# Undergraduate Programs

## Mathematical Modeling in Political Science and Economics

#### Committee

- Jonathan Pakianathan, PhD (Princeton), Professor of Mathematics, Chair of the Committee
- Mark Fey, PhD (Caltech), Professor of Political Science
- William Thomson, PhD (Stanford), Professor of Economics

#### Certificate Requirements

Long a domain of the natural and applied sciences, the use of mathematical techniques has gained growing acceptance in fields like Political Science, Economics, Business and Psychology. Departments in the University of Rochester have made numerous contributions to the increasingly mathematical aspects of their fields and are uniquely positioned to teach students who wish to focus on the uses of mathematics in the social sciences. This program draws on classes in Economics, Mathematics, and Political Science. Students must achieve a minimum overall grade point average of 2.0 in these courses. **Ordinarily, interested students should apply by spring semester of their junior year.**

#### 1. Calculus/Linear Algebra (3-4 courses):

- MTH 161-162 (Or MTH 141-143) (Or MTH 171-172). These classes comprise a standard two (three)-semester calculus sequence and teach the standards of tools of calculus, which are indispensable for most applied settings.

- MTH 165 (Linear Algebra with Differential Equations). An elementary understanding of linear algebra and differential equations is essential. Linear algebra enters directly into the study of statistics and, at a more advanced level, game theory.

#### 2. Statistics (1 course):

- Statistics provide the main tool for testing competing hypotheses through the analysis of empirical evidence. ECO 230 (Economic Statistics), PSC 200 (Applied Data Analysis), MTH 203 (Mathematical Statistics), or STT 213 (Elements of Probability and Math Statistics) would satisfy this field.

#### 3. Modeling Rational Behavior (1 course):

- This field provides students with a degree of flexibility to tailor the certificate to their specific interests. Students will have three options, drawing from each of the three departments, from which they will choose one course: MTH 217 (Mathematical Modeling in Political Science) covers some game theory, social choice theory, and power indices, PSC/ECO 288 (Intro to Game Theory) covers the general types of games, their representations, and equilibrium (solution) concepts, and ECO 207 (Microeconomics) exposes students to the fundamentals of rational decision-making in exchange environments (markets).

#### 4. Social Science Applications (3 courses):

- For the certificate to be truly interdisciplinary, students need a strong foundation in both the tools for analysis and their application. For this reason, students will additionally choose three approved classes in Political Science and Economics, with at least one from each department.

#### 5. Additional Math (or Social Science) course (1 course):

- Students who select MTH 203 (for statistics) and MTH 217 (for modeling) are required to take an additional social science application course rather than an additional math course. All other students will take an additional math course selected from the approved list.

*Students must fulfill all five of these requirements. No course used to satisfy these requirements may be taken Satisfactory/Fail.*

#### Classes satisfying the certificate program requirements 4 and 5:

- MTH 164 Multivariable Calculus
- MTH 201 Introduction to Probability
- MTH 202 Introduction to Stochastic Processes
- MTH 203 Mathematical Statistics
- MTH 208 Methods of Operations Research
- MTH 210 Financial Mathematics
- MTH 217 Mathematical Modeling in Political Science
- MTH 235 Linear Algebra
- MTH 240 Introduction to Topology
- MTH 265 Functions of a Real Variable
- ECO 207 Microeconomics
- ECO 209 Macroeconomics
- ECO 220 Fair Allocation
- ECO 231 Econometrics
- ECO 256 Game Theory and Social Choice/Topics in Game Theory
- ECO 273 Economic Growth and Development
- ECO 274 Mathematical Economics
- ECO 282 Introduction to Positive Political Theory
- ECO 288 Introduction to Game Theory
- PSC 203 Survey Research Methods
- PSC 272 Theories of International Relations
- PSC 280 Political Accountability
- PSC 281 Formal Models in Political Science
- PSC 288 Game Theory
- PSC 404 Probability and Inference
- PSC 405 Linear Models
- PSC 407 Mathematical Modeling
- PSC 408 Positive Political Theory