The general GRE has three parts: English, Math and Quantitative Reasoning. There is also a writing assessment exam, frequently not required by graduate departments in mathematics. We will not discuss these. This file talks about the Subject Mathematics GRE (meant for students going to graduate school in mathematics).
50% of the exam is calculus and its applications. 25% consists of elementary algebra, linear algebra, abstract algebra and number theory. The remaining 25% consists of others areas commonly studied by undergraduates. Therefore, a thorough review of calculus is very important.
The following is a report based on the study of four sample exams (which Prof. Schaefer has - you can check them out for a week or two). There is also a sample exam online if you want to download it. The calculus questions cover pretty much everything we teach in Math 11 - 21. Here is a very small sample of things that appear on the exam from these courses: i) interval of convergence of a power series, ii) Green's theorem, iii) a continuous function on a closed, bounded set takes on maximum and minimum values, and iv) if f is continuous on [b,c] then there's a d in [b,c] such that the integral from b to c of f equals f(d)(c-b). With the exception of one problem on the four sample exams, all differential equation problems could be tackled with techniques from Math 11 - 21.
Much, though not all of the 25% algebra is covered in our Math 52 and 53. An important source of review would be the theorems in Math 52 about finite groups and their subgroups. From Math 53, know about matrices and operations on them, vector spaces and their subspaces, eigenvalues and characteristic polynomials.
The literatures says that the additional topics in the remaining 25% include elementary topology of R (the reals) and R^n, properties of continuous functions, differentiability and integrability, general topology, complex variables, probability and statistics, set theory, logic, combinatorics, discrete mathematics, algorithms and numerical analysis. There were also some problems where you follow through an algorithm and describe the output; a student who completed Math 10 should have no problem with these.
In the following table is a list of the number of problems (from the four sample exams) that would require knowledge from a course that we do not require.
| Course name (course number) | Number of problems |
| Probability (122) | 13 |
| Abstract Algebra (111) | 8 |
| Intermediate Analysis (153) | 8 |
| Complex Variables (105) | 7 |
| Topology (113) | 6 |
| Number Theory (175) | 5 |
| Combinatorics (176) | 5 |
| Linear Algebra 2 (196) | 3 |
| Theory of alg'ms (163) | 1 |
| Differential Equations (22) | 1 |
When advising a student as to which courses are most important for preparation for graduate school in pure mathematics, we would recommend 111, 112, 153, 154, 105 and 113 before 122. So we find it strange that the GRE emphasizes Math 122 so much.
GRE (Graduate Record Exam) Home Page.
Last update 10/4/01 by E. Schaefer.