Upper Division College

Modern Algebra

1 Definition of a Group
2 Fundamentals of Groups

Real Analysis

1 Supremum and Infimum

Graph Theory

1 Definition of Graphs
2 Definition of Paths
3 Definition of Cycles

Probability

1 Introduction to Probability
2 Fundamental Results
3 Conditional Probability
4 Bayes' Rule
5 Independent Events
6 Conditional Probability Function \(P(\cdot|F)\)
7 Random Variables
8 Independent Random Variables
9 Functions of Independent Random Variables
10 Discrete Random Variables and pmf
11 Expectated Value of Discrete Random Variables
12 Standard Deviation and Variance of Discrete Random Variables
13 Properties of Variance
14 Bernoulli, Binomial, and Geometric Distributions
15 Poisson Distribution
16 Continuous Random Variables
17 Cumulative Distributions Functions (cdf)
18 Joint Distributions
19 Conditioning on Continuous Random Variables
20 Independent Continuous Random Variables
21 Order Statistics
22 Expected Value of Continuous Random Variables
23 Continuous Uniform and Exponential Distributions
24 Normal Distribution
25 Median and Percentiles
26 Covariance and Correlation
27 Variance of Sums of Random Variables
28 Conditional Expectation
29 Sums of Independent Random Variables
30 Moments and Moment Generating Functions
31 Strong Law of Large Numbers
32 Central Limit Theorem

Stochastic Processes

1 Discrete Time Stochastic Process

Maching Learning

1 Supervised vs Unsupervised Learning
2 Regression vs Classification

3 Feature Enhancements

4 Dimensionality Reduction

5 Over Fitting and Under Fitting

6 Gradient Descent

7 Gradient Boosting

8 Kernel Density Classification
9 K Means
10 K Nearest Neighbors
11 Naive Bayes
12 Decision Trees
13 Linear Regression
14 Support Vector Machine (Linear)

15 Neural Nets

Mathematical Biology

1 SIR Model