**Math 227:Combinatorics, Spring 2022**

**Instructor: **Noah Aydin**
Office/Phone**: RBH 319, 5674

Zoom Link for student hours.

Room & Time

Textbook:

**Course Description**: This course** **introduces students to combinatorics, one of the active and important branches of modern mathematics. Combinatorics is concerned with the existence, enumeration, analysis, and optimization of discrete structures. It is an exciting, active, and applicable area of mathematics which blends the use of general principles with ad hoc arguments. Unlike many other areas of mathematics -- e.g., analysis, algebra, topology--the core of combinatorics is neither its subject matter nor a set of “fundamental" theorems. More than anything else, combinatorics is a collection of techniques, attitudes, and general principles for solving problems about discrete structures. This course will be an introduction to the techniques and methods of combinatorics. In the process of learning how to solve combinatorial problems, you will develop an appreciation for the fun, power, and the vast scope of this area of mathematics. Combinatorial techniques are useful in a broad range of fields including computer science, many other areas of mathematics, linguistics, engineering, natural and social sciences, biological sciences, and operations research. The course will focus on problem solving. Active learning methods will be used throughout the semester. The main topics for the course are: (1) Induction and Recurrence Relations, (2) The Pigeonhole Principle and Ramsey Theory, (3) Permutations and Combinations, (4) Binomial coefficients, (5) Stirling Numbers, (6) Integer Partitions, (7) The Inclusion-Exclusion Principle, (8) Generating Functions, and (9) Graph Theory.

Course Calendar and Hmw/Reading Assignments