二十世纪伟大的数学书

章节摘录

版权页：   插图：   Due to active development in approximation theory and numerical analysis, interestin orthogonal polynomials has been revived. This book is a very good introduction tothis classical and current subject. According to MathSciNet, "The book presents, in a very readable way, backgroundand development for an introduction to the general theory of orthogonal polynomials.A first undergraduate course in real analysis should be quite adequate preparation and,with the author's clear style and good selection of exercises for developing many ofthe established properties, the book gives a solid basis for (real) orthogonal polynomialtheory." 3.1.11 Problem books The importance of problems has been explained in the preface of the book Problems andtheorems in analysis by PSlya and G. SzegS, which was quoted in ~3.1.9. Another morerecent, famous book based on mathematical problems (or rather known and importanttheorems) and their elegant proofs is the next one. M. Aigner,G. Ziegler, Proofs from The Book, Fourth edition, Springer-Verlag,Berlin, 2010. viii+274 pp. If the beauty of mathematics theorems and formulas is important, the beauty of theirproofs probably matters too. It is perhaps helpful to point out that Gauss gave eightdifferent proofs of the quadratic reciprocity law in his life. This unusual book containselegant proofs of many beautiful results in elementary mathematics. It is more thanproofs. Indeed, there is treasure buried in each page, one gem after another. Some ofthe proofs are classics, but many are new and brilliant. They are all beautiful. This is afun book to read. The review of the first edition in MathSciNet, "Paul ErdSs maintained that God kepta Book with only the most elegant mathematical arguments. This volume, conceivedin consultation with ErdSs and published in his memory, suggests some of the Book'scontents. Thirty sections treat results drawn from number theory, geometry (mainlycombinatorial), analysis, combinatorics and graph theory; these can be followed by oneversed in undergraduate mathematics including discrete topics. The proofs date mainlyfrom the entire span of the twentieth century; many are due to ErdSs himself... The pre-sentation is clear and attractive with wide margins for portraits, diagrams and sketches." Here is another review on this book. "This is one of those books that a seriousmathematician will probably enjoy picking up and reading from time to time.

内容概要

季理真 ji is a professor of mathematics at university of michigan and studies subjects related to lie groups, discrete subgroups of lie groups, transformation groups and related spaces. he loves books and is a chief-editor of four book series:advanced lectures in mathematics, mathematics and humanities, panorama of mathematics, surveys of modern mathematics, and of the journal pure and applied mathematics quarterly. he is also an editor of journals asian journal of mathematics and science in china: mathematics. he was a sloan fellow and received the nsf postdoctoral fellowship and the morningside silver medal of mathematics. he enjoys listening to good mathematics talks on diverse topics and has organized over 30 summer schools, conferences or workshops. he is also an active organizer of seminars and colloquiums. for example, he is the organizer of one of the first seminars called "what is ..." in the world.

书籍目录

1、Introduction 2、Expository Books On Mathematics And Mathematicians 2.1 Popular And Expository Books On Mathematics 2.1.1 R. Courant, H.Robbins, What Is Mathematics? Oxford University Press, NewYork, 1941. Xix+521 Pp 2.1.2 A.D. Aleksandrov, A.N. Kolmogorov, M.A. Lavrent'ev, Mathematics： Its Content, Methods, And Meaning. Vol.I, Vol. Ii, Vol. Iii, The M.I.T. Press, Cambridge, Mass., 1963, Xi+359 Pp.; Xi+377 Pp.; Xi+356 Pp.. Translated By S.H. Gould And T. Bartha; S.H. Gould; K. Hirsch 2.1.3 G. P\'Olya, How To Solve It. A New Aspect Of Mathematical Method. Expanded Version Of The 1988 Edition, With A New Foreword By John H. Conway, Princeton Science Library, Princeton University Press, 2004. Xxviii+253 Pp 2.1.4 G.H. Hardy, A Mathematician's Apology, With A Foreword By C.P. Snow, Reprint Of The 1967 Edition, Canto, Cambridge University Press, Cambridge, 1992 2.1.5 J.E. Littlewood, Littlewood's Miscellany, Edited And With A Foreword By Bola Bollobas, Cambridge University Press, Cambridge, 1986. Vi+200 Pp 2.1.6 Autobiographies Of Mathematicians 2.1.7 H. Weyl, Symmetry. Reprint Of The 1952 Original. Princeton Science Library. Princeton University Press, Princeton, N.J.,1989 2.1.8 D. Hilbert, S. Cohn-Vossen, Geometry And The Imagination, American Mathematical Society, 1, 1999. 357 Pages 2.2 Biographies Of Mathematicians And History Of Mathematics 2.2.1 E.T. Bell, Men Of Mathematics, Touchstone, 1986. 608 Pages …… 3、Analysis 4、Algebra 5、Geometry 6、Topology 7、Number Theory 8、Differential Equations 9、Lie Theories 10、Mathematical Physics, Dynamical Systems And Ergodic Theory 11、Discrete Mathematics And Combinatorics 12、Probability And Applications 13、Foundations Of Math, Computer Science, Numerical Math

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《二十世纪伟大的数学书:个人之旅(英文版)》由高等教育出版社出版。

作者简介

海量的数学书，哪些值得我们认真读，哪些读后让我们对数学有更好的认识，这些对门外汉、学生、年轻的学者和专家都是非常需要解决的问题。季理真教授的新作《二十世纪伟大的数学书――个人之旅》（great mathematics books of the twentieth century: a personal journey）在这个问题上为我们带来了极大的便利。本书比较全面收列了二十世纪以来最有影响的数学书并恰当地加以简评和引述其他评论。本书收列的书目范围之广，数量之大令人吃惊，这需要作者广阔的视野、艰辛的工作，并花大量的时间请教很多不同方向的专家。本书的作者完成了一项很有意义的工作，本书定会让喜爱数学的读者受益。

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