About Mathematics for Computer Science - MIT - Lec 01

Discrete Random Variables in Probability Theory Independence of Events, the Product Rule, and the Birthday Problem in Probability Congestion-Free Routing in Butterfly and Benes Communication Networks The Stable Marriage Problem and the Gale-Shapley Matching Algorithm in Graph Theory Gambler's Ruin and Random Walks in Probability Theory Euler Tours, Tournament Graphs, and King Chickens in Graph Theory Expected Value and Linearity of Expectation for Random Variables in Probability Theory Greatest Common Divisor Algorithm for Integers Valuing Annuities with Geometric Series in Discrete Mathematics Proof by Mathematical Induction in Discrete Mathematics The RSA Encryption Algorithm in Number Theory The Monty Hall Problem and the Probability of Switching Doors Linear difference equations Recursion Relation Development in Algorithms Bounding Event Probabilities with Indicator Random Variables and Murphy's Law in Probability Theory The Inclusion-Exclusion Principle in Combinatorics Spanning Trees and Minimum Spanning Tree Construction in Graph Theory Markov, Chebyshev, and Chernoff Bounds for Random Variable Deviation Combinatorial Counting Techniques: Bijections and the Pigeonhole Principle Partial Orders and Topological Sorting in Discrete Mathematics Graph Coloring Problems in Combinatorial Optimization The Base Rate Fallacy and False Positive Paradox in Conditional Probability Invariants and Strong Induction in Mathematical Proof Asymptotic Notation in Algorithm Analysis