Lecture Notes

Many of these lecture notes were based on a draft version of an upcoming textbook developed from 15-251.
Please do not distribute them outside of CMU.

• Solving Problems and Writing Proofs
• Games: Which Player Wins?
• Pancakes With A Problem
• Inductive Reasoning: One Step at a Time
• Finite Automata
• Counting I: Choice Trees and Correspondences
• Counting II
• Counting III
• Ancient Wisdom: Unary and Binary
• The Math of the 1950's Dating
• Probability I: Counting in Terms of Proportions
• Probability II: Random Variables and Great Expectations
• Probability III: Random Walks
• Ancient Wisdom: Raising a Number to a Power
• Ancient Wisdom: Primes, GCD, and Continued Fractions
• The Golden Ratio, Fibonacci, and Other Recurrences
• Number Theory and RSA
• Algebraic Structures: Groups, Rings and Fields.
• Polynomials, Secret Sharing, and Error Correction
• Graphs I
• This is the Big-Oh!
• Grade School Revisited: How to Add and Multiply
• Cantor's Legacy: Infinity And Diagonalization
• Turing's Legacy: The Limits of Computation
• Thales' and Godel's Legacy: What is a Proof?

Icons

: Directly copy/pasted drafts, and still in MediaWiki format

: This has a few TODOs left / needs a bit of editing. Can boost class participation grade!