Explore the wonderful world of combinatorics with this course exploring simple and efficient ways to count. 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.
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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.
What topics will you cover?
- Convert counting problems into precise mathematical models
- Count the basic combinatorial objects like sequences and collections
- Applications on counting anagrams, derangements of a sequence (hats problem)
- Count card shuffles and understand astonishing magic tricks
- Basic probabilities (birthday problem)
- Algebraic tools that allow to solve subtle combinatorial problems
What will you achieve?
By the end of the course, you‘ll be able to...
- Apply the principles of combinatorics to solve the basic combinatorial problems
- Model some real life counting problems into that of counting precsie 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 collections 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 numberded boxes (possibly empty)
- Calculate the number of distributions of distinguishable/indistinguishable objects in a given number of numberded non-empty boxes
Who is the course for?
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.
