The Mathematics of Choice

This chapter presents the top stratum, or surface layer of combinatorics. Special cases of numbers are addressed from a combinatorial perspective followed by a discussion of probability theory and an excursion into the theory of binary codes. A later discussion reveals that even the most basic combinatorial ideas have real-life applications. Next, we present a study of relations among binomial coefficients, followed by a discussion of choice, with or without replacement, where order does or doesn't matter. The chapter concludes with elementary symmetric functions and their association with power sums followed by an introduction to algorithms.