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Discrete
Mathematics
The math that makes computer science possible. Logic, sets, graphs, and proofs that sharpen how you reason about problems and systems.
What You'll Learn
A full semester of discrete mathematics — completed at your own pace, with no deadlines or fixed class times.
What You'll Be Able to Do
- Apply discrete mathematical concepts essential for advanced mathematical reasoning and problem-solving
- Construct logical proofs, including identifying fallacies, manipulating logical connectors, and interpreting conditional statements
- Apply set theory, functions, sequences, and series to solve counting problems and analyze probabilistic scenarios; solve recursive solutions to advanced counting problems and combinatorial scenarios, utilizing techniques such as generating functions and the inclusion-exclusion principle
- Evaluate core principles in graph theory, including graph properties, algorithms, and their practical applications in computer science and engineering
- Design and optimize circuits in digital electronics and computer science using tree structures, matrices, and Boolean Algebra
Major Course Topics
Course chapters and lessons
Discrete Mathematics has 13 chapters across 46 instructional hours, as listed in the course syllabus. Expand any chapter to see the lessons inside it.
- Chapters
- 13
- Lessons
- 87
- Instructional hours
- 46 hrs
- Semester hours
- 4
Chapter 1
Logic and Mathematical Proof
- 1.1 What Is Logic and Why It Matters in Mathematics
- 1.2 Types of Logical Fallacies and How to Recognize Them
- 1.3 Propositions, Truth Values, and Truth Tables
- 1.4 Logical Connectives: AND, OR, NOT and More
- 1.5 Conditional Statements and Their Forms
- 1.6 Laws of Logic and Logical Equivalence
- 1.7 Writing Direct Proofs
- 1.8 Tautologies and Contradictions
Chapter 2
Set Theory and Functions
- 2.1 Introduction to Sets and Set Notation
- 2.2 The Universal Set and Subsets
- 2.3 Set Complement and Set Difference
- 2.4 Cardinality and Types of Subsets
- 2.5 Partially Ordered Sets and Lattices
- 2.6 Functions: Definitions and Terminology
- 2.7 Injective Functions: One-to-One Mappings and Their Properties
- 2.8 Surjective and Bijective Functions: Onto Mappings and Perfect Pairings
Chapter 3
Sequences and Series
- 3.1 Introduction to Mathematical Sequences
- 3.2 Finite vs. Infinite Sequences
- 3.3 Arithmetic Sequences
- 3.4 Geometric Sequences
- 3.5 Sigma Notation and Series
- 3.6 Sum of Arithmetic Series
- 3.7 Sum of Geometric Series
- 3.8 Practice: Arithmetic and Geometric Series
Chapter 4
Mathematical Induction
- 4.1 Principles of Mathematical Induction
- 4.2 Constructing Proofs by Induction
Chapter 5
Counting Methods and Basic Probability
- 5.1 Counting Outcomes and Sample Spaces
- 5.2 Fundamental Counting Principles: The Addition and Multiplication Rules
- 5.3 The Pigeonhole Principle: Why Overlaps Are Guaranteed in Finite Collections
- 5.4 Permutations and Ordered Arrangements
- 5.5 Probability of Permutation Events
- 5.6 Circular Permutations
- 5.7 Combinations and Unordered Selections
- 5.8 Probability of Combination Events
Chapter 6
Discrete Probability: Random Variables and Expected Value
- 6.1 Random Variables in Discrete Probability
- 6.2 Expected Value: Meaning and Calculation
- 6.3 Theoretical Discrete Probability Distributions
- 6.4 Empirical Discrete Probability Distributions
- 6.5 Applied Discrete Probability Problems
Chapter 7
Probability in Games, Gambling, and Strategic Decision
- 7.1 Probability in Dice Games
- 7.2 Probability in Blackjack
- 7.3 Probability of Poker Hands
- 7.4 Probability of Low-Hand Poker Variants
- 7.5 Probability and Expected Value in Lotteries
- 7.6 Comparing Game Strategies with Expected Value
Chapter 8
Binomial Probability, Recurrence Relations, and Generating Functions
- 8.1 Binomial Experiments and Their Conditions
- 8.2 The Binomial Probability Formula
- 8.3 Solving Binomial Probability Problems
- 8.4 Using Binomial Probability Tables
- 8.5 Finding the Mean of a Binomial Distribution: The np Formula and Its Interpretation
- 8.6 Measuring Spread in Binomial Distributions: Standard Deviation and Variance Calculations
- 8.7 Applied Binomial Experiment Problems
- 8.8 Recursive Functions and Self-Referential Definitions
- 8.9 First-Order Linear Recurrence Relations
- 8.10 Solving Linear Recurrence Relations
- 8.11 Recurrences in Divide-and-Conquer Algorithms
- 8.12 Introduction to Generating Functions
- 8.13 The Inclusion-Exclusion Principle
Chapter 9
Graph Theory: Foundations and Euler Paths
- 9.1 Graphs: Vertices, Edges, and Basic Definitions
- 9.2 Graph Terminology and Key Concepts
- 9.3 Types of Graphs and Their Properties
- 9.4 Graph Isomorphism and Homomorphism
- 9.5 Euler Paths and Circuits: Definitions and the Degree Conditions That Determine Their Existence
- 9.6 Fleury's Algorithm
- 9.7 Euler's Theorems: Degrees, Paths, and Circuits
- 9.8 Eulerizing a Graph
Chapter 10
Graph Theory: Hamiltonian Circuits, Coloring, and Representations
- 10.1 Hamiltonian Paths and Circuits
- 10.2 Weighted Graphs and Optimization Methods for Finding the Most Efficient Hamiltonian Circuit
- 10.3 Graph Coloring and Traversal
- 10.4 Adjacency Matrix and List Representations
Chapter 11
Trees, Spanning Trees, and Minimum Cost Networks
- 11.1 Trees: Properties and Definitions
- 11.2 Tree Traversal Methods
- 11.3 Sorting with Trees: Benefits and Limitations
- 11.4 Spanning Trees and Their Properties
- 11.5 Kruskal's Algorithm for Minimum Spanning Trees
- 11.6 Prim's Algorithm for Minimum Spanning Trees
Chapter 12
Matrices and Transformations
- 12.1 Introduction to Matrices
- 12.2 Matrix Operations and Inverses
- 12.3 Rotation Matrices and Their Applications
- 12.4 Translation Matrices and Their Applications
Chapter 13
Boolean Algebra and Logic Circuits
- 13.1 Foundations of Boolean Logic
- 13.2 Boolean Algebra: Laws and Properties
- 13.3 Boolean Expressions and Logical Operators
- 13.4 Karnaugh Maps
- 13.5 The Arithmetic Logic Unit (ALU)
- 13.6 Logic Gate Design: AND, OR, NOT, NAND, NOR, XOR, and How They Build Circuits
- 13.7 Simplifying Logic Circuits
These chapters come straight from the official course syllabus, which also sets out the graded assignment and the proctored final exam.
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HD video lectures broken into short, focused modules. Watch at your own pace — pause, rewind, replay any time.
Quizzes & Final Exam
Evaluate your understanding after every section with quizzes and a comprehensive final exam that mirrors real college assessment.
Structured College-Level Course
Structured lessons covering every topic — designed as a standard Discrete Mathematics college-level course.
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