Combinatorics Courses and Certifications

Combinatorics and Probability

874 ratings at Coursera

Count without listing: use basic counting rules, binomial coefficients, and combinations with repetitions, then compute probabilities, work with random variables, and program an optimal dice-game strategy.

• Coursera
• 6 weeks, 4 hours a week
• Self-Paced
• Paid Course

Analytic Combinatorics

76 ratings at Coursera

Derive precise asymptotics for large combinatorial structures: use the symbolic method to build ordinary, exponential and multivariate generating functions, then apply singularity and saddle point analysis.

• Coursera
• 8 weeks, 2 hours a week
• Self-Paced
• Free Online Course

Probabilistic Methods in Combinatorics

Graduate course on using random constructions and probabilistic inequalities to prove the existence and properties of combinatorial objects.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Combinatorics and Algorithms Design

Count with permutations, generating functions and the inclusion-exclusion principle, then design algorithms using incremental, divide-and-conquer, randomized and dynamic programming paradigms.

• XuetangX
• Self-Paced
• Free Online Course

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

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

Probabilistic Methods in Combinatorics - Fall 2024

Discover powerful probabilistic techniques for solving complex combinatorial problems, including Ramsey theory, extremal set theory, and random graph analysis.

• YouTube
• 3 hours 37 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Combinatorics - Math History - NJ Wildberger

A historical tour of combinatorics through counting problems, graph theory, generating functions, Fibonacci and Catalan sequences, and Ramsey theory.

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

Steve Brunton

Counting Probabilities with Combinatorics and the Factorial

Master combinatorics and factorial concepts in probability. Learn to count event occurrences, analyze sampling methods, and apply formulas for various probability scenarios, including coin flips and poker hands.

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

Lower Bounds to Ramsey Numbers - MIT 18.226 Probabilistic Methods in Combinatorics

Delve into probabilistic methods in combinatorics, exploring Ramsey numbers through alteration techniques and the Lovász Local Lemma for advanced mathematical problem-solving.

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

Linearity of Expectations in Combinatorics - Applications to Permutations and Hamilton Paths

Master probabilistic combinatorics through practical applications, exploring random permutations and Hamilton paths in tournaments while learning key concepts of linearity of expectations.

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

Ryan O'Donnell

Analysis of Boolean Functions at CMU - Additive Combinatorics

Explore additive combinatorics on F₂ⁿ through approximate subgroups, density increments, and the polynomial Freiman–Ruzsa conjecture.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Professor Knudson

Combinatorics

1 rating

Learn to count ordered and unordered arrangements using permutations, multinomial coefficients, and combinatorial probability, including a poker example.

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

Kimberly Brehm

Discrete Math II - Combinatorics

A second course in discrete mathematics covering combinatorial counting, generating functions, recurrence relations, group actions, and graph theory.

• YouTube
• 12 hours
• Self-Paced
• Free Video

Principles of Computing (Part 1)

30 ratings

Build Python mini-projects around strategy games while applying coding standards, testing, grids, probability, combinatorics, and counting to computational problem solving.

• Coursera
• 5 weeks, 4 hours a week
• Self-Paced
• Paid Course