# Intro Math How to Think Like a Mathematician by Houston

## For those who have used this book

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4. ### Strongly don't Recommend

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1. Jan 24, 2013

### micromass

Staff Emeritus

Code (Text):

[LIST]
[*] Preface
[*] Study skills for mathematicians
[LIST]
[*] Sets and functions
[*] Writing mathematics I
[*] Writing mathematics II
[*] How to solve problems
[/LIST]
[*] How to think logically
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[*] 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
[/LIST]
[*] Definition, theorems and proofs
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[*] 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
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[*] Techniques of proof
[LIST]
[*] 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
[/LIST]
[*] Mathematics that all good mathematicians need
[LIST]
[*] Divisors
[*] The Euclidean Algorithm
[*] Modular arithmetic
[*] Injective, surjective, bijective - and a bit about infinity
[*] Equivalence relations
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[*] Closing remarks
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[*] Putting it all together
[*] Generalization and specialization
[*] True understanding
[*] The biggest secret
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[*] Appendices
[LIST]
[*] Greek alphabet
[*] Commonly used symbols and notation
[*] How to prove that ...
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[*] Index
[/LIST]

Last edited by a moderator: May 6, 2017
2. Jan 24, 2013