What is combinatorics?

Combinatorics is a branch of math that explores counting and possible ways to count items. It includes concepts like enumeration, combination, and permutation of sets. Combinatorics is related to other branches of math, such as graph theory, coding, and probability.

Why learn combinatorics?

Learning combinatorics teaches more than how to calculate permutations—which on its own is a useful skill. It also helps boost your problem-solving skills. You can practice the process of dissecting a problem, exploring all of the possible solutions to the problem, and considering the best possible outcomes. An understanding of combinatorics can come in handy when you play games of chance, too.

What career opportunities can arise from learning combinatorics?

Combinatorics plays a role in many different fields—from software development to medicine—where you can find career opportunities after learning combinatorics. There are opportunities as a math or computer science researcher or algorithm designer. With an understanding of combinatorics, you may choose to work as an analyst and offer consulting services to companies that need help streamlining processes and increasing profit margins. Combinatorics is helpful when people and organizations need to examine possible outcomes. Epidemiologists who want to know how a virus spreads through a population may explore possibilities through combinatorics. Investors who need to decide where to invest their money use math models as they make a decision. A transportation company that wants to reduce fuel costs and increase efficiency can turn to combinatorics to examine the best changes to make within the company.

How can online courses help me learn combinatorics?

Online courses can help you learn combinatorics by giving you a way to work on material at your own pace. You can slow down, speed up, or review lessons as needed. Best of all, you can work wherever you’re comfortable and have the time to completely focus on the material.

What skills or experience do I need to already have before starting to learn combinatorics?

You should have basic arithmetic skills before starting to learn combinatorics. It’s also helpful to have a solid understanding of algebra before taking a combinatorics course. A background in another field of math like graph theory or probability may also be beneficial.

What are the benefits of taking an online Combinatorics course?

Online Combinatorics courses offer a convenient and flexible way to enhance your knowledge or learn new Combinatorics skills. Choose from a wide range of Combinatorics courses offered by top universities and industry leaders tailored to various skill levels.

What Combinatorics courses are best for training and upskilling employees or the workforce?

When looking to enhance your workforce's skills in Combinatorics, it's crucial to select a course that aligns with their current abilities and learning objectives. Our Skills Dashboard is an invaluable tool for identifying skill gaps and choosing the most appropriate course for effective upskilling. For a comprehensive understanding of how our courses can benefit your employees, explore the enterprise solutions we offer. Discover more about our tailored programs at Coursera for Business here .

Best Combinatorics Courses & Certificates [2025]

