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主 编 杨劲根
副主编 楼红卫 李振钱 郝群
编写人员（按汉语拼音为序）
陈超群 陈猛 东瑜昕 高威 郝群 刘东弟 吕志 童裕孙 王巨平 王泽军 徐晓津 杨劲根 应坚刚 张锦豪 张永前 周子翔 朱胜林
1. 序言
2. 非数学专业的数学教材
3.数学分析和泛函分析
4.单复变函数
5.多复变函数
6.代数
7.数论
8.代数几何
9.拓扑与微分几何
10.偏微分方程
11.概率论
12.计算数学
13.其他
14.附录
书名： An Introduction to probability theory and its applications, Vol 1
作者： William Feller
出版商： John Wiley & Sons
页数： 509
适用范围：大学数学系本科
预备知识：微积分
习题数量：中等
习题难度：一般
推荐强度： 10
书评： 本书是概率界公认的经典教材 , 作者是现代概率论的大师 , 本教材多年来曾经多次再版多次重印 , 内容包括古典概率 随机序列 , 极限理论 , 更新过程 , 随机游动与马氏链等 , 此书之所以成为经典是因为 其中包含有大量的直观的概率模型 , 涵盖物理生物经济等几乎所有科学分支 , 直到 今天 , 许多研究论文都可以在本书的例子中捕捉到其背景 . 本书虽然经典 , 但使用它作为教材对教师和学生都需要勇气 , 它要求授课者有非常广泛的知识背景 , 它也要求读者有通过现象看清 本质的能力 , 另外本教材并不象传统的教材那样具有 Bourbaki 风格 , 也就是说不是通常的教材那么系统 , 所以采用本书作为概率论教材的 学校并不很多 , 但它的确是一本富有宝藏的参考书 . ( 应坚刚 )
国外评论摘选
1) Although people often recommend K.L. Chung at our math department as an introduction to probability theory, i think that Feller is just another view of the problem. If you prefer a concise writing style then Chung is better. On the other hand, Feller's books are full of examples so that you cannot go through this book without having an accurate picture of the historical developments of probability theory and its many applications (even if sometimes applications are driving the need for theory...). This is anyway something you must have read if you want to get an intuitive understanding of probability theory. Whatever your preferred writing style is, Feller is probably a must-read if you're involved on probability theory, just because of its importance in the literature, not because you like it. Maths are not just about formalism, they're also a matter of culture.
2) I came across Vol 1 as a maths student in the 1970s. Indeed, the book was suggested to me by a quantum physicist recommended for the Nobel Prize in 1965 (John Ward, now deceased)- Feynman, Schwinger and Tomonaga shared the prize.
This is a difficult book and was not widely used even in the 70s as a textbook. I can recall the word idiosyncratic being used by someone to describe the book. The problem is that the book seeks to address deep issues and that requires hard work. It is not the sort of book a struggling student will find helpful. As one matures as a mathematician one can appreciate the incredible depth of the material. As a practical example - about 30 years after I first touched this book a Head of Quant approached me in relation to a paper by Marsaglia on distributions of ratios of normal variates. The verification of Marsgalia's derivation (which is non-trivial) is to be found as a series of 3 problems in Vol 1.
With the development of stochastic calculus in the finance world Feller can look a bit outdated but if you can understand the core material you are doing well. Stochastic calculus would be a push over.
Vols 1 and 2 present a treasure trove for those who want to delve into the area. I still use Feller's coin tossing example from Vol 1 to demonstrate to those in the finance world that their understanding of the law of averages is imperfect.
The funny thing is that Vol 2 (which I could never afford as a student) is so hard to get. I think that was because Vol 2 was regarded as even more obscure than Vol 1. I got a copy from Amazon second hand and it is now united with its twin in my study.
Peter Haggstrom, Bondi Beach Australia
书名： A course in Probability Theory
作者： Kai Lai Chung
出版商： Academic Press
页数： 353
适用范围：大学数学系本科
预备知识：实变函数
习题数量：较大
习题难度：难
推荐强度： 9
书评： Chung 的这本概率论教材是 Stanford 大学数学系用的一学年课程的教材 , 从严格的测度论开始 , 内容非常广泛并且深入 , 包括收敛性 , 大数定律 , 强大数定律 , 特征函数 , 中心极限定理 , 重对数律 , 无穷可分分布 , 随机游动理论 , 条件期望 , 鞅与马氏 链等 , 虽然不需要很多的预备知识 , 但要求读者有很好的数学素养和对纯粹数学 的兴趣 , 与 Chung 一贯风格一样 , 教材本身写得非常严谨 , 某些部分也可以说 非常难 , 侧重于概率的纯理论方面 , 对概率的应用和直观背景说得不多 . 此书约共有 500 个习题 , 其中一些习题需要很高的技巧 .
本教材比现在大多数高校数学系使用的教材要难 , 但是使用于那些对数学真正 有兴趣的人 , 也是那些程度较好的学生一本很好的参考书 . ( 应坚刚 )
国外评论摘选
1) This text by Chung was one of the texts that I used when I was taking a graduate course in probability at Stanford in 1975. It is carefully written but challenging. It provides good coverage of the central limit theorem, the law of large numbers and the law of the iterated logarithm. It also covers stable laws very well. The style is one of rigorous mathematics with theorems, and lemmas given with their mathematical proofs. The book was recently revised. The revised text does not change much but new material on measure and integration that is now commonly included in the first graduate course in probability has been added. In the 1970s at Stanford a course in measure theory was a prerequisite for the course in advanced probability although some student took it concurrently.
If you plan to get this text, the revised edition is probably worth it. If you already have this edition and know your measure theory, it may not be worth it to get the new edition.
2) A course in probability theory, written by Kai Lai Chung, has been referred by not only mathematicians but also mathematical economists.This book is written very rigorously, but almost all of the theorems have easy-to-understand proofs. So it is not difficult to follow. Moreover, there are lots of exercises in this book. So I do recommend this book.