Examples of Mathematical Tools
The Cube Law
Edward R. Tufte. "The Relationship between Seats and Votes in Two-party Systems." The American Political Science Review 67, no. 2 (June, 1973): 540-554.
|Part 1: Introduction: Research Methods and Challenges|
|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||Chiang. Chaps. 2 and 6|
|3||Derivatives||Chiang. Chap. 7|
|4||Maximization||Chiang. Chap. 9|
|5||Sums and Integrals||Chiang. Chap. 13|
|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||Snedecor and Cochran. Chap. 1|
|7||Probability: Two Laws of Probability, Bayes Theorem|
|8||Probability Functions: Binomial, Bernoulli, Poisson
|9||Expected Value: Mean, Variance, Covariance|
|10||Sums of Random Variables and Limit Theorems, Law of Large Numbers, Central Limit Theorem||Additional Reading
Kendall and Stuart
|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|