# Mathematics Preparation for a Ph.D.

in Economics

Preparing to enter a Ph.D. program in economics requires a lot of time. The courses you need to take are likely to surprise you. If you are contemplating a Ph.D. in economics, chances are that you have taken some economics courses already and that you have enjoyed them and performed well in them. It is natural to assume that this is sufficient to obtain admission to a Ph.D. program; that is, if you major in economics with a high GPA, one might naturally assume this will earn you admission into a solid Ph.D. program. Nothing could be further from the truth! The fact is that competition for a limited number of spots in Ph.D. programs in economics is fiercer than ever, and nowadays no one is accepted without extensive coursework and a high level of performance in mathematics. The level of mathematical preparation that is required for entrance into a Ph.D. program is considerably higher than it was for some of your economics professors at CSUEB when they entered graduate school. The following tips shed light on what Ph.D. admissions committees expect to see and what you can do to be a more competitive applicant.

**1. Start early!** An economics Ph.D. is not like a law degree. In law, you can decide in your senior year that you wish to attend law school, and as long as you have taken a broad range of courses and have obtained a high GPA, you have the necessary preparation for law school. In contrast, preparing for an economics Ph.D. takes years of heavy coursework in mathematics. By the time most students have taken enough economics courses to conclude that they like the discipline enough to earn a Ph.D. in it, they are usually far behind schedule for obtaining the necessary mathematics skills. If you think an economics Ph.D. might be in your future, you must start taking mathematics courses early!

**2. Talk to the faculty.** If you think you might want a Ph.D. in economics (or in a related area, such as public policy or business economics) you should solicit advice from members of the economics faculty concerning what courses to take. While there are exceptions, in most cases the youngest members of the faculty know best what coursework is most valuable. The mathematics preparation required for economics Ph.D. programs has increased over time, and the youngest members of the faculty usually are in a position to offer the best advice, since their experience is most recent.

**3. Obtain admissions standards early.** Even if you do not plan to apply to Ph.D. programs for several years, contact several graduate programs now, or visit their websites, to find out what mathematics preparation is required for admission. This will help you prepare for the programs of greatest interest to you. The necessary coursework is very similar across all programs. However, beware! Typically the mathematics requirements stated on the websites of graduate programs, or in their application materials, are minimum requirements. This can be quite misleading. These requirements represent that absolute lightest mathematics preparation that could result in admission, though the reality is that most admitted students will have significantly more preparation, and those who have only the minimum are likely to struggle.

**4. How much math do I need? **The more the better! Each additional mathematics course you take will strengthen your preparation. However, some courses are more important than others, as will be discussed below. At the end of this document is a list of selected courses offered at CSUEB, at the undergraduate and graduate levels, that are particularly useful as preparation for doctoral work in economics. You are probably surprised by how long the list is and thinking if you spent all your time taking courses from that list, there would be no time to take any economics. You’re right, and oddly enough, that strategy would actually give you a greater chance of getting into a good economics Ph.D. program. Consider two students. Student A has an undergraduate degree in economics and has taken a few mathematics courses from the undergraduate list below. Student B has majored instead in mathematics, taking many courses from the undergraduate list below, a few from the graduate list, and few if any courses in economics. Generally, Student B has a greater chance of being accepted into a good Ph.D. program in economics. Many students enter economics Ph.D. programs with backgrounds in mathematics, physics, statistics, operations research, computer science, and electrical engineering, and may have undergraduate or M.A. degrees in these fields. You might consider doing some graduate work in mathematics, or perhaps even obtaining an M.A., before applying to Ph.D. programs in economics, if you wish to maximize your chances of admission.

**5. What about the GRE?** A high score on the quantitative section of the GRE is an absolute must. Most programs focus on the mathematics GRE score, the list of mathematics courses taken (and the grades obtained) above all else. Prepare carefully for the GRE so that you can obtain the highest score on the mathematics section of which you are capable.

**6. Which mathematics courses are most important?** The list below contains the undergraduate and graduate courses of greatest relevance for economics. Start by taking Calculus I, II, and III, and linear algebra. Then take “real analysis” which is the most important topic for preparing for economics graduate school, in part because of the training it offers in writing and understanding proofs. You should probably take several courses in real analysis. The relevant material is sometimes called simply “analysis” or “theory of functions of a real variable” or similar names. When in doubt, show the course descriptions to a member of the economics faculty, and ask for advice. Many Ph.D. programs will not even consider your application unless you have taken some real analysis. Your grades in such courses are also important. Of all the courses listed below, the one course that would be most impressive to a Ph.D. admissions committee would probably be MATH 6350, the MA-level course in real analysis. That is not to say that you absolutely need an MA-level course to gain admission, but striving for such a goal will serve you well. In addition to real analysis, coursework in probability and statistics is also extremely valuable, and coursework in differential equations and numerical optimization may also be helpful. When in doubt, always select the more rigorous, theoretical versions of such courses.

