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TL;DR My understanding is that the Math GRE is supposed to test knowledge that is expected of someone who wants to pursue a math masteral or math PhD. So shouldn't it test knowledge that is expected of someone whose bachelor's or master's degree is pure math, applied math, physics or statistics? It seems biased to pure math. Also why is numerical analysis in the Math GRE? How much of the Math GRE is the pure math stuff?


Those who pursue a postgraduate degree in pure or applied math usually have a bachelor's or master's in pure math, applied math, physics, engineering or statistics. Less common would be economics, chemistry or biology.

The Math GRE includes topics that not everyone from those backgrounds have taken up in their bachelor's or master's.

It would make sense that some people would have to study more in preparation for the math GRE (and their intended program). For example:

  1. Those from less common backgrounds likely haven't had much calculus or linear algebra. They likely haven't had any linear algebra, ordinary differential equations, basic probability theory, basic discrete mathematics or introductory real analysis.

  2. Those from engineering likely haven't had basic probability theory, basic discrete mathematics or introductory real analysis.

However, the Math GRE apparently:

  1. includes pure math topics such as abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis and seems to do so at a greater extent than ordinary differential equations, basic probability theory, basic discrete mathematics, basic statistical theory and introductory real analysis.

Those from applied math, physics or statistics are expected to know ordinary differential equations, basic probability theory, basic discrete mathematics, basic statistical theory and introductory real analysis but are not expected to know abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis.

However, those from pure math are expected to know the latter topics.

  1. includes numerical analysis, an applied math topic.

I would expect very few people who have a bachelor's or master's in pure math to have taken numerical analysis. Far fewer for and.

However, some of those from applied math, physics or statistics may be expected to know numerical analysis.

Questions:

  1. Why doesn't the Math GRE test include more basic probability theory, introductory real analysis, basic discrete mathematics, basic statistical theory and ordinary differential equations than abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis?

  2. Why in the first place does the Math GRE include pure math topics such as abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis that aren't expected of those with a bachelor's or master's in applied math, physics or statistics?

  3. Why does the Math GRE include numerical analysis, an applied math topic, when very few of those with a bachelor's and master's in math would have taken it up?

  4. In your best estimate, around how many questions out of 66 would one expect to cover topics other than calculus, linear algebra, basic probability theory, introductory real analysis, basic discrete mathematics, basic statistical theory and ordinary differential equations?

I don't really want to look at some of the past or practice exams out of fear of having the exam compromised for me if I were to try them out.

1 Answer 1

1) Why doesn't the test include more basic and introductory topics? Well, if you're applying to do research in mathematics, one might expect you to have a good coverage of broad aspects of the field beforehand.

2 and 3) The majority of the material on that paper is first year engineering level maths, and first term for people studying mathematics. Other areas shouldn't take longer than a couple days to cover to the level required for that paper.

4) Look at a past paper. The fact that you have an idea as to what is on the paper does not 'compromise' it. 50% calculus, 25% algebra and 25% advanced topics.