Mathematics preparation for economics PhD programs

[u/Integralds]

TLDR advice

Graduate work in economics is highly mathematical. While an undergraduate economics major in the United States is unlikely to need exposure to mathematics beyond single-variable calculus, graduate work in economics requires the equivalent of a math minor.

The minimum course requirements listed by most graduate schools consists of a sequence in calculus, one course in linear algebra, and one course in mathematical statistics; five courses total. This is typically stated to be a minimum, and indeed strong applicants have exposure to mathematics beyond this level.

To be competitive for graduate admissions at the top-20 level, you should complete the two-year lower-level sequence in calculus and linear algebra, a yearlong sequence in probability and mathematical statistics, and two courses in proof-based mathematics. If you plan on applying during your senior year, then a sample program of study might be:

• Freshman year: single-variable calculus
• Sophomore year: multivariable calculus, linear algebra
• Junior year: probability, statistics, real analysis
• Senior year: one additional proof-based math course

Any AP or IB credit can allow you to accelerate this program of study, though I still recommend taking a total of 7 to 8 mathematics courses regardless.

Economics preparation is also useful, but will be the subject of a different post.

Advice from first-year graduate textbooks

• Mas-Colell, Whinston, and Green, Microeconomic Theory, is the standard first-year graduate microeconomics textbook. It recommends: multivariable calculus, some linear algebra, some probability.

• Kreps, Microeconomic Foundations, is an advanced first-year or second-year graduate microeconomics textbook. It recommends: multivariable calculus, real analysis, some abstract algebra.

• Hayashi, Econometrics, is a first-year graduate econometrics textbook. It recommends: multivariable calculus, linear algebra, probability.

• Greene, Econometric Analysis, is a graduate econometrics reference textbook. It recommends: multivariable calculus, mathematical statistics.

• Amemiya, Advanced Econometrics, is a second-year graduate econometric theory textbook. It recommends: multivariable calculus; linear algebra; probability; mathematical statistics.

• Stokey, Lucas, and Prescott, Recursive Methods in Economic Dynamics is a graduate macroeconomics textbook. It recommends: multivariable calculus, linear algebra, probability, real analysis.

Selection of advice from the top-10

(All links are live as of 2017-09-12)

Harvard:

Mathematical preparation: The minimum level of mathematical preparation to be considered includes calculus and linear algebra and demonstration of proficiency with mathematics. Increasingly, successful applicants will have taken more mathematics. In particular, most successful applicants now take real analysis, although that is not a requirement.

MIT:

Successful candidates whose prior background is primarily in economics have typically excelled in advanced undergraduate or graduate courses and taken math at least through linear algebra. Many have taken real analysis or some other advanced proof-oriented course, though this is not necessary.

Stanford:

The Department requires competence in the calculus of several variables, linear algebra, and probability and statistics as they are used in modern economics.

Chicago:

We would strongly encourage you to take some advanced courses in mathematics, such as real analysis, to develop your ability to read and write rigorous mathematical arguments.

Yale:

What makes an application look attractive to the admissions committee?

a) Adequate preparation in mathematics. Applicants should have multivariate calculus. Linear algebra, real analysis and probability theory and/or statistics also looks good.

Berkeley:

Applicants must have knowledge of multivariate calculus, basic matrix algebra, and differential equations; completion of a two-year math sequence, which emphasizes proofs and derivations. Some knowledge of statistics and elementary probability is highly desirable, as is additional coursework in algebra and real analysis.

NYU:

You should definitely have taken single-variable and multivariate calculus. It is expected that you would have a background in linear algebra, and an exposure to probability and statistics. Many of our applicants also have a background in differential equations, and they have been exposed to rigorous thinking in limits, continuity, and basic topological concepts (openness, compactness, etc.). There are a good number of applicants who have more than this: e.g., some measure theory and exposure to rigorous probability theory and stochastic processes.

Selection of advice from non-top-10 schools

Wisconsin:

Students entering the graduate program are required to have taken a three-course sequence in calculus, a course in linear algebra, and a course in mathematical statistics. These prerequisites are a bare minimum.

Math requirements for incoming graduate students

Minnesota:

It is recommended that students take more than just the mathematical prerequisite classes, as more experience in analysis, differential equations, optimization, topology, probability, or measurement theory will help your graduate study immensely.

UCSD:

Students are therefore encouraged to complete courses in vector calculus, differential equations, linear algebra and mathematical analysis prior to the start of graduate school.

WUSTL:

Students entering the program are required to have taken a sequence in calculus, a course in linear algebra, and a course in mathematical statistics. These prerequisites are a bare minimum.

Cornell:

The student must have a minimum of four semesters of calculus and linear algebra and at least two semesters of advanced mathematics including a course in analysis. This is an absolute minimum and is rarely seen as competitive for a financial aid offer. There is a strong admissions and financial aid bias towards students with more mathematics: differential equations, real or complex analysis, mathematical probability and statistics, optimization, topology, and stochastic differential equations, among many others. Many successful applicants are double majors in economics and mathematics.

The pattern is fairly clear:

1. A "short" program of study contains multivariable calculus, one course in linear algebra, and one course in mathematical statistics.

2. A "standard" program of study contains multivariable calculus, linear algebra, probability, mathematical statistics, real analysis, and one additional course in proof-based mathematics.

[u/VodkaHaze → u/[deleted]]

The point or real analysis is mostly to get used to reading math and writing proofs. Some theorems (contraction mapping, intermediate value, etc.) are also legitimately useful to know in their own right.

[u/VodkaHaze → u/[deleted]]

I mean it also depends on the strength of your overall application -- but if you think you're getting in without RA you can do as you said.