Math 1007: Mathematics and Politics
Section 14
Fall 2025

Contact Info
Spring 2025

Office: Phillips Hall 720E
Email: jaydaigle@gwu.edu

Office Hours:

Course Information

Lecture:

  • MW 12:45 PM–2:000 PM
  • Duques 151

Official textbook:

  • The Mathematics of Politics, Second Edition
  • Robinson and Ullman
  • ISBN: 9781498798907

Course Information

Lecture:

  • MW 12:45 PM–2:000 PM
  • Duques 151

Official textbook:

  • The Mathematics of Politics, Second Edition
  • Robinson and Ullman
  • ISBN: 9781498798907

Daily Assignments

Week 1: August 25-29
August 25: Mathematical Reasoning
August 27: Voting Systems
Week 2: September 1 – 5
September 1: No Classes for Labor Day
September 3: Two-Candidate Elections
Week 3: September 8 – 12
September 8: Criteria for Voting Systems
September 10: Multi-Candidate Criteria
Week 4: September 15 – 19
September 15: Evaluating Voting Systems I
September 17: Evaluating Voting Systems II
Week 5: September 22 – 26
September 22: Evaluating Voting Systems III
September 24: Arrow’s Impossibility Theorem
Week 6: September 29 – October 3
September 29: Test 1 on Voting
  • Rules
    • Plan to take the whole class
    • Will have 6-7 questions
    • Bring a one-sided handwritten note sheet
    • You can bring a calculator but it probably won’t be useful
  • Topics
    • Two-candidate methods and criteria
    • Multi-candidate methods and criteria
    • Short proofs and counter-examples
    • Drawing conclusions from criteria

  • Read the solutions to Quiz 2

  • Before the midterm on Monday September 29, I recommend you work on the following problems in the textbook. All are odd-numbered and thus have solutions in the back of the book. You do not need to submit them to us.
    • 1.1
    • 1.7
    • 2.3
    • 2.5
    • 3.7
    • 3.9
    • 4.1
    • 4.5
    • 5.3
October 1: The Problem of Apportionment
Week 7: October 6 – 8
October 6: Hamilton’s Method
October 8: Jefferson’s Method
Week 8: October 13 – 17
October 13: Divisor Methods
October 15: More on Divisor Methods
Week 9: October 20 – 24
October 20: Evaluating Apportionment Methods
October 22: Criteria and Impossibility
Week 10: October 27 – 31
October 27: The Balinski and Young Apportionment Method
October 29: Test 2 on Apportionment
  • Read the solutions to Quiz 4
  • Rules
    • Plan to take the whole class
    • Will have 6-7 questions
    • Bring a one-sided handwritten note sheet
    • You can bring a calculator but it probably won’t be useful
  • Topics
    • Hamilton’s method and Lownde’s method
    • Divisor Methods and Critical Divisors
    • Short proofs relating criteria
    • Understanding criteria and which methods satisfy which criteria
    • Interpreting simple algebraic formulas
  • Before the midterm on Wednesday October 29, I recommend you work on the following problems in the textbook. All are odd-numbered and thus have solutions in the back of the book. You do not need to submit them to us.
    • 7.5
    • 7.7
    • 8.3
    • 8.9
    • 8.13
    • 9.1
    • 9.5
    • 11.5
Week 11: November 3 – 7
November 3: Zero-Sum Games
November 5: Strategies, Outcomes, and Saddle Points
Week 12: November 10 – 14
November 10: Probability and Randomness
November 12: Expected Value and Strategies
Week 13: November 17 – 21
November 17: Nash Equilibria
November 19: Solving Zero-Sum Games
Thanksgiving Break: November 24-28

No class! Happy Thanksgiving!

Week 14: December 1 – 5
December 1: Conflict and Cooperation
December 3: Some Important Games
Week 15: December 8-10
December 8: Class Choice: Gerrymandering
December 10: No class
Finals Week
Reading Days
Office Hours Schedule
  • Tuesday December 9: Noon – 2 PM
  • Wednesday December 10: 2 – 4 PM
  • Thursday December 11: 11 AM – 2 PM
  • Sunday December 14: 1 – 4 PM
Final Exam Monday, December 15 12:40 – 2:40 PM
  • Read the solutions to
  • In the usual classroom
  • Exam Structure:
    • Expect about ten questions
    • Bring a two-sided handwritten note sheet
    • You can bring a calculator, and should
    • 1-2 questions on voting
    • 1-2 questions on apportionment
    • Remaining questions on game theory
  • Practice Problems:
    • 13.7
    • 13.11
    • 14.3
    • 14.7
    • 14.9
    • 15.1
    • 15.7
    • 15.17 (Edit: This one is much harder than I thought!)
    • 16.1
    • 16.3
    • 16.7
    • 18.1

Syllabus

The course syllabus is available here.

Course notes

Homework

Tests

Calculators will be allowed on quizzes and tests. I particularly encourage you to bring a calculator for tests during unit 2, on apportionment.

For all in-class assignments, I will allow you to bring a cheat sheet in your own handwriting. For quizzes and midterms I will allow a one-sided cheat sheet, and for the final I will allow a two-sided cheat sheet.

Textbook

The official textbook for Math 1007 is The Mathematics of Politics, Second Edition by E. Arthur Robinson and Daniel H. Ullman. It should be available free online through the library website, and you can buy a hard copy for under $50 if you wish. I will be expecting you to read sections of the textbook and assigning problems out of it.