Combinatorics: Strategies and Methods for Counting

See combinatorics made simple and how to avoid errors in counting principles

Combinatorics is an area of mathematics primarily concerned with counting. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry.

On this free online combinatorics course, you’ll discover a simple and efficient method to translate a combinatorial problem into counting the elements of a reference mathematical structure.

You’ll learn basic counting principles, and be able to explain the most frequent errors in their misuse. Ultimately, you’ll discover that combinatorics isn’t as difficult as it seems.

Hear from our courses team

You can sign up at any time. However, if you’d like to take advantage of feedback from the educators and your mentors, you can do so within the following periods:

June 1 - July 15

December 1 - January 15

This course is ideal for anyone interested in mathematical problems, with a basic background in precalculus. It would be useful for anyone wanting to study or work in mathematics, or anyone who wants to develope their critical thinking and problem-solving skills.

This course is ideal for anyone interested in mathematical problems, with a basic background in precalculus. It would be useful for anyone wanting to study or work in mathematics, or anyone who wants to develope their critical thinking and problem-solving skills.

• Apply the principles of combinatorics to solve the basic combinatorial problems
• Model some real life counting problems into that of counting precise mathematical structures
• Identify the mathematical structure which lies besides a combinatorial problem: sequences, collections, sharings, compositions, partitions, derangements.
• Identify the principle to face a combinatorial problem: bijiection, multiplication, division
• Calculate the probability of an event when the sample space is composed by equiprobable elementary events
• Calculate the number of possible outcomes of an aleatory experiment
• Calculate the number of sequences of prescribed length, with or without repetitions, from a given alphabet
• Calculate the number of sets of given cardinality
• Calculate the number of partitions of a given set in a prescribed number of subsets
• Calculate the number of permutations of a sequence without repetitions
• Calculate the number of distributions of distinguishable/indistinguishable objects in a given number of numbered boxes (possibly empty)
• Calculate the number of distributions of distinguishable/indistinguishable objects in a given number of numbered non-empty boxes