Func Eqn
Functional equations, I guess.
Unit Summary
This unit is all about exploring a staple of olympiad algebra, being functional equations. The unit teaches basic substitution strategies, injectivity, surjectivity, pointwise trap, Cauchy's functional equation, amongst other strategies you will encounter while attempting the problems. The problems are quite varied, with several real, integer, positive real, polynomial FEs.
The unit is pretty easy for a D unit, although there are certainly some challenging problems. After taking this unit, other good FE units include Monster FE and Wrapped FE.
The unit has 71 clubs across 20 questions in total, not counting the multiplier.
Notable Problems
2013 IMO 5: Tricky one, from positive rationals to reals. Involves quite a bit of heavy bounding.
2017 IMO 2: Legendary IMO problem, given as walkthrough.
2016 USAMO 4: Walkthrough, canonical example of a certain technique ;)
2015 JMO 4: Basic, fun, example;
2010 SL A6: Hardest in the set. Over positive integers to positive integers, heavy work with cycles and friends.