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Discrete Mathematics for Computer Science
Mark Fitch
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Front Matter
Colophon
About Mark A. Fitch
Preface
1
Basics
1.1
Terminology
1.2
Sets
1.2.1
Understanding Sets
1.2.2
Terminology
1.2.3
Practice
1.3
Set Operations
1.3.1
Terminology
1.3.2
Practice
1.4
Sets in Relational Database
1.5
Combinatorics: First Counts
1.5.1
Terminology
1.5.2
Practice
1.6
Sorting: Part 0
1.6.1
Practice
2
Logic
2.1
Formal Logic
2.1.1
Terminology
2.1.2
Practice
2.2
Circuits
2.2.1
Background
2.2.2
Practice
2.3
Predicate Logic
2.3.1
Quantifiers
2.3.1.1
Terminology
2.3.2
Negation
2.3.2.1
Negate a statement
2.3.2.2
Discover
2.3.2.3
Examples
2.3.2.4
Practice
2.3.3
Exercises
2.4
Mathematical Proof
2.4.1
First set proofs
2.4.2
Practice
3
Functions
3.1
Functions
3.1.1
Terminology
3.1.2
Practice
3.2
Boolean Algebra
3.2.1
Terminology
3.2.2
Practice
3.2.3
Representation
3.2.3.1
Terminology
3.2.3.2
Practice
3.3
Modulo Arithmetic
3.3.1
Terminology
3.3.2
Practice
3.3.3
Proofs
3.4
Combinatorics: Second Counts
3.4.1
Terminology
3.4.2
Practice
3.4.2.1
Discover a Method
3.4.2.2
Use the Method
3.5
Proof by Contradiction
3.5.1
First proof using contradiction
4
Relations
4.1
Example: Error Correcting Codes
4.1.1
Illustrated
4.1.2
Practice
4.2
Mathematical Relations
4.2.1
Terminology
4.2.2
Practice
4.2.3
Closure
4.2.4
Practice
4.3
Equivalence Relations
4.3.1
Defined
4.3.2
Equivalence Classes
4.3.3
Characterizing Equivalence Classes
4.4
Partially Ordered Sets
4.4.1
Terminology
4.4.2
Practice
4.4.3
Poset Properties
4.4.3.1
Terminology
4.4.3.2
Practice
4.5
Combinatorics: Inclusion/Exclusion
4.5.1
Terminology
4.5.2
Practice
5
Graph Theory
5.1
Discovering Graphs
5.2
Properties of Graphs
5.2.1
Definitions of Graph Properties
5.2.2
Practice
5.3
Graph Isomorphism
5.4
Paths
5.4.1
Paths
5.4.2
Practice
5.4.3
Connected
5.4.4
Practice
5.5
Cycles
5.5.1
Terminology
5.5.2
Practice
5.6
Trees
5.6.1
Terminology
5.6.2
Practice
5.7
Linear Recurrence Relations
5.7.1
A couple interesting illustrations
5.7.2
Recurrence Relations
5.7.3
Practice
Back Matter
A
University Database Example
B
Glossary
Chapter
2
Logic
The previous chapter used words like ‘and’ and ‘or’ and required deciding what is true. This chapter presents a formal approach to these topics and ends by applying it to program and circuit logic.
🔗
2.1
Formal Logic
2.2
Circuits
2.3
Predicate Logic
2.4
Mathematical Proof
🔗
