Combinatorics: Strategies and Methods for Counting

Apply the principles of combinatorics to solve the basic combinatorial problems

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

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 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 probability of an event when the sample space is composed by equiprobable elementary events

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

Model some real life counting problems into that of counting precise mathematical structures

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