction to Group Theory Model theory. An Introduction, 592 and Its Applications, 30 Markushevich Mehta Theory of Functions of a Complex Variable, Random Matrices, 580 120 Melrose Marsden, Ratiu The Atiyah-Patodi-Singer Index Theorem, 424 Introduction to Mechanics and Symmetry. A Meyer, Coifman Basic Exposition of Classical Mechanical Wavelets and Operators, 161 Systems, 501 Meyn, Tweedie Marshall, Olkin Markov Chains and Stochastic Stability, 566 Inequalities: Theory of Majorization and Its Milman, Schechtman Applications, 112 Asymptotic Theory of Finite-dimensional Maskit Normed Spaces, 313 Kleinian Groups, 469 Milne Maslov, Fedoriuk Etale´ Cohomology, 390 Semiclassical Approximation in Quantum Milnor Mechanics, 416 Dynamics in One Complex Variable. Matousek Introductory Lectures, 531 Lectures on Discrete Geometry, 540 Introduction to Algebraic K-theory, 334 Matsumura Lectures on the h-cobordism Theorem, 339 Commutative Algebra, 221 Morse Theory, 339 Commutative Ring Theory, 222 Singular Points of Complex Hypersurfaces, 289 Mattila Topology from the Differentiable Viewpoint, Geometry of Sets and Measures in Euclidean 340 Spaces. Fractals and Rectifiability, 266 Milnor, Stasheff Mawhin, Willem Characteristic Classes, 324 Critical Point Theory and Hamiltonian Misner, Thorne, Wheeler Systems, 420 Gavitation, 507 May Mitrinovi´c Simplicial Objects in Algebraic Topology, 328 Analytic Inequalities, 111 Maz’ja Miyake Sobolev Spaces, 427 Modular Forms, 401 McCleary Moeglin, Waldspurger User’s Guide to Spectral Sequences, 230 Spectral Decomposition and Eisenstein Series. McConnell, Robson Une paraphrase de l’Ecriture,´ 403 Noncommutative Noetherian Rings, 224 Monastyrsky McDuff, Salamon Riemann, Topology, and Physics, 52 660 INDEX

Montgomery, D., Zippin Mumford, Fogarty, Kirwan Topological Transformation Groups, 477 Geometric Invariant Theory, 293 Montgomery, H. Mumford, Series, Wright Ten Lectures on the Interface Between Indra’s Pearls, 36 Analytic Number Theory and Harmonic Munkres Analysis, 378 Elements of Algebraic Topology, 327 Montgomery, H., Vaughan Topology: A First Course, 327 Multiplicative Number Theory. I. Classical Murray Theory, 381 Mathematical Biology, 526 Montgomery, R. A Tour of Subriemannian Geometries, Their N Geodesics and Applications, 247 Montgomery, S. Nadler Hopf Algebras and Their Actions on Rings, Continuum Theory. An Introduction, 320 481 Nag Moore The Complex Analytic Theory of Teichm¨uller Spaces, 135 Foundations of Point Set Theory, 319 Nagata Morgan Local Rings, 223 Geometric Measure Theory, A Beginner’s Guide, Modern Dimension Theory, 322 267 Nakajima Morrey Lectures on Hilbert Schemes of Points on Multiple Integrals in the Calculus of Surfaces, 294 Variations, 267 Nathanson Morrow, Kodaira Additive Number Theory. Inverse Problems Complex Manifolds, 274 and the Geometry of Sumsets, 380 Morse Necas The Calculus of Variations in the Large, 339 Les m´ethodes directes en th´eorie des ´equations Moschovakis elliptiques, 421 Descriptive Set Theory, 588 Nehari Moser Conformal Mapping, 121 Stable and Random Motions in Dynamical Neugebauer Systems, 519 A History of Ancient Mathematical Mostow Astronomy, 70 Strong Rigidity of Locally Symmetric Spaces, Neukirch 464 Algebraic Number Theory, 369 Motohashi Neukirch, Schmidt, Wingberg Spectral Theory of the Riemann Zeta-function, Cohomology of Number Fields, 372 376 Newman Mukai The World of Mathematics. Vols. I-IV, 66 An Introduction to Invariants and Moduli, 295 Newstead Mumford Introduction to Moduli Problems and Orbit Abelian Varieties, 387 Spaces, 293 Algebraic Geometry. I, 284 Nielsen, Chuang Lectures on Curves on an Algebraic Surface, Quantum Computation and Quantum 302 Information, 597 Tata Lectures on Theta, 387 Nocedal, Wright The Red book of Varieties and Schemes, 283 Numerical Optimization, 609 INDEX 661

