Professor: Shabnam Akhtari
- CRN 26171: Tuesday & Thursday, 1615-1745 @ REMOTE
Counting lies at the heart of mathematics and combinatorics is an area primarily concerned with counting, both as a means and an end in obtaining results. Combinatorics is connected to different branches of mathematics, and has many applications to statistical physics, evolutionary biology, computer science, and network and coding theory. We will not discuss the applications. We will seek a deep and fundamental understanding of the basic facts and concepts in combinatorics, including permutation, binomial coefficients, the inclusion-exclusion principle, combinatorial probability, partitions of numbers, and the pigeonhole principle. We will examine certain aspects of the question "how many?''. A simple such question would be in any calendar year how many Friday the thirteenth can there be? What is the smallest possible number?. We will discuss more advanced questions such as in how many ways can one express a given whole number in terms of the summation of smaller whole numbers?. Some of the skills we will focus on are trying examples, looking for patterns, making conjectures, testing conjectures, and modifying conjectures.