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Constructing and Writing Mathematical Proofs:
A Guide for Mathematics Students
Ted Sundstrom, Professor Emeritus
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Contents
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Front Matter
Colophon
Note to Students
1
Preliminaries
Definitions
Useful Logic for Constructing Proofs
2
Direct Proofs
Using the Definitions of Congruence and Divides
A Direct Proof Involving Sets
Practice Problems for Chapter 2
3
Some Other Methods of Proof
Using the Contrapositive
Using Other Logical Equivalencies
Proofs of Biconditional Statements
Practice Problems for Chapter 3
4
Proof by Contradiction
Explanation and an Example
Proving that Something Does Not Exist
Rational and Irrational Numbers
Practice Problems for Chapter 4
5
Using Cases in Proofs
Some Common Situations to Use Cases
Using Cases with the Division Algorithm
Practice Problems for Chapter 5
6
Mathematical Induction
Using the Principle of Mathematical Induction
The Extended Principle of Mathematical Induction
The Second Principle of Mathematical Induction
Practice Problems for Chapter 6
7
Injective and Surjective Functions
Definitions and Notation
Some Examples and Proofs
Practice Problems for Chapter 7
Backmatter
A
Guidelines for Writing Mathematical Proofs
B
Answers and Hints for the Practice Problems
Index
Colophon
Authored in PreTeXt
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A
Guidelines for Writing Mathematical Proofs
B
Answers and Hints for the Practice Problems
Index
Colophon
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