Sets and Combinatorics

URL study guide

https://studiegids.vu.nl/en/courses/2024-2025/X_400621

Course Objective

After completing this course, the student is able to prove identities between sets using Venn diagrams and the algebra of sets or logical reasoning; can compose sets using set operations to produce a desired set, and conversely, determine the elements of such a composed set; can work with the standard sample spaces of Probability Theory to compute the sizes of such sample spaces and of typical events; can decide whether a given function is injective, surjective and/or bijective; can determine images and preimages of sets under a given function; is able to construct proofs by mathematical induction and apply the binomial and multinomial theorem in calculations.

Course Content

Sets, set operations, the algebra of set theory, the laws of De Morgan, product sets and power sets, standard sample spaces of Probability Theory, basic rules of combinatorics, permutations and combinations, binomial and multinomial coefficients, binomial and multinomial theorem, cardinality and (un)countability, functions and graphs, the principle of mathematical induction.

Teaching Methods

In each of the first three weeks: two lectures of 2 hours, and one tutorial of 2 hours. In the fourth week: one lecture of 2 hours and one tutorial of 2 hours before the final exam.

Method of Assessment

A written exam at the end of the course (counting for 100% towards the final grade). There will be one resit exam.

Literature

Lecture Notes for the course and all additional course materials will be provided through Canvas.

Target Audience

1BA