How to Think Like a Mathematician A Companion to Undergraduate Mathematics

ISBN-10: 052171978X

ISBN-13: 9780521719780

Edition: 2008

Authors: Kevin Houston

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Description:

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

List price: $40.99
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 2/12/2009
Binding: Paperback
Pages: 274
Size: 7.25" wide x 9.50" long x 0.75" tall
Weight: 1.100
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
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