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 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
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