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Discrete Mathematics
An Active Approach to Mathematical Reasoning
Jennifer Firkins Nordstrom
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Front Matter
Colophon
Preface
1
Introduction to Mathematical Language
1.1
Variables and Statements
1.1
Check Your Understanding
1.1
Exercises
1.2
Introduction to Sets
1.2
Check Your Understanding
1.2
Exercises
1.3
Introduction to Relations and Functions
1.3
Check Your Understanding
1.3
Exercises
2
Logic
2.1
Truth-Tables and Logical Equivalence
2.1
Check Your Understanding
2.1
Exercises
2.2
Conditional Statements
2.2
Check Your Understanding
2.2
Exercises
2.3
Valid and Invalid Arguments
2.3
Check Your Understanding
2.3
Exercises
3
Logic with Quantifiers
3.1
Quantifiers
3.1
Check Your Understanding
3.1
Exercises
3.2
Negating Quantified Statements
3.2
Check Your Understanding
3.2
Exercises
3.3
Statements with Multiple Quantifiers
3.3
Check Your Understanding
3.3
Exercises
3.4
Arguments with Quantifiers
3.4
Check Your Understanding
3.4
Exercises
4
Proof Techniques
4.1
Direct Proof and Counterexample
4.1
Check Your Understanding
4.1
Exercises
4.2
Rational Numbers
4.2
Check Your Understanding
4.2
Exercises
4.3
Divisibility
4.3
Check Your Understanding
4.3
Exercises
4.4
Proof by Cases
4.4
Check Your Understanding
4.4
Exercises
4.5
Proof by Contradiction and Contrapositive
4.5
Check Your Understanding
4.5
Exercises
4.6
More Proof by Contradiction and Contrapositive
4.6
Check Your Understanding
4.6
Exercises
5
Sequences and Mathematical Induction
5.1
Sequences
5.1
Check Your Understanding
5.1
Exercises
5.2
Mathematical Induction
5.2
Check Your Understanding
5.2
Exercises
5.3
More Mathematical Induction
5.3
Check Your Understanding
5.3
Exercises
5.4
Strong Induction
5.4
Check Your Understanding
5.4
Exercises
5.5
Defining Sequences Recursively
5.5
Check Your Understanding
5.5
Exercises
5.6
Solving Recurrence Relations by Iteration
5.6
Check Your Understanding
5.6
Exercises
6
Set Theory
6.1
Set Theory
6.1
Check Your Understanding
6.1
Exercises
6.2
Properties of Sets
6.2
Check Your Understanding
6.2
Exercises
6.3
Algebraic Proofs and Counterexamples
6.3
Check Your Understanding
6.3
Exercises
7
Functions
7.1
Functions
7.1
Check Your Understanding
7.1
Exercises
7.2
One-to-One, Onto, Inverse Functions
7.2
Check Your Understanding
7.2
Exercises
8
Relations
8.1
Relations on Sets
8.1
Check Your Understanding
8.1
Exercises
8.2
Reflexive, Symmetric, Transitive Properties
8.2
Check Your Understanding
8.2
Exercises
8.3
Equivalence Relations
8.3
Check Your Understanding
8.3
Exercises
8.4
Modular Arithmetic
8.4
Check Your Understanding
8.4
Exercises
9
Probability and Counting
9.1
Probability
9.1
Check Your Understanding
9.1
Exercises
9.2
Multiplication Rule
9.2
Check Your Understanding
9.2
Exercises
9.3
Addition Rule
9.3
Check Your Understanding
9.3
Exercises
9.4
Pigeonhole Principle
9.4
Check Your Understanding
9.4
Exercises
9.5
Combinations
9.5
Check Your Understanding
9.5
Exercises
9.6
Binomial Theorem
9.6
Check Your Understanding
9.6
Exercises
10
Graph Theory
10.1
Graphs
10.1
Check Your Understanding
10.1
Exercises
10.2
Paths and Circuits
10.2
Check Your Understanding
10.2
Exercises
10.3
Trees
10.3
Check Your Understanding
10.3
Exercises
Back Matter
References
A
Notation
Index
Colophon
Discrete Mathematics
An Active Approach to Mathematical Reasoning
Jennifer Firkins Nordstrom
Department of Mathematics and Computer Science
Linfield University
McMinnville, OR
jfirkins@linfield.edu
June 21, 2025
Colophon
Preface
