How to Think Like a Mathematician: A Companion to Undergraduate Mathematics

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作者：Kevin Houston
文件大小：2.11MB
文件类型：文字PDF
语言：英语
出版：Cambridge，2009年
页数：279
书签：有

内容简介：
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

目录：
I Study skills for mathematicians 1
II How to think logically 51
III Definitions, theorems and proofs 97
IV Techniques of proof 137
V Mathematics that all good mathematicians need 185
VI Closing remarks 241
Appendices 257
Index 263

地址：
http://u.115.com/file/f8a3065566