Discrete Math: Free online course and PDF textbook

Episode 1: IntroductionWhat is “discrete mathematics,” anyway?

Key Topics

1. What does “discrete” mean?

Discrete Math, Episode 1: Introduction
What does “discrete” mean?
Discrete Mathematics, Episode I: Introduction
Key Topic: What does “discrete” mean?

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. What does “mathematics” mean?

Discrete Math, Episode 1: Introduction
What does “mathematics” mean?
Discrete Mathematics, Episode I: Introduction
Key Topic: What does “mathematics” mean?

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 2: SetsA simple building block for all the rest of math

Key Topics

1. Sets and tuples

Discrete Math, Episode 2: Sets
Sets and tuples
Discrete Mathematics, Episode II: Sets
Key Topic: Sets and tuples

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. Ways to Define Sets

Discrete Math, Episode 2: Sets
Ways to Define Sets
Discrete Mathematics, Episode II: Sets
Key Topic: Ways to Define Sets

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. Some “Special” Sets

Discrete Math, Episode 2: Sets
Some “Special” Sets
Discrete Mathematics, Episode II: Sets
Key Topic: Some “Special” Sets

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. The “Cardinality” of a Set

Discrete Math, Episode 2: Sets
The “Cardinality” of a Set
Discrete Mathematics, Episode II: Sets
Key Topic: The “Cardinality” of a Set

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
5. Set Membership

Discrete Math, Episode 2: Sets
Set Membership
Discrete Mathematics, Episode II: Sets
Key Topic: Set Membership

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
6. Subsets

Discrete Math, Episode 2: Sets
Subsets
Discrete Mathematics, Episode II: Sets
Key Topic: Subsets

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
7. Set Operators

Discrete Math, Episode 2: Sets
Set Operators
Discrete Mathematics, Episode II: Sets
Key Topic: Set Operators

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
8. Laws of “Set Algebra”

Discrete Math, Episode 2: Sets
Laws of “Set Algebra”
Discrete Mathematics, Episode II: Sets
Key Topic: Laws of “Set Algebra”

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
9. “Power Sets”

Discrete Math, Episode 2: Sets
“Power Sets”
Discrete Mathematics, Episode II: Sets
Key Topic: “Power Sets”

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
10. Partitions

Discrete Math, Episode 2: Sets
Partitions
Discrete Mathematics, Episode II: Sets
Key Topic: Partitions

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 3: RelationsA special way of combining sets that pops up everywhere

Key Topics

1. Relations

Discrete Math, Episode 3: Relations
Relations
Discrete Mathematics, Episode III: Relations
Key Topic: Relations

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. Relation Examples

Discrete Math, Episode 3: Relations
Relation Examples
Discrete Mathematics, Episode III: Relations
Key Topic: Relation Examples

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. “Relational” Databases

Discrete Math, Episode 3: Relations
“Relational” Databases
Discrete Mathematics, Episode III: Relations
Key Topic: “Relational” Databases

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. Properties of “Endorelations”

Discrete Math, Episode 3: Relations
Properties of “Endorelations”
Discrete Mathematics, Episode III: Relations
Key Topic: Properties of “Endorelations”

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
5. More Relation Examples

Discrete Math, Episode 3: Relations
More Relation Examples
Discrete Mathematics, Episode III: Relations
Key Topic: More Relation Examples

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
6. Functions

Discrete Math, Episode 3: Relations
Functions
Discrete Mathematics, Episode III: Relations
Key Topic: Functions

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
7. Composing Functions

Discrete Math, Episode 3: Relations
Composing Functions
Discrete Mathematics, Episode III: Relations
Key Topic: Composing Functions

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
8. Properties of functions

Discrete Math, Episode 3: Relations
Properties of functions
Discrete Mathematics, Episode III: Relations
Key Topic: Properties of functions

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 4: ProbabilityDoing the (seeming) impossible: quantifying uncertainty

Key Topics

1. Probability basics

Discrete Math, Episode 4: Probability
Probability basics
Discrete Mathematics, Episode IV: Probability
Key Topic: Probability basics

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. Probability Measures

Discrete Math, Episode 4: Probability
Probability Measures
Discrete Mathematics, Episode IV: Probability
Key Topic: Probability Measures

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. Conditional Probability

Discrete Math, Episode 4: Probability
Conditional Probability
Discrete Mathematics, Episode IV: Probability
Key Topic: Conditional Probability

