How to Think Like a Mathematician: A Companion to Undergraduate Mathematics - Couverture souple

Houston, Kevin

Couverture souple

ISBN 10 : 052171978X ISBN 13 : 9780521719780

Editeur : Cambridge University Press, 2009

Synopsis

This arsenal of tips and techniques eases new students into undergraduate mathematics, unlocking the world of definitions, theorems, and proofs.

A propos du livre

Présentation de l'éditeur

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.

Revue de presse

"In this book, Houston has created a primer on the fundamental abstract ideas of mathematics; the primary emphasis is on demonstrating the many principles and tactics used in proofs. The material is explained in ways that are comprehensible, which will be a great help for people who seem to hit the wall regarding what to do when confronted with the creation of a proof... In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof."
Charles Ashbacher, Journal of Recreational Mathematics

"The author provides concise, crisp explanations, including definitions, examples, tips, remarks, warnings, and idea-reinforcing questions. Houston expresses thoughts clearly and concisely, and includes succinct remarks to make points, clarify arguments, and reveal subleties."
W.R. Lee, Choice Magazine

Détails de l'édition

• Éditeur: Cambridge University Press
• Date d'édition: 2009
• ISBN 10: 052171978X
• ISBN 13: 9780521719780
• Reliure: Broché
• Langue: anglais
• Nombre de pages: 278