The Binomial Theorem

CSE Teaching Faculty Candidate Seminar

Zoom link for remote participants

Abstract: The binomial theorem is a powerful theorem that allows for the counting of sequences of binomial coefficients that can appear near intractable otherwise. We begin by discussing Pascal’s triangle (also known as Pingala’s triangle, Yang Hui’s triangle, and numerous other names) which has strong ties to the binomial theorem. We show how Pascal’s triangle can be used to solve otherwise difficult problems and then, through investigation of Pascal’s triangle, discover the binomial theorem. While the binomial theorem is seldom applied directly to problems, it is the tool used in many proofs of other combinatorial identities. We prove several of these identities, show their connection to important concepts, and conclude with a discussion of difficult problems that we are able to solve only with a combination of the techniques from this talk.

Bio: I am a 6th year Ph.D. student with a long-time interest in theoretical CS research and in teaching pedagogy with respect to these topics. I graduated from the University of Rochester with a B.A. in Logic and Computation in 2018. My research interests are in computational complexity, combinatorics, cryptography, and algorithms. My recent research includes extremal combinatorial and structural results on finite tilings as well as cryptographic research into reconstructing cloud databases from highly restricted forms of leakage.”