## Interesting Observations on the Math GRE

Forum for the GRE subject test in mathematics.
rsk
Posts: 28
Joined: Sun Sep 14, 2014 6:07 pm

### Interesting Observations on the Math GRE

So, I've been curious for a while as to how I should BEST focus my study time for the math GRE. Part of this is deciding which subjects deserve focus more than others. I know most people just heuristically follow the "50% calculus, 25% algebra, etc." (except for the 90th percentile hard-chargers out there using Dummit&Foote and Royden to prep, lol). Out of curiosity, I decided to actually go through the 4 exams available and categorize in more detail which subjects get all the attention. The results, in some ways, are a little surprising. I realize that it's difficult to gather statistics from only 4 exams, but it's all we have, so it is what it is there. For those who've taken the math GRE already, if you've noticed significant differences from what's given below, please do feel free to comment. It'll help anyone preparing for this thing.

Now, let me just quickly say how I did this. I decided to break up the vague "calculus" into single variable, multivariable, and differential equations. Questions that looked sort of calculus like, but were more theoretical than you'd see much in a typical calculus class got thrown into the real analysis section (including general topology questions about Rn specifically). Precalculus includes anything that would've likely been covered before college. Abstract algebra includes groups, rings, and fields, with linear algebra getting its own section. Number theory includes anything dealing with digits, prime numbers, divisibility, etc. Set Theory and Logic include questions about evaluating proofs, (general) set properties, and basic logic stuff. Numerical methods includes algorithms, root-finding, and approximations. Topology includes non-Rn stuff only. Everything else is pretty self-explanatory I think.

The numbers given are raw questions, each column representing its given test. Disclaimer: There's bound to be a couple errors in here, as I didn't double-check these. Also, there's obviously some ambiguity as to in which category some questions should be placed. Last: I apologize in advance for the sucky formatting. I was too tired to figure out how to do this in Latex, and couldn't get the align features in BBCode to work.

_____________________________8767___9367___9768___0568

Precalculus__________________10______5_______7_______4
Single-Variable Calculus_____19______23______24_____16
Multi-Variable Calculus_______5_______6_______2_______4
Differential Equations_________2_______1_______0_______1
Linear Algebra _______________8_______9_______8_______8
Abstract Algebra______________4_______5_______5_______7
Number Theory_______________1_______2_______2_______3
Numerical Methods___________1_______0_______2_______2
Real Analysis_________________3_______2_______7_______9
Combinatorics________________3_______5_______3_______4
Set Theory and Logic__________1_______2_______1_______4
Complex Analysis_____________1_______1_______2_______3
Probability and Statistics_______3_______4_______4_______2
General Topology______________2_______2_______0_______0

If I may hypothesize a little bit, a few things seem worthy of note. First, single-variable calculus is BY FAR the most important piece, covering 1/4 to 1/3 of the exam. In contrast, differential equations, which gets lumped--sadly--under that "50% calculus" chunk, is barely a blip on the radar, and clearly not worth too much study time on its own. After single-variable, linear algebra and abstract algebra are extremely important, at about 1/4 of the test on their own. Again, sadly, number theory gets lumped together with these, yet it shows up only slightly more than DIFF EQ.

Second, if one regards these as a meager time scale over the almost 30 years between these tests (again, only 4 exams, so it's tough), it seems like usual single-variable questions have declined in favor of real analysis type (i.e. more theoretical) questions. Whereas the balance between the two was something like 19:3 in 1987, it seems to have evened out a little more to 16:9 in 2005. In conjunction, multi-variable questions seem to have decreased slightly as well, and similarly for the precalculus questions.

Again, it's tough to speculate too much, but it was interesting to do this. It at least helped me not freak out too much about spending so much time on the single-variable stuff, and reminded me to allot a good chunk of time to linear and abstract algebra as well. At any rate. Hope it helps.