MAT 3650 - INTRODUCTION TO COMBINATORICS

credits: 3.0
Combinatorics is the study of counting and enumeration problems that arise from discrete structures in mathematics such as sets, graphs and sample spaces. Problems within this realm are compelling; it is typically simple to state them, but their solutions can require ingenuity and powerful techniques. This is particularly true when the set of objects being counted cannot be easily listed. Will explore combinatorial problems and methods of their solution. Topics may include fundamental counting techniques, Pascal’s Triangle, the Binomial Theorem, the principle of inclusion-exclusion, recurrence relations, equivalence relations, distribution problems and an introduction to Graph Theory. Objectives: A) Be able to use basic counting techniques such as the Fundamental Counting Principle, the addition principle, permutations and combinations; B) Able to combine basic counting techniques to count more complicated objects; C) Apply a number of important theorems such as the Principle of Inclusion/Exclusion, the Pigeonhole Principle and the Binomial Theorem; D) To use the basic terminology and techniques of within other areas of Combinatorics; E) Able to read and write combinatorial proofs; F) Successfully complete combinatorial tasks, demonstrate coherent logic, and provide clear and complete explanations; G) To able to define mathematical concepts carefully and use these definitions in writing proofs; H) To construct their own original proofs and write these proofs in a logically correct and clear way. Method of Instruction: Lecture and in-class presentations and activities. Method of Evaluation: Weekly homework, tests, and a comprehensive final.

Prerequisite(s): MAT 2100 - DISCRETE MATHEMATICS