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. Conditional Probability, continued

Discrete Math, Episode 4: Probability
Conditional Probability, continued
Discrete Mathematics, Episode IV: Probability
Key Topic: Conditional Probability, continued

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
5. The Law of Total Probability

Discrete Math, Episode 4: Probability
The Law of Total Probability
Discrete Mathematics, Episode IV: Probability
Key Topic: The Law of Total Probability

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
6. Independence

Discrete Math, Episode 4: Probability
Independence
Discrete Mathematics, Episode IV: Probability
Key Topic: Independence

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
7. Independence Pitfalls

Discrete Math, Episode 4: Probability
Independence Pitfalls
Discrete Mathematics, Episode IV: Probability
Key Topic: Independence Pitfalls

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
8. Bayes’ Rule

Discrete Math, Episode 4: Probability
Bayes’ Rule
Discrete Mathematics, Episode IV: Probability
Key Topic: Bayes’ Rule

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
9. Naive Bayes classifiers

Discrete Math, Episode 4: Probability
Naive Bayes classifiers
Discrete Mathematics, Episode IV: Probability
Key Topic: Naïve Bayes classifiers

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 5: StructuresSexy ways to organize data

Key Topics

1. Graph terms

Discrete Math, Episode 5: Structures
Graph terms
Discrete Mathematics, Episode V: Structures
Key Topic: Graph Terms

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. Graph Traversal

Discrete Math, Episode 5: Structures
Graph Traversal
Discrete Mathematics, Episode V: Structures
Key Topic: Graph Traversal

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. Dijkstra’s Shortest Path Algorithm

Discrete Math, Episode 5: Structures
Dijkstra’s Shortest Path Algorithm
Discrete Mathematics, Episode V: Structures
Key Topic: Dijkstra’s Shortest Path Algorithm

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. “Free” Trees

Discrete Math, Episode 5: Structures
“Free” Trees
Discrete Mathematics, Episode V: Structures
Key Topic: “Free” Trees

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
5. (Rooted) Trees

Discrete Math, Episode 5: Structures
(Rooted) Trees
Discrete Mathematics, Episode V: Structures
Key Topic: (Rooted) Trees

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
6. Binary Trees

Discrete Math, Episode 5: Structures
Binary Trees
Discrete Mathematics, Episode V: Structures
Key Topic: Binary Trees

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
7. Binary Search Trees

Discrete Math, Episode 5: Structures
Binary Search Trees
Discrete Mathematics, Episode V: Structures
Key Topic: Binary Search Trees

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 6: CountingWrapping our heads around really really large numbers

Key Topics

1. Counting basics

Discrete Math, Episode 6: Counting
Counting basics
Discrete Mathematics, Episode VI: Counting
Key Topic: Counting Basics

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. The Fundamental Theorem of Counting

Discrete Math, Episode 6: Counting
The Fundamental Theorem of Counting
Discrete Mathematics, Episode VI: Counting
Key Topic: The Fundamental Theorem of Counting

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. Permutations

Discrete Math, Episode 6: Counting
Permutations
Discrete Mathematics, Episode VI: Counting
Key Topic: Permutations

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. Partial Permutations

Discrete Math, Episode 6: Counting
Partial Permutations
Discrete Mathematics, Episode VI: Counting
Key Topic: Partial Permutations

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
5. Combinations

Discrete Math, Episode 6: Counting
Combinations
Discrete Mathematics, Episode VI: Counting
Key Topic: Combinations

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
6. Summary and combinatorics examples

Discrete Math, Episode 6: Counting
Summary and combinatorics examples
Discrete Mathematics, Episode VI: Counting
Key Topic: Summary and combinatorics examples

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 7: NumbersRewiring your brain to separate “quantities” from “strings of digits”

Key Topics

1. What is a Number?

Discrete Math, Episode 7: Numbers
What is a Number?
Discrete Mathematics, Episode VII: Numbers
Key Topic: What is a Number?

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. Number Systems

Discrete Math, Episode 7: Numbers
Number Systems
Discrete Mathematics, Episode VII: Numbers
Key Topic: Number Systems

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. Converting Between Bases

Discrete Math, Episode 7: Numbers
Converting Between Bases
Discrete Mathematics, Episode VII: Numbers
Key Topic: Converting Between Bases

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. Addition, Revisited

Discrete Math, Episode 7: Numbers
Addition, Revisited
Discrete Mathematics, Episode VII: Numbers
Key Topic: Addition, Revisited

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
5. Why “Hex,” Anyway?