Explore the Combinatorics Course Catalog

Status: Free
Princeton University
Analytic Combinatorics
Skills you'll gain: Combinatorics, Mathematical Theory & Analysis, Advanced Mathematics, Theoretical Computer Science, Calculus, Probability, Applied Mathematics
4.7
Rating, 4.7 out of 5 stars
70 reviews
Intermediate · Course · 1 - 3 Months
Status: Free Trial
University of California San Diego
Combinatorics and Probability
Skills you'll gain: Combinatorics, Probability, Probability Distribution, Algorithms, Bayesian Statistics, Mathematical Modeling, Statistics, Arithmetic, Python Programming, Simulations
4.6
Rating, 4.6 out of 5 stars
865 reviews
Beginner · Course · 1 - 3 Months
Status: New
Status: Free Trial
Birla Institute of Technology & Science, Pilani
Mathematics for Engineering
Skills you'll gain: Integral Calculus, Engineering Calculations, Data Analysis, Probability & Statistics, Engineering Analysis, Computational Logic, Statistical Analysis, Linear Algebra, Logical Reasoning, Deductive Reasoning, Mathematical Modeling, Trigonometry, Bayesian Statistics, Advanced Mathematics, Statistical Methods, Artificial Intelligence and Machine Learning (AI/ML), Statistical Inference, Theoretical Computer Science, Programming Principles, Descriptive Analytics
4.6
Rating, 4.6 out of 5 stars
154 reviews
Beginner · Specialization · 3 - 6 Months
Status: Free Trial
University of California San Diego
Introduction to Discrete Mathematics for Computer Science
Skills you'll gain: Graph Theory, Logical Reasoning, Cryptographic Protocols, Combinatorics, Computational Logic, Deductive Reasoning, Cryptography, Probability, Key Management, Computational Thinking, Encryption, Probability Distribution, Network Analysis, Public Key Cryptography Standards (PKCS), Theoretical Computer Science, Bayesian Statistics, Python Programming, Data Structures, Algorithms, Arithmetic
4.5
Rating, 4.5 out of 5 stars
3.7K reviews
Beginner · Specialization · 3 - 6 Months
The University of Sydney
Introduction to Linear Algebra
Skills you'll gain: Linear Algebra, Markov Model, Geometry, Arithmetic, Algebra, General Mathematics, Advanced Mathematics, Probability, Mathematics and Mathematical Modeling, Mathematical Theory & Analysis, Mathematical Modeling, Applied Mathematics, Statistical Methods, Engineering Analysis
4.8
Rating, 4.8 out of 5 stars
35 reviews
Intermediate · Course · 1 - 4 Weeks
Status: Free Trial
DeepLearning.AI
Mathematics for Machine Learning and Data Science
Skills you'll gain: Descriptive Statistics, Bayesian Statistics, Statistical Hypothesis Testing, Probability & Statistics, Sampling (Statistics), Probability Distribution, Linear Algebra, Statistical Inference, A/B Testing, Statistical Analysis, Applied Mathematics, NumPy, Probability, Calculus, Dimensionality Reduction, Numerical Analysis, Mathematical Modeling, Machine Learning, Machine Learning Methods, Data Transformation
4.6
Rating, 4.6 out of 5 stars
2.9K reviews
Intermediate · Specialization · 1 - 3 Months

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Status: Preview
Stanford University
Introduction to Mathematical Thinking
Skills you'll gain: Mathematical Theory & Analysis, Mathematics and Mathematical Modeling, Calculus, Deductive Reasoning, Logical Reasoning
4.8
Rating, 4.8 out of 5 stars
3K reviews
Intermediate · Course · 1 - 3 Months
Status: Preview
Shanghai Jiao Tong University
Discrete Mathematics
Skills you'll gain: Combinatorics, Graph Theory, Theoretical Computer Science, Mathematical Theory & Analysis, Advanced Mathematics, Network Analysis, Computational Thinking, Algorithms, Data Structures, Computer Science
3.3
Rating, 3.3 out of 5 stars
200 reviews
Intermediate · Course · 1 - 3 Months
Status: Free Trial
University of California San Diego
Introduction to Graph Theory
Skills you'll gain: Graph Theory, Combinatorics, Network Analysis, Data Structures, Network Routing, Algorithms, Theoretical Computer Science, Program Development
4.5
Rating, 4.5 out of 5 stars
1.1K reviews
Beginner · Course · 1 - 3 Months
Status: Preview
University of Zurich
An Intuitive Introduction to Probability
Skills you'll gain: Probability, Probability Distribution, Probability & Statistics, Statistics, Descriptive Statistics, Applied Mathematics, Risk Analysis, Finance
4.8
Rating, 4.8 out of 5 stars
1.9K reviews
Beginner · Course · 1 - 3 Months
Status: Free Trial
University of Colorado Boulder
Trees and Graphs: Basics
Skills you'll gain: Graph Theory, Data Structures, Algorithms, Tree Maps, Theoretical Computer Science, Analysis, Computational Thinking, Network Analysis, Computer Programming, Python Programming
Build toward a degree
4.6
Rating, 4.6 out of 5 stars
172 reviews
Advanced · Course · 1 - 4 Weeks
Status: Preview
Stanford University
Introduction to Logic
Skills you'll gain: Logical Reasoning, Computational Logic, Deductive Reasoning, Computational Thinking, Problem Solving, Business Logic, Complex Problem Solving, Decision Making
4.4
Rating, 4.4 out of 5 stars
652 reviews
Intermediate · Course · 1 - 3 Months