Permutation grou

《群论导论(第4版)(英文版)》介绍了：Group Theory is a vast subject and, in this Introduction （as well as in theearlier editions）, I have tried to select important and representative theoremsand to organize them in a coherent way. Proofs must be clear, and examplesshould illustrate theorems and also explain the presence of restrictive hypo-theses. ！ also believe that some history should be given so that one canunderstand the origin of problems and the context in which the subjectdeveloped. Just as each of the earlier editions differs from the previous one in a signifi-cant way, the present （fourth） edition is genuinely different from the third.Indeed, this is already apparent in the Table of Contents. The book nowbegins with the unique factorization of permutations into disjoint cycles andthe parity of permutations; only then is the idea of group introduced. This isconsistent with the history of Group Theory, for these first results on permu-tations can be found in an 1815 paper by Cauchy, whereas groups of permu-tations were not introduced until 1831 （by Galois）But even if history

《P进数,P进分析和ζ函数(第2版)(英文版)》讲述了：在数论，表示理论等许多现代数学研究领域中，p进分析占据着非常重要的地位。《P进数,P进分析和ζ函数(第2版)(英文版)》是p进分析的入门教材。主要分两部分内容，首先论述p进分析理论的基本思想，其次介绍p进理论的两个重要应用，即在黎曼ζ函数值为负整数时的p进内插和在一个有限域内方程组的δ函数有理性的证明。可供数学系数论专业的研究生和研究人员参考。

《伽罗瓦理论》内容简介：This exposition of Galois theory was originally going to be Chapter 1 of thecontinuation of my book Fermat's Last Theorem, but it soon outgrew anyreasonable bounds for an introductory chapter, and I decided to make it aseparate book. However, this decision was prompted by more than just thelength. Following the precepts of my sermon "Read the Masters！" [E2], Imade the reading of Galois' original memoir a major part of my study ofGalois theory, and I saw that the modern treatments of Galois theory lackedmuch of the simplicity and clarity of the original. Therefore I wanted towrite about the theory in a way that would not only explain it, but explain itin terms close enough to Galois' own to make his memoir accessible to thereader, in the same way that I tried to make Riemann's memoir on the zetafunction and Kummer's papers on Fermat's Last Theorem accessible in myearlier books, [El] and [E3]. Clearly I could not do this within the confinesof one expository chapter.

《代数拓扑导论(英文版)》介绍了：There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to .I.H.C. Whitehead. Of course, this is false, as a giance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details.

《纤维丛(第3版)》讲述了：The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950, the definition of fibre bundle had been clearly formulated, the homotopy classification of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians: Chern, Pontrjagin, Stiefel, and Whitney. Steenrod's book, which appeared in 1950, gavea coherent treatment of the subject up to that time.
About 1955, Miinor gave a construction ora universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal.

《算术教程(英文版)》讲述了：The first one is purely algebraic. Its objective is the classification ofquadratic forms over the field of rational numbers （Hasse-Minkowskitheorem）. It is achieved in Chapter IV. The first three chapters contain somepreliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols.Chapter V applies the preceding results to integral quadratic forms indiscriminant + 1. These forms occur in various questions: modular functions,differential topology, finite groups. The second part （Chapters VI and VII） uses "analytic" methods （holomor-phic functions）. Chapter VI gives the proof of the "theorem on arithmeticprogressions" due to Dirichlet; this theorem is used at a critical point in thefirst part （Chapter 111, no. 2.2）. Chapter VII deals with modular forms,and in particular, with theta functions. Some of the quadratic forms ofChapter V reappear here.

In 1970 I gave a graduate course in ergodic theory at the University of Maryland in College Park, and these lectures were the basis of the Springer Lecture Notes in Mathematics Volume 458 called "Ergodic Theory--Introductory Lectures" which was published in 1975. This volume is nowout of print, so I decided to revise and add to the contents of these notes. I have updated the earlier chapters and have added some new chapters on the ergodic theory of continuous transformations of compact metric spaces. In particular, I have included some material on topological pressure and equilibrium states. In recent years there have been some fascinating interactions of ergodic theory with differentiable dynamics, differential geometry,number theory, von Neumann algebras, probability theory, statistical mechanics, and other topics. In Chapter 10 1 have briefly described some of these and given references to some of the others. I hope that this book will give the reader enough foundation to tackle the research papers on ergodictheory and its applications.

《有限群的线性表示》是著名法国数学家、菲尔兹奖获得者JeanPierreserre的经典著作。全书分三部分。第一部分讲述有限群的线性表示的最基本的内容，主要是群表示和特征标的对应关系；第二部分对群的常表示做了进一步的阐述，如诱导表示、有理性问题等；第三部分简单讨论了群的模表示理论。《有限群的线性表示》深入浅出，对内容的处理极有特色，是学习有限群的线性表示的经典书籍。
《有限群的线性表示》根据原书第二版的英译本翻译，并根据法文修订第三版作了校订。

This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology. The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples. Then the methods of schemes and cohomology are developed in Chapters II and III, with emphasis on applications rather than excessive generality. The last two chapters of the book (IV and V) use these methods to study topics in the classical theory of algebraic curves and surfaces.
本书为英文版。

The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I￡ogroups, rings, fields, homomorphisms, is presup-posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume.References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any 'student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra.
此书为英文版！

The present volume is the first of three that will be published under the general title Lectures in lbstract fllgebra. These vol-umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale University. The general plan of the work is as follows.The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraic concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond ?the foundations and elementary properties of the algebraic sys-tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under-standing of a few topics is to be preferred to a superficial under-standing of many.
此书为英文版！

《200道物理学难题》旨在使学生在实际应用中增强对物理概念和物理定律的掌握。与其用费力而复杂的数学技巧来解决书中的问题，倒不如利用物理直觉来得简单。问题的选择仅限于经典（非量子）物理学，但难度却并不因此而降低。书中大多数问题都采用常见的非技术性语言进行表述，这要求学生必须自己选择正确的杠架来分析问题。一般而言，书中问题的难度适合出众的高中生、优秀的本科生，以及良好的硕士生的水平。《200道物理学难题》对准备参加普通物理考试的本科生和准备参加各种物理竞赛的高中生无颖是有益的，可用于自学、课堂练习或者研讨会。物理教授们亦可望从中找到一些具有挑战性的难题。尽管物理上有难度，但是《200道物理学难题》对数学方面的要求很少，最多只是简单的微积分而已。这本题集不仅富于挑战性和指导性，而且富趣味性。

Apart from a number of minor corrections and changes, a substantial reformulation and up-dating of Chapters 14 and 15 has taken place. This reformulation and up-dating is a major and very welcome contribution from my friend and colleague, Dr J.W. Sanders, to whom I express my sincere thanks. His efforts have produced a much better result than I could have achieved on my own. Warm thanks are also due to Dr Jo Ward, Who checked some of the revised material. New Sections 16.9 and 16.10 have also been added. The bibliography has been expanded and brought up to date, though it is still not exhaustive. In spite of these changes, the third paragraph in the Preface to the revised edition of Volume I is applicable here. What has been aeeomplished here is not a complete account of developments over the past 15 years; such an account would require many volumes. Even so, it may assist some readers who wish to appraise some of these developments. More ambitious readers should consult Mathematical Reviews from around Volume 50 onwards.
本产品为英文版。