Proof: Table of Contents

Proof: Introduction to Higher Mathematics
Fifth Edition, 2011

by Warren W. Esty and Norah C. Esty

Table of Contents:

Part I: Theory of Proof: Language and Logic.

CHAPTER 1    1
Introduction to Proofs
        1.1. Preview of Proof 2
        1.2. Sets 12
        1.3. Logic for Mathematics 30
        1.4. Important Logical Equivalences 50
        1.5. Negations 62
        1.6. Tautologies and Proofs 74
        RESULTS FROM LOGIC 86

CHAPTER 2    89
Sentences with Variables
        2.1. Sentences with One Variable 89
        2.2. Existence Statements and Negation 99
        2.3. Reading Theorems and Definitions 115
        2.4. Equivalence 134
        2.5. Rational Numbers and Form 147

CHAPTER 3    152
Proofs
        3.1. Inequalities 153
        3.2. Absolute Values 166
        3.3. Theory of Proofs 174
        3.4. Proofs by Contradiction or Contrapositive 189
        3.5. Mathematical Induction 195
        3.6. Bad Proofs 205

Part II: Practice

CHAPTER 4
Set Theory
        4.1. Set Theory
        4.2. Bounds (including suprema)

CHAPTER 5
Functions
        5.1. One-to-One and Onto
        5.2. Functions Applied to Sets
        5.3. Cardinality

----- This finishes one semester of a sophomore-level course at Montana State University. Some of the following sections are used in subsequent course entitled "Higher Mathematics for Secondary Teachers."

CHAPTER 6
Number Theory
        6.1. Number Theory
        6.2. Common Divisors
        6.3. Prime Numbers
        6.4. Modular Arithmetic
        6.5. Cryptography

CHAPTER 7
Group Theory
        7.1 Groups
       7.2 Subgroups, Cosets, and Lagrange's Theorem
        7.3 Isomorphism
        74. Quotient Groups

CHAPTER 8
Topology
        8.1. Open and Closed Sets
        8.2. Interior Points and Accumulation Points

CHAPTER 9
Calculus
        9.1. Limits of Sequences
        9.2. Limits and Derivatives

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