×

Uh-oh, it looks like your Internet Explorer is out of date.

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

ISBN-10: 052171978X

ISBN-13: 9780521719780

Pub. Date: 02/23/2009

Publisher: Cambridge University Press

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

## Product Details

ISBN-13:
9780521719780
Publisher:
Cambridge University Press
Publication date:
02/23/2009
Edition description:
New Edition
Pages:
278
Sales rank:
1,351,128
Product dimensions:
7.20(w) x 9.60(h) x 0.60(d)

## Related Subjects

Preface; Part I. Study Skills For Mathematicians: 1. Sets and functions; 2. Reading mathematics; 3. Writing mathematics I; 4. Writing mathematics II; 5. How to solve problems; Part II. How To Think Logically: 6. Making a statement; 7. Implications; 8. Finer points concerning implications; 9. Converse and equivalence; 10. Quantifiers - For all and There exists; 11. Complexity and negation of quantifiers; 12. Examples and counterexamples; 13. Summary of logic; Part III. Definitions, Theorems and Proofs: 14. Definitions, theorems and proofs; 15. How to read a definition; 16. How to read a theorem; 17. Proof; 18. How to read a proof; 19. A study of Pythagoras' Theorem; Part IV. Techniques of Proof: 20. Techniques of proof I: direct method; 21. Some common mistakes; 22. Techniques of proof II: proof by cases; 23. Techniques of proof III: Contradiction; 24. Techniques of proof IV: Induction; 25. More sophisticated induction techniques; 26. Techniques of proof V: contrapositive method; Part V. Mathematics That All Good Mathematicians Need: 27. Divisors; 28. The Euclidean Algorithm; 29. Modular arithmetic; 30. Injective, surjective, bijective - and a bit about infinity; 31. Equivalence relations; Part VI. Closing Remarks: 32. Putting it all together; 33. Generalization and specialization; 34. True understanding; 35. The biggest secret; Appendices: A. Greek alphabet; B. Commonly used symbols and notation; C. How to prove that ...; Index.

Average Review: