These worksheets form the basis for the CS22 recitation section at Brown University, designed to make the material fun, engaging and accessible. Assistance from Sarah Pratt, Neil Chandra, Nathan Malimban, and Professor Caroline J. Klivans.
Section 1: Numbers and Proofs
An introduction to the integers, rationals, and reals in addition to many proof techniques.
Section 2: Relations and the Infinite
Relations, functions, power sets, and a guided proof of different sizes of infinity.
Section 3: Induction and Algorithms
What is Induction and why does it work? How can I use induction to prove the correctness of algorithms?
Section 4: Threes Trick
An introduction to number theory and modular inverses via tricks to determine if a number is divisble by 3.
Section 5: Logic and Complexity
What is logic? What is P, NP, NP-Hard, and NP-Complete?
Section 6: Computability
Using the proof from section 2, we can prove that there are problems that a computer cannot solve.
Section 7: Intro To Counting
A short introduction to Big-O and Pigeonhole.