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Great Mathematics Books of the Twentieth Century 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 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) 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 N)- ##--)"QQ#"-)/NQY- )QY&)- 9QY)Y^NQ> — René Descartes NQ)- N)Q#-#)"> — Ernest Hemingway )-^)YN&)- NN)Y#%Q-^#Q")"QNQ> — Ralph Waldo Emerson N---)"QQ#")-^YQ-^> — Marcus Tullius Cicero -^-)"QQ#"N----Q> — Horace Mann ^QQYNN)/N)-^)"Q> — John Steinbeck -Y))-&))"Q-#)Y&-N> — Patricia A. 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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 Representation Theory 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.
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