• Lectures: 4:10-5:25pm on Mondays & Wednesdays, Room 825 in the Seeley W. Mudd Building.
• Exercise sessions: 10:10-12:00am on Friday, Hamilton 302.
• Instructor: Thibault Vatter, tv2233@columbia.edu
• TA: Thomas Leavitt, tl2624@columbia.edu

This course introduces students to (i) basic mathematical tools frequently used in political science and (ii) approaches to mathematical proofs. The course, or knowledge of the mathematics taught, is a prerequisite for the advanced statistics (POLS 4912) and formal modeling courses (POLS 4210).

The course has two equally important components:

• Lectures with the instructor focus on introducing the new concepts with references to practical or theoretical issues and deriving the main theoretical results.
• Exercise sessions with the TA focus on clarifying and illustrating the theoretical concepts, improving your mathematical problem-solving skills, help you with the problem sets, and offer preparation for the midterm and final exams.

Grading

• Homework assignments (40%).
• Midterm exam (30%).
• Final exam (30%).

I recommend you work on your own and only consult your friends or us if you get stuck. In any case, you must write your own solutions. I will hand out eight problem sets.

Your final grade may be anywhere between an F and an A+, depending exclusively on how well you perform in the problem sets and exams. The final grade for this class is based on academic performance only. I will absolutely not consider your degree requirements or the implications of a low grade for your academic or professional future. If you are not willing to accept this grading policy, then you should not enroll in this class. Grade appeals are only considered based on clear, documented errors in grading. All other grade appeals are automatically rejected.

If you have a disability or a medical condition that requires special accommodations for an exam, you should provide documentation in advance of the exam.

Prerequisites

No prior knowledge of calculus or linear algebra is necessary. However, students are assumed to have a firm command of basic high school algebra. If your foundational mathematical skills are weak, this class will be very difficult and frustrating for you.

Textbooks

No mandatory textbook, all the material will be provided.

Schedule

This is a TENTATIVE schedule for the course. The exact dates for each topic will depend on progress and integration may start before the midterm.

• Before Midterm
  • Linear Algebra
    • System of linear equations
    • Matrix algebra
    • Vector spaces
    • Eigenvalues and eigenvectors
    • Orthogonality and least squares
    • Symmetric matrices and quadratic forms
  • Differential Calculus
    • Functions and limits
    • Continuity
    • Derivatives
    • Analysis of functions
    • Multivariate calculus
• After Midterm
  • Integration
    • Concept of integral
    • Integration techniques
  • Optimization
    • Unconstrained optimization
    • Linear programming
    • Convex optimization
  • Probability and statistics.
    • Combinatorics and probabilities
    • Random variables and vectors
    • Stochastic convergence
    • Statistical inference
    • Hypothesis testing

Office Hours

By appointment only.