How to Think Like a Mathematician

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Sprache: Englisch

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Beschreibung

Looking for a head start in your undergraduate degree in mathematics? This friendly companion eases beginning students into real mathematical thinking, unlocking important techniques for effective mathematics so you can communicate with clarity, solve problems, and explore the world of definitions, theorems and proofs with real confidence.

Über den Autor

Kevin Houston is Senior Lecturer in Mathematics at the University of Leeds.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2009
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9780521719780
ISBN-10:	052171978X
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Houston, Kevin
Hersteller:	Cambridge University Press
Maße:	246 x 189 x 16 mm
Von/Mit:	Kevin Houston
Erscheinungsdatum:	02.12.2009
Gewicht:	0,544 kg

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