How to Think Like a Mathematician A Companion to Undergraduate Mathematics

Name: How to Think Like a Mathematician A Companion to Undergraduate Mathematics
Price: 12.99 USD
Availability: InStock
ISBN: 9780521719780

ISBN-10: 052171978X

ISBN-13: 9780521719780

Edition: 2008

Authors: Kevin Houston

List price: $41.99

This item qualifies for FREE shipping.

30 day, 100% satisfaction guarantee!

Buy new: $36.21

Marketplace

4 new & used from $12.99

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

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

Book details

List price: $41.99
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 2/12/2009
Binding: Paperback
Pages: 274
Size: 7.68" wide x 10.00" long x 0.75" tall
Weight: 1.408
Language: English

Kevin Houston is a senior lecturer at the University of Leeds and specializes in singularity theory. He is the author of over twenty published research papers and author of the undergraduate textbook How to Think Like a Mathematician published by Cambridge University Press in 2009.



Preface



Study skills for mathematicians



Sets and functions



Reading mathematics



Writing mathematics I



Writing mathematics II



How to solve problems



How to think logically



Making a statement



Implications



Finer points concerning implications



Converse and equivalence



Quantifiers-For all and There exists



Complexity and negation of quantifiers



Examples and counterexamples



Summary of logic



Definitions, theorems and proofs



Definitions, theorems and proofs



How to read a definition



How to read a theorem



Proof



How to read a proof



A study of Pythagoras' Theorem



Techniques of proof



Techniques of proof I: Direct method



Some common mistakes



Techniques of proof II: Proof by cases



Techniques of proof III: Contradiction



Techniques of proof IV: Induction



More sophisticated induction techniques



Techniques of proof V: Contrapositive method



Mathematics that all good mathematicians need



Divisors



The Euclidean Algorithm



Modular arithmetic



Injective, surjective, bijective-and a bit about infinity



Equivalence relations



Closing remarks



Putting it all together



Generalization and specialization



True understanding



The biggest secret


Appendices



Greek alphabet



Commonly used symbols and notation



How to prove that


Index