The aim of this course is to familiarize students with fundamental concepts in combinatorics, especially those used in enumeration. Topics covered include permutation groups, linear codes, Stirling and Bell numbers. Generating functions are introduced and their applications are discussed. Applications of group theory to enumeration: Burnside's Lemma and Polya's theory of counting are covered. Students are introduced to error correcting codes and linear codes over finite fields.
Students develop familiarity with fundamental combinatorial objects that appear in other fields of mathematics and computer science.
Students learn how to use combinatorial structures to represent mathematical problems and solve them.
Given a hypothetical combinatorial object, students learn how to compute the number of such objects.
Students learn to apply algebraic methods to solve combinatorial problems.