PS 5052 Mathematical Modeling in Political Science

Fall 2017

This course is an introduction to mathematical techniques used to model phenomena studied in political science, with special attention to the analysis of individual action. Mathematical topics covered include: sets, functions, and graphs; matrix algebra; differential calculus and optimization; probability, mathematical statistics, and decisions under risk; integral calculus; and sequences, series, and limits. All these topics are useful in many settings in political science, including game theory, dynamic modeling, and statistics.

This course website will be updated to reflect any changes in schedule, topics covered, or assignments, as well as to provide relevant links to materials associated with the course.


Course Outline and Approximate Schedule

0. Some Preliminaries

Monday and Wednesday, 8/28-8/30

Sets, real numbers, and intervals (reference: Pemberton & Rao sections 3.1-3.2; 31.2)

Logic and proofs (P&R 31.1)

Sequences, convergence, and limits (P&R 5.1, 5.4; for advanced help, 31.3, 31.4)

  • Exercises on sequences and convergence: prepare your answers using LaTeX and bring them to class next time.

Areas, sums, and integrals (P&R 19.1)


1. Probability and Statistical Inference

Text:   Excerpts from  Wasserman, All of Statistics, chapters 1-10

1.1 Probability

W 8/30; W 9/6

For Wednesday 9/6 read: chapters 1 and 2.1-2.2

Exercises to turn in Monday 9/11: Chapter 1, exercises 5, 12, 13, 15.

Exercises to turn in Monday 9/18:

  • Chapter 1, Exercise 19; Computer Experiments 21, 22
  • Chapter 2:  Exercises 2, 6

Exercises to turn in Monday 9/25 (subject to adjustment):

  • Chapter 2:  Exercises 4, 7, 9, 18


1.2 Expectations and Moments

M 9/25-F 9/29

Read: sections 3.1-3.5

Exercises to turn in Monday 10/2 (subject to adjustment):

  • Chapter 2:  Exercise 17
  • Chapter 3:  Exercises 3, 4, 5, 11, 13


1.3 Convergence of Random Variables

F 9/29 to M 10/2

Read: sections 5.1-5.4


First Exam 10/4 - 10/9

  • Wed. 10/4:  Review session
  • Wed. or Fri.:  distribute exam
  • Exam due at beginning of class, Mon. 10/9



1.4 Statistical Inference and Hypothesis Testing

M 10/9, W 10/11

Read: sections 6.3, 10.1, 10.2, 13.1

  • 6.3 estimation, confidence sets, and hypothesis testing
  • 10.1 the Wald test
  • 10.2 p-values
  • 13.1 example: linear regression


Exercises to be assigned (subject to revision)

  • Chapter 1:  Exercises 5, 12, 13, 15, 19; Computer Experiments 21, 22
  • Chapter 2:  Exercises 2, 4, 6, 7, 9, 17, 18
  • Chapter 3:   Exercises 3, 4, 5, 11, 13
  • Chapter 6: Exercise 2, 3
  • Chapter 10: TBA

1.5 Subjective Probability and Expected Utility

W 10/18

Recommended: Peter C. Fishburn, "The Axioms of Subjective Probability." Statistical Science, Vol. 1, No. 3 (Aug., 1986), pp. 335-345. Click here to obtain via JSTOR.



2. Linear algebra

dates TBA
(note Fall Break 10/16)


3. Sets and relations, with applications to choice theory

dates TBA


4. Sequences and series; limits and continuity

dates TBA


Second Exam out about W 11/1 in M 11/6


5. Differential calculus and applications

dates TBA
(note Thanksgiving Break W 11/22)
About 1 day on each subtopic below:

5.1 Newton's Quotient

5.2 Differentiation and Optimization

5.3 The Exponential and Logarithmic Functions

5.4 Approximation

5.5 Multivariate calculus


6. Integral Calculus

dates TBA


Third Exam following 12/6

  • Fri. 12/8 or M 12/11 optional review session
  • within a day after review session:  distribute exam
  • Exam due F 12/15




This page written by Randall Calvert  2017
Email comments and questions to calvert at
Monday & Wednesday 10:00-11:30
classroom: Seigle 104

Jump directly to CURRENT topics & assignments

Assistant to Instructor
Ryden Butler
WU email address r.butler
Office Hours:  TBA

Optional Help Sessions: Fridays 10:00-11:30 in Seigle 104


The following are available in the campus store. We will use them extensively, and they will be useful to you as reference books once the course is finished.

  • Malcolm Pemberton and Nicholas Rau, Mathematics For Economists: An Introductory Textbook, 4th ed. (Manchester University Press, 2016). Answers to "exercises" and to "problems" in Pemberton and Rau. along with errata for the book, are available online at the textbook website.
  • Larry Wasserman, All of Statistics (Springer, 2004). Wasserman's textbook website offers data and rough R code for some exercises and examples.

Course Requirements

All assignments are to be turned in as LaTeX documents; hand-drawn illustrations OK.

  • Exams 75%.  Three, non-cumulative, closed-book, take-home, un-timed. Dates are indicated in the course outline; I will give at least two weeks warning of any changes in exam dates.
  • Homework 25%.  Problem sets drawn mostly from the textbooks; due every Monday, with few exceptions. Collaboration is encouraged. Grading will be based heavily on (1) completion and (2) effort.
  • Possible short quizzes.  I retain the option of administering a short quiz from time to time. These would be graded more for accuracy than are the homeworks, and the scores will be counted in with the 25% for homework.
  • Attendance.  Provided you're not contagious, I expect your attendance at every class meeting. Please let me know, in advance if possible, if problems arise that will require you to be absent.