Novikov, Manakov, Pitaevskii, Zakharov Semigroups of Linear Operators and Applica- Theory of Solitons. The Inverse Scattering tions to Partial Differential Equations, 176 Method, 515 Pedersen Nualart C∗-algebras and Their Automorphism Groups, The Malliavin Calculus and Related Topics, 182 575 Penrose The Road to Reality. A complete Guide to the O Laws of the Universe, 508 Perko O’Meara Differential equations and dynamical systems, Introduction to Quadratic Forms, 392 522 O’Neill Pesin Semi-Riemannian Geometry, 246 Dimension Theory in Dynamical Systems, 323 Oda Petersen, K. Convex Bodies and Algebraic Geometry, 306 Ergodic Theory, 534 Olver, F. Petersen, P. Asymptotics and Special Functions, 88 Riemannian Geometry, 241 Olver, P. Petkovsek, Wilf, Zeilberger Applications of Lie Groups to Differential A = B, 599 Equations, 461 Petrovski Classical Invariant Theory, 451 Ordinary Differential Equations, 409 Equivalence, Invariants, and Symmetry, 462 Phillips Onishchik, Vinberg Scattering Theory for Automorphic Functions, Lie Groups and Algebraic Groups, 443 402 Orlik, Terao Pierce Arrangements of Hyperplanes, 344 Associative Algebras, 215 Ortega, Rheinboldt Pisier Iterative Solution of Nonlinear Equations in The Volume of Convex Bodies and Banach Space Several Variables , 616 Geometry, 313 Oxley Platonov, Rapinchuk Matroid Theory, 542 Algebraic Groups and Number Theory, 448 Podlubny P Fractional Differential Equations, 95 P´olya Paley, Wiener How to Solve it. A New Aspect of Fourier Transforms in the Complex Domain, Mathematical Method, 15 143 Mathematical Discovery. On Understanding, Papadimitriou Learning, and Teaching Problem Solving, Computational Complexity, 604 17 Parshall, Rowe Mathematics and Plausible Reasoning, 16 TheEmergenceoftheAmerican Mathematical P´olya,Szeg¨o Research Community, 1876–1900, 71 Isoperimetric Inequalities in Mathematical Physics, Passman 263 The Algebraic Structure of Group Rings, 217 Problems and Theorems in Analysis, 104 Payne, Thas Pommerenke Finite Generalized Quadrangles, 456 Boundary Behaviour of Conformal Maps, 123 Pazy Pontryagin 662 INDEX

