A Cool Brisk Walk Through Discrete Mathematics

A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!

Combinatorics and Discrete Mathematics Mathematics

Author: Stephen Davies
Publisher: University of Mary Washington
Source: LibreTexts
License: CC BY-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 65 sections

01: Meetup at the Trailhead
1.0: Introduction
1.1: Exercises
02: Sets
2.0: Introduction
2.1: The idea of a set
2.2: Defining sets
2.3: Finite and infinite sets
2.4: Sets are not arrays
2.5: Sets are not ordered pairs (or tuples)
2.6: Sets of sets
2.7: Cardinality
2.8: Some special sets
2.9: Combining sets
2.10: Subsets
2.11: Power sets
2.12: Partitions
2.13: Exercises
03: Relations
3.0: Introduction
3.1: The idea of a relation
3.2: Defining relations
3.3: Relations between a set and itself
3.4: Finite and infinite relations
3.5: Properties of endorelations
3.6: Functions
3.7: Properties of functions
3.8: Exercises
04: Relations
4.0: Introduction
4.1: Outcomes and events
4.2: Probability measures
4.3: Philosophical interlude
4.4: Conditional probability
4.5: Total probability
4.6: Bayes Theorem
4.7: Independence
4.8: Exercises
05: Probability
5.0: Introduction
5.1: Graphs
5.2: Trees
5.3: Final word
06: Structures
6.0: Introduction
6.1: The Fundamental Theorem
6.2: Permutations
6.3: Combinations
6.4: Summary
07: Counting
7.0: Introduction
7.1: What is a number
7.2: Bases
7.3: Hexadecimal (base 16)
7.4: Binary (base 2)
08: Logic
8.0: Introduction
8.1: Propositional logic
8.2: Predicate logic
09: Proof
9.0: Introduction
9.1: Proof concepts
9.2: Types of proof
9.3: Proof by induction
9.4: Final word