Title How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
Book Condition New
Edition First Edition
Size 185 x 245 Mm
Publisher New Delhi, India Cambridge University Press 2009
052171978X / 9780521719780
Seller ID 026203
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. Contents 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. Printed Pages: 275 with 1 halftone 10 tables 335 exercises 195 worked examples.