# The Prerequisites in Mathematics for a Ph.D. in Economics

#### 26 SEP 2017

#### COLLEGE

One of the most important prerequisites for a Ph.D. in economics is a solid foundation in mathematics. This is essential because it allows the student to be adequately prepared for graduate economics courses. Most graduate programs require a minimum of two semesters of calculus, one or two post-calculus courses, such as linear or matrix algebra, and upper-level mathematics courses, like real analysis.

## 1 Calculus

Calculus is one of the most basic prerequisites in mathematics for a Ph.D. in economics. Undergraduate programs typically offer two to four semesters of calculus. A good understanding of college-level calculus is essential for higher-level mathematics work as well as graduate-level economics courses. The University of Chicago, for example, requires at least two semesters of college calculus and the University of California at Los Angeles requires two years of calculus.

## 2 Linear or Matrix Algebra

In addition to calculus, Ph.D. programs in economics also require upper-level undergraduate courses in linear or matrix algebra. This algebra is not the same algebra which is a prerequisite for calculus, but an upper-division mathematics course. The University of Chicago requires a semester or quarter of matrix algebra, while Indiana University requires a semester of linear algebra.

## 3 Statistics

At least one mathematical course in statistics in required for Ph.D. programs in economics. For example, UCLA requires a year of "probability and statistics," while the University of Chicago requires one course in “mathematical statistics.” Unlike statistics courses for social science majors, which do not use calculus, courses such as mathematical statistics and probability and statistics do use calculus and are therefore appropriately mathematically rigorous.

## 4 Advanced Prerequisites

Economics graduate departments encourage prospective applicants to take as many courses in mathematics as possible. A commonly mentioned advanced prerequisite is the upper-division math course called real analysis. Real analysis teaches the fundamentals of mathematical analysis and college-level calculus and linear or matrix algebra are typically its prerequisites. In addition to real analysis, UCLA and Indiana University also recommend advanced probability theory, while Cornell University also encourages prospective applicants to take courses in differential equations, stochastic differential equations and optimization.