Part 1: Introduction: Research Methods and Challenges
1 Introduction
Part 2: Mathematical Tools

This section of the course reviews basic mathematical tools. You will also perform simple regression analyses using STATA® and we will use the functions that you estimate in the mathematics review.
2 Functions and Limits
3 Derivatives
4 Maximization
5 Sums and Integrals
Part 3: Probability and Models of Data

This section of the course develops the mathematical concepts used in statistics. Three ideas are essential: Random Variable, Density Functions, and Expectations.
6 Random Variables, Populations and Samples
7 Probability: Two Laws of Probability, Bayes Theorem
8 Probability Functions: Binomial, Bernoulli, Poisson Uniform, Normal
9 Expected Value: Mean, Variance, Covariance
10 Sums of Random Variables and Limit Theorems, Law of Large Numbers, Central Limit Theorem
Part 4: Statistical Methods

In this section of the course, we develop the three ideas of statistics using probability theory. These ideas are (1) data can be summarized with a probability function, (2) we can optimize that function to estimate unknown parameters of the population, and (3) our estimates are uncertain measures of the population parameters, but we can summarize that uncertainty succinctly.
11 Data Model: Summary and Assumptions
12 Estimation: MLE and MOM
13 Inference: Confidence Interval and MSE
Part 5: Statistical Models: Conditional Distributions and Causality

In this section, we apply the mathematical and statistical ideas develop to specific problems. The main idea in this section is that social scientific reasoning involves conditional statements of the form if X then Y. We focus on the tools for studying such relationships.
14 Differences of Means
15 Analysis of Frequencies and Variance
16 Regression
17 Regression (cont.)