Topological Groups, 145 Ritt Pressley, Segal Differential Algebra, 460 Loop Groups, 479 Roberts, Varberg Protter, Weinberger Convex Functions, 311 Maximum Principles in Differential Equations, Robinson, A. 422 Non-standard Analysis, 593 Robinson, D. R A Course in the Theory of Groups, 210 Rockafellar Rabinowitz Convex Analysis, 309 Minimax Methods in Critical Point Theory with Rockafellar, Wets Applications to Differential Equations, 419 Variational analysis, 101 Rademacher, Toeplitz Rogers The Enjoyment of Mathematics; Selections from Hausdorff Measures, 99 Mathematics for the Amateur, 8 Packing and Covering, 373 Raghunathan Theory of Recursive Functions and Effective Discrete Subgroups of Lie Groups, 464 Computability, 594 Ransford Rolfsen Potential Theory in the Complex Plane, 150 Knots and Links, 328 Ratcliffe Ronan Foundations of Hyperbolic Manifolds, 348 Lectures on Buildings, 454 Ravenel Symmetry and the Monster. One of the Complex Cobordism and Stable Homotopy Greatest Quests of Mathematics, 32 Groups of Spheres, 332 Reed, Simon Rosen, J. Methods of Modern Mathematical Physics, 514 Symmetry Discovered: Concepts and Reid Applications in Nature and Science, 29 Julia. A Life in Mathematics, 45 Symmetry in Science. An Introduction to the Courant in G¨ottingen and New York, 45 General Theory, 30 Hilbert, 44 Symmetry Rules. How Science and Nature Are Neyman–From Life, 45 Founded on Symmetry, 30 The Search for E.T. Bell, 45 Rosen, M. Reiner Number Theory in Function Fields, 359 Maximal Orders, 217 Rosenberg K Remmert Algebraic -theory and Its Applications, 334 Classical Topics in Complex Function Theory, Ross 117 Introduction to Probability Models, 559 Theory of Complex Functions, 116 Rotman Revuz, Yor An Introduction to Homological Algebra, 228 Continuous Martingales and Brownian Motion, Rourke, Sanderson 568 Introduction to Piecewise-linear Topology, 351 Richardson, Urbanke Rudin n Modern Coding Theory, 601 Function Theory in the Unit Ball of C ,90 Richtmyer, Morton Functional Analysis, 166 Difference Methods for Initial-value Problems, Real and Complex Analysis, 90 619 The Way I Remember It, 26 Riesz, Sz.-Nagy Ruelle Functional Analysis, 164 Statistical Mechanics: Rigorous Results, 509 INDEX 663

Thermodynamic Formalism. The Mathemat- My Brain is Open. The Mathematical ical Structures of Classical Equilibrium Journeys of Paul Erd˝os, 48 Statistical Mechanics, 510 Schneider Russell Convex Bodies: the Brunn-Minkowski Theory, Introduction to Mathematical Philosophy, 586 312 Schoen, Yau S Lectures on Differential Geometry, 259 Lectures on Harmonic Maps, 259 Saad Schrijver Iterative Methods for Sparse Linear Systems, Theory of Linear and Integer Programming, 614 606 Sachs, Wu Schroeder General Relativity for Mathematicians, 505 Number Theory in Science and Sagan Communication, 360 The Symmetric Group. Representations, Schumaker Combinatorial Algorithms, and Symmet- Spline Functions: Basic Theory, 622 ric Schwartz Functions, 487 Th´eorie des Distributions, 171 Sakai Seifert, Threlfall C∗-algebras and W ∗-algebras, 181 Seifert and Threlfall: A Textbook of Topology, Salsburg 318 The Lady Tasting Tea. How Statistics Serre Revolutionized Science in the Twentieth A Course in Arithmetic, 385 Century, 45 Complex Semisimple Lie Algebras, 441 Samko, Kilbas, Marichev Galois Cohomology, 372 Fractional Integrals and Derivatives. Theory Linear Representations of Finite Groups, 484 and Applications, 95 LocalAlgebra,220 Samorodnitsky, Taqqu Local Fields, 371 Stable non-Gaussian Random Processes, 570 Trees, 466 Santal´o Shafarevich Integral Geometry and Geometric Probability, Basic Algebraic Geometry, 281 251 Basic Notions of Algebra, 204 Sarnak Shannon, Weaver Some Applications of Modular Forms, 467 The Mathematical Theory of Communication, Sato 599 L´evy Processes and Infinitely Divisible Sharpe Distributions, 569 Differential Geometry, 250 Schaefer Shelah Banach Lattices and Positive Operators, 202 Proper and Improper Forcing, 591 Topological Vector Spaces, 168 Shilov Scharlau Linear Algebra, 191 Quadratic and Hermitian Forms, 392 Shimura Scharlau, Opolka Introduction to the Arithmetic Theory of From Fermat to Minkowski. Lectures on the Automorphic Functions, 384 Theory of Numbers and its Historical The Map of My Life, 24 Development, 59 Shiryaev Schechter Probability, 558 664 INDEX

