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Mathematics and Its History

Mathematics and Its History
作者:John Stillwell
副标题:3th Edition
出版社:Springer
出版年:2010-08
ISBN:9781441960528
行业:其它
浏览数:17

内容简介

From the reviews of the third edition: "The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... Mathematics and its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. ... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics. ... While Stillwell does a wonderful job of tying together seemingly unrelated areas of mathematics, it is possible to read each chapter independently. I would recommend this fine book for anyone who has an interest in the history of mathematics. For those who teach mathematics, it provides lots of information which could easily be used to enrich an opening lecture in most any undergraduate course. It would be an ideal gift for a department’s outstanding major or for the math club president. Pick it up at your peril — it is hard to put down!" (Richard Wilders, MAA Reviews) From the reviews of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." (European Mathematical Society) "Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact." (Denis Bonheure, Bulletin of the Belgian Society)

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作者简介

John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.

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目录

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

1 The Theorem of Pythagoras

2 Greek Geometry

3 Greek Number Theory

4 Infinity in Greek Mathematics

5 Number Theory in Asia

6 Polynomial Equations

7 Analytic Geometry

8 Projective Geometry

9 Calculus

10 Infinity Series

11 The Number Theory Revival

12 Elliptic Functions

13 Mechanics

14 Complex Numbers in Algebra

15 Complex Numbers and Curves

16 Complex Number and Functions

17 Differential Geometry

18 Non-Euclidean Geometry

19 Group Theory

20 Hypercomplex Numbers

21 Algebraic Number Theory

22 Topology

23 Simple Groups

24 Sets, Logic, and Computation

25 Combinatorics

Bibliography

Index

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读书文摘

读者要注意,高斯年轻时的故事是他本人年老时讲出来的。。。

我们要讲的是可以将亏格=1的3次曲线参数化的函数,这样的函数就是椭圆函数。。。

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