Skip to main content
\(\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\M}{\mathcal M} \newcommand{\modulo}[3]{#1 \equiv #2 \pmod #3} \newcommand{\notmodulo}[3]{#1 \not \equiv #2 \pmod #3} \newcommand{\abs}[1]{\left| #1 \right|} \newcommand{\dom}[1]{\text{ dom} ( #1 )} \newcommand{\codom}[1]{\text{ codom} ( #1 )} \newcommand{\range}[1]{\text{ range} ( #1 )} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Constructing and Writing Mathematical Proofs:
A Guide for Mathematics Students
Ted Sundstrom, Professor Emeritus
š
x
Search Results:
Contents
Index
Prev
Up
Next
Contents
Prev
Up
Next
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 ChapterĀ 2
3
Some Other Methods of Proof
Using the Contrapositive
Using Other Logical Equivalencies
Proofs of Biconditional Statements
Practice Problems for ChapterĀ 3
4
Proof by Contradiction
Explanation and an Example
Proving that Something Does Not Exist
Rational and Irrational Numbers
Practice Problems for ChapterĀ 4
5
Using Cases in Proofs
Some Common Situations to Use Cases
Using Cases with the Division Algorithm
Practice Problems for ChapterĀ 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 ChapterĀ 6
7
Injective and Surjective Functions
Definitions and Notation
Some Examples and Proofs
Practice Problems for ChapterĀ 7
Backmatter
A
Guidelines for Writing Mathematical Proofs
B
Answers and Hints for the Practice Problems
Index
Colophon
Authored in PreTeXt
Colophon
Colophon
This book was authored in PreTeXt.