Discrete Math, Episode 7: Numbers
Why “Hex,” Anyway?
Discrete Mathematics, Episode VII: Numbers
Key Topic: Why “Hex,” Anyway?

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
6. Representing Negative Numbers

Discrete Math, Episode 7: Numbers
Representing Negative Numbers
Discrete Mathematics, Episode VII: Numbers
Key Topic: Representing Negative Numbers

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
7. Two’s-Complement

Discrete Math, Episode 7: Numbers
Two’s-Complement
Discrete Mathematics, Episode VII: Numbers
Key Topic: Two’s-Complement

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
8. Overflow

Discrete Math, Episode 7: Numbers
Overflow
Discrete Mathematics, Episode VII: Numbers
Key Topic: Overflow

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 8: LogicA way to represent, and automate, human reasoning

Key Topics

1. Logic

Discrete Math, Episode 8: Logic
Logic
Discrete Mathematics, Episode VIII: Logic
Key Topic: Logic

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. Propositional Logic

Discrete Math, Episode 8: Logic
Propositional Logic
Discrete Mathematics, Episode VIII: Logic
Key Topic: Propositional Logic

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. Truth Tables

Discrete Math, Episode 8: Logic
Truth Tables
Discrete Mathematics, Episode VIII: Logic
Key Topic: Truth Tables

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. Identities

Discrete Math, Episode 8: Logic
Identities
Discrete Mathematics, Episode VIII: Logic
Key Topic: Identities

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
5. Predicate Logic

Discrete Math, Episode 8: Logic
Predicate Logic
Discrete Mathematics, Episode VIII: Logic
Key Topic: Predicate Logic

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
6. Quantifiers

Discrete Math, Episode 8: Logic
Quantifiers
Discrete Mathematics, Episode VIII: Logic
Key Topic: Quantifiers

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
7. Expressing Assertions in First-Order Predicate Calculus

Discrete Math, Episode 8: Logic
Expressing Assertions in First-Order Predicate Calculus
Discrete Mathematics, Episode VIII: Logic
Key Topic: Expressing Assertions in First-Order Predicate Calculus

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
8. Drawing conclusions

Discrete Math, Episode 8: Logic
Drawing conclusions
Discrete Mathematics, Episode VIII: Logic
Key Topic: Drawing logical conclusions

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Episode 9: ProofGoing beyond the shadow of a doubt

Key Topics

1. Direct proofs

Discrete Math, Episode 9: Proof
Direct proofs
Discrete Mathematics, Episode IX: Proof
Key Topic: Direct Proofs

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
2. Indirect Proofs

Discrete Math, Episode 9: Proof
Indirect Proofs
Discrete Mathematics, Episode IX: Proof
Key Topic: Indirect Proofs

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
3. Mathematical Induction (Weak Form)

Discrete Math, Episode 9: Proof
Mathematical Induction (Weak Form)
Discrete Mathematics, Episode IX: Proof
Key Topic: Mathematical Induction (Weak Form)

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$
4. Mathematical Induction (strong form)

Discrete Math, Episode 9: Proof
Mathematical Induction (strong form)
Discrete Mathematics, Episode IX: Proof
Key Topic: Mathematical Induction (strong form)

$An icon with a light blue background and a Venn diagram of two interconnected green circles with the outsides of both circles shaded with scribbled green lines. Icon is meant to demonstrate discrete math concepts of logic, sets, and relations.$

Explore the world of discrete math for computer science!

Volume 1: Discrete Math

Episode 1: IntroductionWhat is “discrete mathematics,” anyway?

Key Topics

Episode 2: SetsA simple building block for all the rest of math

Key Topics

Episode 3: RelationsA special way of combining sets that pops up everywhere

Key Topics

Episode 4: ProbabilityDoing the (seeming) impossible: quantifying uncertainty

Key Topics

Episode 5: StructuresSexy ways to organize data

Key Topics

Episode 6: CountingWrapping our heads around really really large numbers

Key Topics

Episode 7: NumbersRewiring your brain to separate “quantities” from “strings of digits”

Key Topics

Episode 8: LogicA way to represent, and automate, human reasoning

Key Topics

Episode 9: ProofGoing beyond the shadow of a doubt

Key Topics

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