Shoenfield The Topology of Fibre Bundles, 325 Mathematical Logic, 584 Stein Shohat, Tamarkin Harmonic Analysis: Real-variable Methods, The Problem of Moments, 96 Orthogonality, and Oscillatory Shubin Integrals, 159 Pseudodifferential Operators and Spectral Singular Integrals and Differentiability Theory, 424 Properties of Functions, 157 Siegel Stein, Weiss Topics in Complex Function Theory, 276 Introduction to Fourier Analysis on Euclidean Siegel, Moser Spaces, 158 Lectures on Celestial Mechanics, 518 Steinberg Silverman Lectures on Chevalley Groups, 448 Advanced Topics in the Arithmetic of Sternberg Elliptic Curves, 386 Group Theory and Physics, 482 The Arithmetic of Elliptic Curves, 385 Stewart Smith Introduction to Matrix Computations, 613 Monotone Dynamical Systems, 525 Why Beauty is Truth, 28 Smith, Kahanp¨a¨a, Kek¨l¨ainen, Traves Stichtenoth An Invitation to Algebraic Geometry, 288 Algebraic Function Fields and Codes, 601 Smoller Stillwell Shock Waves and Reaction-diffusion Mathematics and its History, 63 Equations, 433 Strang, Fix Soare An Analysis of the Finite Element Method, Recursively Enumerable Sets and Degrees. 618 A Study of Computable Functions and Strebel Computably Generated Sets, 593 Quadratic Differentials, 139 Spanier Stroock Algebraic Topology, 326 Probability Theory, an Analytic View, 559 Spicci Stroock, Varadhan Beyond the Limit: The Dream of Sofya Multidimensional Diffusion Processes, 570 Kovalevskaya, 47 Struik Spitzer A Concise History of Mathematics, 60 Principles of Random Walks, 562 Struwe Spivak Variational Methods. Applications to Non- A Comprehensive Introduction to Differential linear Partial Differential Equations and Geometry, 243 Hamiltonian Systems, 431 Calculus, 82 Stubhaug Calculus on Manifolds. A Modern Approach Niels Henrik Abel and His Times, 46 to Classical Theorems of Advanced Sturmfels Calculus, 82 Gr¨obner Bases and Convex Polytopes, 541 Springer, G. Sweedler Introduction to Riemann Surfaces, 130 Hopf Algebras, 481 Springer, T. Switzer Linear Algebraic Groups, 447 Algebraic Topology—Homotopy and Stanley Homology, 327 Enumerative Combinatorics, 538 Sz.-Nagy, Foias Steenrod Harmonic Analysis of Operators on Hilbert Space, INDEX 665

146 Interpolation Theory, Function spaces, Szeg¨o Differential Operators, 155 Orthogonal Polynomials, 106 Theory of Function Spaces, 154 Tsuji T Potential Theory in Modern Function Theory, 149 Takesaki Turaev Theory of operator algebras, 180 Quantum Invariants of Knots and 3-manifolds, Tauvel, Yu 331 Lie Algebras and Algebraic Groups, 449 Taylor U Partial Differential Equations, 423 Pseudodifferential Operators, 424 Ulam Pseudodifferential Operators and Nonlinear A Collection of Mathematical Problems, 108 PDE, 423 Adventures of a Mathematician, 23 Temam Infinite-dimensional Dynamical Systems in V Mechanics and Physics, 526 Navier-Stokes Equations. Theory and van der Put, Singer Numerical Analysis, 615 Galois Theory of Linear Differential Equations, Tenenbaum 461 Introduction to Analytic and Probabilistic van der Vaart, Wellner Number Theory, 377 Weak Convergence and Empirical Processes. Thirring With Applications to Statistics, 571 A Course in Mathematical Physics. Vol. I. van der Waerden Classical Dynamical Systems, 513 Algebra, 194 Thom van Heijenoort Structural Stability and Morphogenesis. An From Frege to G¨odel. A Source Book in Outline of a General Theory of Models, Mathematical Logic, 1879–1931, 585 529 van Lint Thurston Introduction to Coding Theory, 601 The Geometry and Topology of Three Varadarajan Manifolds, 345 Lie Groups, Lie Algebras, and Their Three-dimensional Geometry and Topology, Representations, 444 Vol. 1, 346 Varopoulos, Saloff-Coste, Coulhon Titchmarsh Analysis and Geometry on Groups, 147 The Theory of Functions, 117 Vaughan The Theory of the Riemann Zeta-Function, The Hardy-Littlewood Method, 379 375 Vign´eras Tits Arithm´etique des alg`ebres de quaternions, 384 Buildings of Spherical Type and Finite Villani BN-pairs, 453 Optimal Transport, Old and New, 430 tom Dieck Topics in Optimal Transportation, 430 Transformation Groups, 476 Voiculescu, Dykema, Nica Totik Free Random Variables, 578 Logarithmic Potentials with External Fields, von Neumann 151 Mathematical Foundations of Quantum Triebel Mechanics, 498 666 INDEX

