Required Texts

Buy at Amazon Snedecor, George W., and William G. Cochran. Statistical Methods. Ames, IA: Iowa State University Press, 1989. ISBN: 9780813815619.

Buy at Amazon Bulmer, M. G. Principles of Statistics. New York, NY: Dover Publications, 1979. ISBN: 9780486637600.

Buy at Amazon Chiang, Alpha C. Fundamental Methods of Mathematical Economics. New York, NY: McGraw-Hill, 1984. ISBN: 9780070108134.

Recommended Texts

Buy at Amazon Goldberg, Samuel. Probability: An Introduction. New York, NY: Dover Publications, 1987. ISBN: 9780486652528. (Discrete Probability)

Buy at Amazon Rice, John A. Mathematical Statistics and Data Analysis. Belmont, CA: Duxbury Press, 1994. ISBN: 9780534209346.
(Mathematical Statistics Course)

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
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 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 
Uniform, Normal
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  
16 Regression  
17 Regression (cont.)