### GRE Math Subject Test preparation sessions 2017 Fall TBA

Dates | Time and room | Instructor | Topic |

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### Introduction to the GRE Math Subject Test

Most US math PhD programs require the Graduate Record Exam (GRE) general test *and *math subject test. These are separate tests. Math is in both, so don’t confuse them: the math in the GRE general test is at the level of the SAT, so math majors should do very well and the score is irrelevant unless you do badly; the GRE math subject test is what math grad schools care about, and is a paper test of **66 questions, all multiple choice, and lasts 2 hours and 50 minutes.** Click here for tips on applying for graduate programs in mathematics.

Here is a rough breakdown of the content of the test.

- Most questions, perhaps surprisingly, are on single and multivariable calculus and linear algebra! UConn students who took this test recently advise that you
- know the Taylor series of common functions and be able to use them (e.g., to find leading terms of the Taylor series of sin(
*x*^{2}) at*x*=0 quickly, which may be useful for indeterminate limits where L’Hospital’s rule is a mess), - know the derivatives of inverse trig functions, especially arctan
*x*. - be able to find saddle points on a surface, differentiate and integrate in polar coordinates, use Green’s theorem, and use Lagrange multipliers,
- know linear (in)dependence, a basis, and the rank-nullity theorem;
- know a noninvertible linear transformation has determinant 0;
- be able to compute eigenvalues, eigenvectors, and the matrix representation of a linear transformation that is described abstractly.

- know the Taylor series of common functions and be able to use them (e.g., to find leading terms of the Taylor series of sin(
- The rest of the exam is a hodgepodge of topics from upper-level math courses:
- basic logic (e.g., recognize equivalent statements and form the contrapositive),
- probability,
- combinatorics (this overlaps with discrete probability),
- real analysis,
- differential equations (including linear of order greater than 2),
- abstract algebra (groups, rings, fields, ideals, modules),
- number theory,
- complex analysis (know Cauchy’s integral formula and residues),
- topology.

An exam could have 6-7 questions on a topic or just 1 question. You need to be ready. In particular, you should try to take classes covering most of the exam topics by the semester *before* you take the math subject test. (Reading about exam topics yourself is another option, but if you only read and don’t solve exercises, which you would get in a course, then you won’t learn the material well.) The math subject test should be taken by the fall of the senior year since grad school applications are due near the end of that semester, so for example don’t wait until your senior year to start learning abstract algebra.

The number one issue you have to prepare for on this exam is *time management*: it is critical that you work efficiently in order to have a chance of answering all the questions. Some students who study for the test but never practice taking it under test conditions, including only using the time allowed, are caught off guard by time running out before they get to many questions. Since this is a paper test you can skip questions and come back to them, so if you don’t know how to start solving a problem shortly after reading it you should consider moving on and returning to the question later. Only with practice under test conditions will you determine how many questions you can expect to answer and which content areas take you the most time.

Top programs in the US expect a score in the 60+ percentile range. (Berkeley says on their website that they expect 80+; applications with lower scores won’t even be read.) The low end of that range corresponds roughly to getting half the questions right. Cutoff math subject test scores for graduate programs outside the top tier are more modest.

For UConn students, feel free to contact us for further information on GRE math subject tests. (Keith Conrad, Vasileios Chousionis, Liang Xiao).

### Useful Links

- http://www.mathematicsgre.com/
- http://ask.metafilter.com/105980/help-with-the-Math-GRE
- http://ask.metafilter.com/94246/A-math-PhD-story
- http://www.physicsforums.com/showthread.php?t=248239
- http://www.physicsforums.com/archive/index.php/t-199672.html
- https://www.mastersdegree.net/how-to-study-for-the-gre/ (for GRE general test)

### Past Training materials

- Always do the Practice Book provided by ETS.
- 2016 Fall: Chousionis Xiao
- 2016 Spring: Chen Chousionis Xiao