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 .

Top Combinatorics Courses - Learn Combinatorics Online

Explore the Combinatorics Course Catalog

Status: Free
Princeton University
Algorithms, Part II
Skills you'll gain: Graph Theory, Data Structures, Algorithms, Theoretical Computer Science, Operations Research, Applied Mathematics, Computational Thinking, Computer Programming, Network Routing, Programming Principles, Network Model, Java Programming, Linear Algebra
4.9
Rating, 4.9 out of 5 stars
2K reviews
Intermediate · Course · 3 - 6 Months
Johns Hopkins University
Algebra: Elementary to Advanced - Polynomials and Roots
Skills you'll gain: Algebra, Advanced Mathematics, Applied Mathematics, Analytical Skills, Mathematical Modeling, Geometry, Graphing
4.9
Rating, 4.9 out of 5 stars
140 reviews
Beginner · Course · 1 - 3 Months
Imperial College London
Mathematics for Machine Learning: Multivariate Calculus
Skills you'll gain: Regression Analysis, Calculus, Advanced Mathematics, Numerical Analysis, Statistical Analysis, Linear Algebra, Artificial Neural Networks, Machine Learning, Mathematical Theory & Analysis, Python Programming, Derivatives
4.7
Rating, 4.7 out of 5 stars
5.7K reviews
Beginner · Course · 1 - 3 Months
DeepLearning.AI
Probability & Statistics for Machine Learning & Data Science
Skills you'll gain: Descriptive Statistics, Bayesian Statistics, Statistical Hypothesis Testing, Probability & Statistics, Sampling (Statistics), Probability Distribution, Probability, Statistical Inference, A/B Testing, Statistical Analysis, Data Science, Exploratory Data Analysis, Data Analysis, Statistical Visualization
4.6
Rating, 4.6 out of 5 stars
533 reviews
Intermediate · Course · 1 - 4 Weeks
Johns Hopkins University
Foundational Mathematics for AI
Skills you'll gain: Descriptive Statistics, Linear Algebra, Exploratory Data Analysis, Data-Driven Decision-Making, Data Analysis, Bayesian Statistics, Statistics, Artificial Intelligence and Machine Learning (AI/ML), Artificial Intelligence, Probability, Regression Analysis, Probability & Statistics, Calculus, Statistical Analysis, Advanced Mathematics, Applied Mathematics, Probability Distribution, Mathematical Modeling, Integral Calculus, Algebra
Beginner · Course · 1 - 3 Months
Johns Hopkins University
Mathematical Biostatistics Boot Camp 2
Skills you'll gain: Statistical Hypothesis Testing, Statistical Analysis, Statistical Methods, Probability & Statistics, Statistical Inference, Biostatistics, Sampling (Statistics), Data Analysis
4.3
Rating, 4.3 out of 5 stars
133 reviews
Mixed · Course · 1 - 4 Weeks
University of Colorado Boulder
Foundations of Data Structures and Algorithms
Skills you'll gain: Theoretical Computer Science, Algorithms, Data Structures, Graph Theory, Operations Research, Public Key Cryptography Standards (PKCS), Computational Logic, Cryptography, Computational Thinking, Pseudocode, Design Strategies, Combinatorics, Programming Principles, Computer Programming, Computer Science, Encryption, Network Model, Linear Algebra, Analysis, Mathematical Modeling
Build toward a degree
4.6
Rating, 4.6 out of 5 stars
702 reviews
Advanced · Specialization · 3 - 6 Months
Status: Free
Johns Hopkins University
The Mathematics of Democracy, Politics and Manipulation
Skills you'll gain: Political Sciences, Policy Analysis, Social Studies, Social Sciences, Public Policies, Game Theory, Demography, Mathematical Modeling, Research, Applied Mathematics, Geometry
4.9
Rating, 4.9 out of 5 stars
12 reviews
Mixed · Course · 1 - 3 Months
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, Probability, Linear Algebra, Statistical Inference, A/B Testing, Applied Mathematics, NumPy, Calculus, Dimensionality Reduction, Machine Learning, Jupyter, Python Programming, Data Transformation, Data Manipulation, Data Science
4.6
Rating, 4.6 out of 5 stars
2.6K reviews
Intermediate · Specialization · 1 - 3 Months
University of Colorado Boulder
Dynamic Programming, Greedy Algorithms
Skills you'll gain: Theoretical Computer Science, Algorithms, Computational Logic, Computational Thinking, Pseudocode, Data Structures, Design Strategies, Combinatorics, Programming Principles, Computer Programming, Computer Science, Graph Theory, Advanced Mathematics, Analysis, Emerging Technologies
4.6
Rating, 4.6 out of 5 stars
192 reviews
Advanced · Course · 1 - 4 Weeks
University of Colorado Boulder
Approximation Algorithms and Linear Programming
Skills you'll gain: Operations Research, Algorithms, Network Model, Linear Algebra, Combinatorics, Computational Thinking, Mathematical Modeling, Theoretical Computer Science, Computer Programming, Python Programming
Build toward a degree
4.9
Rating, 4.9 out of 5 stars
43 reviews
Advanced · Course · 1 - 4 Weeks
Status: Free
Universitat Autònoma de Barcelona
Pre-Calculus
Skills you'll gain: Trigonometry, Integral Calculus, Calculus, Arithmetic, Advanced Mathematics, Algebra, Mathematical Theory & Analysis, Applied Mathematics, Graphing, Derivatives
4.7
Rating, 4.7 out of 5 stars
567 reviews
Beginner · Course · 1 - 3 Months