**7. Is this what you really want?** Keep in mind that there are many other career tracks that draw heavily on economics but with lighter mathematics requirements. There are Ph.D. programs in public policy, public policy in management, political science, sociology, health policy, and many other areas, and these may be worth exploring if you like economics but are unwilling or unable to cope with the heavy mathematics requirements. You may be able to achieve your career goals without a Ph.D. or with a Ph.D. in a related field other than economics. If you know you ultimately want an economics Ph.D., an economics M.A. at CSUEB may not be your best option. The courses in the M.A. economics program at CSUEB are nowhere near as quantitatively rigorous as what you will encounter in most Ph.D. programs. Furthermore, entering a Ph.D. program having completed an economics M.A. at another school will not shorten the duration of the Ph.D. program. If you know you want an economics Ph.D., it might make more sense to directly enter a Ph.D. program, picking up the M.A. degree along the way in the same school that will grant the Ph.D., as is common in such programs. Or, if you really want to increase your preparation for the economics Ph.D. by first doing an M.A., pursue an M.A. in mathematics or statistics instead of economics, as discussed in #4.

However, at least three groups of students who plan to get Ph.D.s may benefit from first taking the CSUEB M.A. in economics. First, students with strong prior backgrounds in mathematics (e.g. those with undergraduate degrees in physics or engineering) with little or no background in economics may wish to learn more about what economics is all about before plunging into a Ph.D. program. Second, students who wish to obtain Ph.D.s in related (though less technical) areas, such as public policy, will find the CSUEB M.A. program useful. Third, students who studied economics as undergraduates but who did not earn a sufficiently high GPA to obtain admission to a Ph.D. program will find the CSUEB M.A. program a useful stepping stone to shore up those weaknesses before entering a doctoral program.

**8. Don’t be intimidated.** The heavy training in mathematics is to equip you to survive the first couple of years of the Ph.D. program. After that, when you reach the research stage, you have significant discretion over how quantitative your work will be. Many very successful research economists use very little mathematics. To a large extent, the purpose of all the mathematics courses is to develop a level of “mathematical sophistication”, but it does not necessarily mean that those advanced tools will be regularly used in your career as a Ph.D. economist. It is important to ask yourself whether you have the fortitude to withstand a rigorous training program in mathematics before entering a Ph.D. program, but at the same time, do not make the mistake of thinking that a Ph.D. in economics will doom you to a life of real analysis and linear algebra.

**UNDERGRADUATE COURSEWORK**

- MATH 2304 Calculus III (*)
- MATH 3100 Linear Algebra (*)
- MATH 3300 Analysis I (*)
- MATH 3301 Analysis II (*)
- MATH 3320 Calculus and Vector Functions (*)
- MATH 3331 Differential Equations
- MATH 3361 Ordinary Differential Equations
- MATH/STAT 3401 Introduction to Probability Theory I
- MATH/STAT 3402 Introduction to Probability Theory II
- MATH/STAT 3502 Statistical Inference I
- MATH/STAT 3503 Statistical Inference II
- MATH/CS 3750 Numerical Analysis I
- MATH/STAT 3865 Mathematical Modeling
- MATH 4301 Analysis III (*)
- MATH 4350 Theory of Functions of a Real Variable (*)
- MATH 4360 Introduction to Topology
- MATH/STAT 4401 Introduction to Stochastic Processes
- MATH/CS 4750 Numerical Analysis II
- MATH 4841 Topics in Optimization

**GRADUATE COURSEWORK**

- MATH 6100 Applied Algebra
- MATH 6201 Topology
- MATH 6331 Topics in Differential Equations
- MATH 6350 Real Analysis (*)
- MATH/STAT 6401 Advanced Probability I
- MATH/STAT 6402 Advanced Probability II
- MATH/STAT 6501 Mathematical Statistics I
- MATH/STAT 6502 Mathematical Statistics II
- MATH 6750 Topics in Advanced Numerical Analysis
- MATH 6841 Nonlinear Optimization
- MATH 6842 Advanced Topics in Optimization
- MATH/STAT 6865 Mathematical Modeling