The art of proving binomial identities

This text has two goals: it provides a unified treatment of the binomial coefficients, and brings together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients).

The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton's binomial series), differentiation (Leibniz's generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.