二十世纪伟大的数学书

出版时间：2013-7  出版社：高等教育出版社  作者：季理真  
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内容概要

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。

作者简介

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

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.

编辑推荐

《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。

用户评论 (总计9条)

•   真的很怀疑是否有“一个人”能在这么广大的专业范围内列书单。写这样的书，更好的做法应该是集体编著。今天刚在当当上拿到书，数学我不懂，就先没看，看了看数学物理的部分，感觉写的十分一般，10.2.4 写量子场论的部分只有半页不到，一本书而已，与这样重要的方向是不匹配的。10.2.6 写Reed和Simon的四卷本数理方法，第3卷连标题都写错了 :-(不过话说回来，有这本书总比没有好，对于想找好书看的人这本书目前是无法取代的，估计这也是那么多大牛推荐的原因之一（另一个原因可能是与作者的人情关系）。这个贡献和作出这个贡献的勇气十分可贵，不能抹杀。只希望下次有人再想出这样的书，比如在物理方面写一本类似的，要找几个领域的专家合作才好。PS: 书的印刷装祯非常好，超出价格给我的期望。
•   内容详实，数学工作者可以收藏
•   想法很好，至少可以引导初学者少走些弯路，但此书科目太全又仅出于一人之力，不禁让我质疑作者是否有能力和精力给出数学的每一分支的经典书籍，当然作者是个牛人，我不堪比拟，我觉得涉于本专业的还是有说服力的，对于其他领域，我更希望这是本合著的书。当然标题给了作者理由，这只是他的personal journey.我不喜欢它的原因有两点：1.太全面，有些书很遗憾的不在书上；2.文中引用了一些网站的评论，令我怀疑作者对此书下的心血是否符合它的厚度。我更希望它能是本数学书籍的游记，所以对于作者写这本书的创意我给5分，内容略看了自己专业的，和自己感兴趣的，由于未通读我给了4分成见分。当然这是一本好书，那么这本书会不会成为像history of the theory of number那样经典的书，我持否定的态度。
•   本书介绍了几乎所有数学分支的经典书籍,适合自学数学的同学寻找参考书.
•   里面涵盖了数学各个分支的书籍，作用更类似于字典，有查阅之用。。
•   书的印刷装祯非常好，超出价格给我的期望
•   发货很快，树叶很好。
•   录入的著作确实都是名著，但是这本书显得用途很有限，只相当于是一份规模较大带有评述的书末文献清单的作用。印刷非常不错，如果里面印刷的是所说的任何一本稀缺原著，就能成指伟大。
•   这样的书对初学者很有用，因数学文献浩如烟海，不知如何选择。而这类书又非常罕见，故更为珍贵。该书这样的篇幅精装，定价相对较低。