How to Think Like a Mathematician
eBook - PDF

How to Think Like a Mathematician

A Companion to Undergraduate Mathematics

,
  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

How to Think Like a Mathematician

A Companion to Undergraduate Mathematics

,
Book details
Table of contents
Citations

About This Book

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.

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Information

Publisher
Cambridge University Press
Year
2009
ISBN
9780511500695
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Contents
  5. Preface
  6. I Study skills for mathematicians
  7. II How to think logically
  8. III Definitions, theorems and proofs
  9. IV Techniques of proof
  10. V Mathematics that all good mathematicians need
  11. VI Closing remarks
  12. Appendices
  13. Index