The Computer and the Brain, 12 West von Neumann, Morgenstern Introduction to Graph Theory, 547 Theory of Games and Economic Behavior, 605 Weyl Space, Time, Matter, 505 W Symmetry, 27 The Classical Groups. Their Invariants and Waldschmidt Representations, 487 Diophantine Approximation on Linear Alge- The Concept of a Riemann Surface, 128 braic Groups. Transcendence Properties The Theory of Groups and Quantum Mechan- of the Exponential Function in Several ics, 497 Variables, 383 Wheeden, Zygmund Walker Measure and Integral, 98 Algebraic Curves, 288 Whitehead Wall Elements of Homotopy Theory, 337 Surgery on Compact Manifolds, 351 Whitham Wallach Linear and Nonlinear Waves, 436 Real Reductive Groups, 491 Whittaker, Watson Walters A Course of Modern Analysis, 85 An Introduction to Ergodic Theory, 533 Whyburn Warner Analytic Topology, 478 Foundations of Differentiable Manifolds and Widder Lie Groups, 235 The Laplace Transform, 145 Washington Wiener Introduction to Cyclotomic Fields, 369 I am a Mathematician. The later Life of a Watson Prodigy, 23 A Treatise on the Theory of Bessel Functions, Cybernetics, or Control and Communication 86 in the Animal and the Machine, 597 Wehrfritz Ex-prodigy. My Childhood and Youth, 23 Infinite Linear Groups. An Account of the Extrapolation, Interpolation, and Smoothing Group-Theoretic Properties of Infinite of Stationary Time Series, 598 Groups of Matrices, 472 Wilkinson Weibel The Algebraic Eigenvalue Problem, 612 An Introduction to Homological Algebra, 228 Willem Weil Minimax Theorems, 420 Basic Number Theory, 368 Woess Elliptic Functions According to Eisenstein and Random Walks on Infinite Graphs and Groups, Kronecker, 57 563 Number theory. An Approach through His- Wolf tory. From Hammurapi to Legendre, 55 Spaces of Constant Curvature, 245 The Apprenticeship of a Mathematician, 22 Weinberger Y The Topological Classification of Stratified Spaces, 344 Yafaev Wells Mathematical Scattering Theory, 516 Differential Analysis on Complex Manifolds, Yaglom 275 Felix Klein and Sophus Lie, 52 Welsh Yosida Matroid Theory, 543 Functional analysis, 174 INDEX 667

Z

Zariski Algebraic Surfaces, 301 Zariski, Samuel Commutative Algebra, 219 Zassenhaus The Theory of Groups, 207 Zee Fearful Symmetry. The Search for Beauty in Modern Physics, 34 Zeidler Nonlinear Functional Analysis and Its Applications, 186 Zhu Operator Theory in Function Spaces, 155 Ziegler Lectures on Polytopes, 539 Ziemer Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation, 428 Zimmer Ergodic Theory and Semisimple Groups, 465 Essential Results of Functional Analysis, 166 Zygmund Trigonometric Series, 147