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Intro Math How to Think Like a Mathematician by Houston

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  1. Jan 24, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Preface
    [*] Study skills for mathematicians
    [LIST]
    [*] Sets and functions
    [*] Reading mathematics
    [*] Writing mathematics I
    [*] Writing mathematics II
    [*] How to solve problems
    [/LIST]
    [*] How to think logically
    [LIST]
    [*] 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
    [LIST]
    [*] 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
    [/LIST]
    [*] 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
    [/LIST]
    [*] Closing remarks
    [LIST]
    [*] Putting it all together
    [*] Generalization and specialization
    [*] True understanding
    [*] The biggest secret
    [/LIST]
    [*] Appendices
    [LIST]
    [*] Greek alphabet
    [*] Commonly used symbols and notation
    [*] How to prove that ...
    [/LIST]
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 24, 2013 #2

    mathwonk

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