Discrete Mathematics Courses and Certifications

Learn to prove or disprove theorems with induction, strong induction, and other proof methods, using Python 3 to represent inductive reasoning.

• Codecademy
• 1 hour
• Self-Paced
• Free Trial Available

Discrete Math: Permutations and Combinations

16 ratings at Codecademy

Count arrangements and selections with permutation and combination notation, then represent them in Python code in about an hour.

• Codecademy
• 1 hour
• Self-Paced
• Free Trial Available

Learn modular congruences, the Chinese Remainder Theorem, and how to apply them by coding a Caesar cipher in Python.

• Codecademy
• 1 hour
• Self-Paced
• Free Trial Available

Learn recurrence relations and their solutions while using Python recursion and dynamic programming to improve computational efficiency.

• Codecademy
• 1 hour
• Self-Paced
• Free Trial Available

IIT Madras;  NPTEL

Combinatorics

Develop combinatorial counting through inclusion-exclusion, Möbius inversion, generating functions, Pólya theory, graphs, and species of structures.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

MA111: Introduction to Mathematical Reasoning

Learn to construct mathematical proofs while working through logic, sets, number theory, rational numbers, mathematical induction, relations and functions, and combinatorics.

• Saylor University
• 112 hours
• Self-Paced
• Free Certificate

Maths for Programmers Tutorial - Full Course on Sets and Logic

An introduction to discrete mathematics for programmers covering set operations, laws, propositions, truth tables, quantifiers, conditional statements, and tautologies.

• freeCodeCamp
• 1-2 hours
• Self-Paced
• Free Video

Graphs and Networks: Concepts and Applications

Learn to model, visualize, and analyze graphs and networks in Wolfram Language using imported or built-in data.

• Wolfram U
• 20 minutes
• Self-Paced
• Free Online Course

Insights into Mathematics

The Algebra of Boole - Logic and Circuit Analysis - MF250-280

Explore Boole's algebra for logic and circuit analysis, covering historical foundations, logical operations, transistors, and systematic deduction methods.

• YouTube
• 14 hours 24 minutes
• Self-Paced
• Free Video

Keith Galli

Algorithms - Recurrences

Master recurrence equations through Fibonacci, merge sort, and binary search examples using recursion-tree and master methods for algorithm analysis.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

UCLA Automated Reasoning Group

Automated Reasoning - Logic, Probabilistic Reasoning and Machine Learning

Explore Boolean logic, probabilistic reasoning, and machine learning through tractable circuits and knowledge compilation techniques for automated reasoning systems.

• YouTube
• 1 day 1 hour 51 minutes
• Self-Paced
• Free Video

Mathemaniac

Deep Dive into Combinatorics

Explore advanced combinatorics beyond school curriculum, covering Catalan numbers, their generalizations, and mathematical research thinking processes.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

tecmath

Permutations and Combinations - Counting Principles, Factorials, and Probability

Master permutations, combinations, and probability through counting principles, factorial shortcuts, and practical tricks in this comprehensive math tutorial.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Professor Leonard

Statistics Lecture: Fundamental Counting Rule, Permutations and Combinations

Learn the fundamental counting rule, permutations, and combinations in a statistics lecture focused on counting arrangements and selections.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

Dr Trefor Bazett

The Bunkbed Conjecture Debunked - A Counterexample with 7222 Vertices

Explore the recent disproval of the famous bunkbed conjecture in probabilistic graph theory, featuring a counterexample with 7222 vertices and its implications.

• YouTube
• 15 minutes
• Self-Paced
• Free Video