Gen Func
Generating functions and their use in algebraic contexts (computing sums, featuring the so-called snake oil method). Of course, some combinatorial problems included as well.
Unit Overview
Gen Func is a unit about Generating Functions. The lecture is essentially the same as section 5 of Evan's Summations Handout. It covers linear recurrences, as well as common generating functions such as the generalized binomial theorem. It also features the Snake Oil method, and a couple of walkthroughs showing how to apply it.
There are 6 "mindless application" problems in the problem set, and the rest of them are actual contest problems. There are also a few computational problems to show how it might come up on AIME style/difficulty contests. It is a relatively short unit, with 18 problems in total and a requirement of 30 clubs (42 if you have time) out of 69. As for difficulty, it's somewhat on the higher end of things, but definitely not too difficult for a B unit. Probably somewhere around B Global level.
Notable Problems
- SNAKE2 - representative of the "mindless application" problems
- Putnam 1990 A6 - very nice problem, representative of the contest problems
- HMMT 2017 C8 - representative of the computational problems