Probability, Statistics, Decision Making

I have taught this course twice at NYU, but the first time I created (part) of the content was when I taught a similar course for undergraduate students at Princeton University. The idea behind this course is to introduce important ideas in mathematics to students with no formal mathematics background. The topics listed below are an accumulation of content created over two years. Each module is self sufficient and can be studied on its own, moving sequentially through the lectures. The slides are meant to be watched as a slide show, instead of a continuous scroll.

Module 1: Probability

Lecture 1: Introduction to Probability

Lecture 2: Conditional Probability

Lecture 3: Conditional Probability Examples

Modele 2: Counting

Lecture 4: Counting Techniques I

Lecture 5: Counting Techniques II

Module 3: Statistics

Lecture 6: Introduction to Statistics

Lecture 7: Measures of Center and Variability

Lecture 8: The Normal Distribution

Lecture 9: The Binomial Distribution

Lecture 10: Sampling, Hypothesis Testing, and Simpson's Paradox

Lecture 11: Approximately Normal Distributions

Module 4: Game Theory

Lecture 12: Introduction to Game Theory, Games of Pure Competition, Games of Cooperation

Lecture 13: Nash equilibrium, Prisoner's Dilemma, Zero-Sum Games

Lecture 14: Mixed Strategy Nash Equilibrium

Lecture 15: Larger Games

Lecture 16: Repeated Games, Evidence of Cooperation

Module 5: Graph Theory

Lecture 17: Basics of Graph Theory, Euler Circuits

Lecture 18: Hamiltonian Circuits, Traveling Salesman Problem

Lecture 19: Algorithms to Find Hamiltonian Circuits

Lecture 20: Scheduling I

Lecture 21: Scheduling II

Module 6: Cryptography

Lecture 22: Substitution Codes, Caesar Ciphers

Lecture 23: Modular Arithmetic, Decimation Cipher, Vigenère Cipher

Lecture 24: Public Key Cryptography

Module 7: Voting

Lecture 25: Voting and Social Choice I

Lecture 26: Voting and Social Choice II

Lecture 27: Voting and Social Choice III

Lecture 28: Voting and Social Choice IV