这是一部在中国科学技术协会主持下，组织数以千计的专家、学者撰写编纂的大型文献。《中国科学技术专家传略》主要分工学、农学、医学、理学四编。工学编分为：力学、机械、交通、航空航天、电子电工、能源、化工、冶金、自动化及仪器仪表、土木建筑、纺织、轻工等12卷，农学编分为：作物、植物保护、林业、养殖、园艺、土壤、综合等7卷；医学编分为：基础医学、临床医学、预防医学、中医、药学等5卷；理科编分为：数学、物理学、天文学、化学、地学、生物学等6卷。本书是一部以介绍中国近、现代科技要物为主线，反映中国科技发展进程的史实性文献，其目的是为中国著名科技专家立传，记载他们的生平及其对祖国乃至对人类科学技术、经济和社会发展作出贡献，为中国科技史的研究提供史料。

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这本小册子是想以平易近人且便于使用的方式，把常用的数学与物理基本公式介绍给大家，至于比较陌生的名词与符号，则在书末附录的词汇里说明。利用数字和符号来模拟现实、并加以预测与控制，是很有魔力的，好像在变法术一样。不幸的是，拥有这些能力不一定会带来足够的智慧与远见，因此，我们发现了危险性技术的发展激增，也看到很多人对数量的迷恋，其中最具代表性的，是几乎所有的事情都屈服于全球经济之下（这里倒没有收录计算高利贷的公式），书里的内容，读者要小心使用。另外一方面，数学工具在很多领域里好像都有共通性，例如，我们以前曾认为光与电是不同的，但在现今电磁场的理论里，它们是一体的两面。爱因斯坦著名的（或许也是所有公式中最最知名的）公式E=mc2，可能是这种“双刃剑”的最佳例证，一方面它将永远是核武器的源头，却也是质量与能量统一的科学发现。但愿大家的喜悦与好奇心永不熄灭。<

This book is based on a first-year graduate course given regularly by the first author at the University of Chicago， most recently in the autumn quarters of 1991，1992，and 1993. The lectures given in this course were expanded and prepared for publication by the second author.The aim of this book is to provide a concise yet thorough treatement of some topics from group theory and representation theory with which every mathematician should be well acquainted. Of course， the topics covered naturally reflect the viewpoints and interests of the authors; for instance， we make no mention of free froups， and the emphasis throughout is admittedly on finite groups. Our hope is that this book will enable graduate students from every mathematical field， as well as bright undergraduates with an interest in algebra， to solidify their knowledge of group theory.本书为英文版。

Following Keller [119] we call two problems inverse to each other if the formulation of each of them requires full or partial knowledge of the other. By this definition， it is obviously arbitrary which of the two problems we call the direct and which we call the inverse problem. But usually， one of the problems has been studied earlier and， perhaps， in more detail. This one is usually called the direct problem， whereas the other is the inverse problem. However， there is often another， more important difference between these two problems. Hadamard （see [91]） introduced the concept of a well-posed problem， originating from the philosophy that the mathematical model of a physical problem has to have the properties of uniqueness， existence， and stability of the solution. If one of the properties fails to hold， he called the problem iU-posed. It turns out that many interesting and important inverse problems in science lead to ill-posed problems，， while the corresponding direct problems are well-posed. Often， existence and uniqueness can be forced by enlarging or reducing the solution space （the space of "models"）. For restoring stability， however， one has to change the topology of the spaces，which is in many cases impossible because of the presence of measurement errors. At first glance， it seems to be impossible to compute the solution of a problem numerically if the solution of the problem does not depend continuously on the data， i.e.， for the case of ill-posed problems. Under additional a priori information about the solution， such as smoothness and bounds on the derivatives， however， it is possible to restore stability and construct efficient numerical algorithms.本书为英文版。

本书是普通高等学校高等数学课程的学习辅导书，全书分上、下两册。上册包括函数与极限、一元函数微分学、一元函数积分学、空间解析几何等四篇；下册包括多元函数微分学、多元函数积分学、无穷级数、常微分方程等四篇。本册为下册。全书以篇为线条，内容包括辅导部分与测试两部分。辅导部分与教学同步，包括：基本概念与理论的总结；重点、难点的分析；典型例题解析与解题方法指导；各篇小结。测试部分包括各篇自测、期中测试和期末测试，全书共有31套试卷，其中上册有16套试卷，下册有15套试卷。本书重视基础，着重数学能力的培养。一方面，针对一年级大学生在对《高等数学》基本概念的理解、基本方法的掌握等方面所存在的问题，通过多种手段去强化解决这些问题的思路与方法的训练。另一方面，为了与“考研”内容衔接，在书中的辅导与测试题中，精选了一定量的历届硕士研究生入学考试试题，并给予解题方法上的指导。本书可作为高等学校学生学习高等数学课程的指导用书或教师的教学参考书，对于准备报考研究生的读者，也是一本系统全面的复习参考书。

This book is based on several courses given by the authors since 1966. It introduces the reader to the representation theory of compact Lie groups. We have chosen a geometrical and analytical approach since we feel that this is the easiest way to motivate and establish the theory and to indicate relations to other branches of mathematics. Lie algebras， though mentioned occasionally， are not used in an essential way. The material as well as its presentation are classical; one might say that the foundations were known to Hermann Weyl at least 50 years ago.本书为英文版。

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One of the most remarkable examples of fast technology transfer from new developments in mathematical probability theory to applied statistical methodology is the use of counting processes， martingales in continuous time， and stochastic integration in event history analysis. By this （or generalized survival analysis）， we understand the study of a collection of individuals， each moving among a finite （usually small） number of states. A basic example is moving from alive to dead， which forms the basis of survival analysis. Compared to other branches of statistics， this area is characterized by the dynamic temporal aspect， making modelling via the intensities useful， and by the special patterns of incompleteness of observation， of which right-censoring in survival analysis is the most important and best known example.

Mathematics has always benefited from its involvement with developing sciences.Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics， it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time.本书为英文版。