Which classes do you recommend for the GRE math subject test?

Question

(Not the quantitative section of the standard GRE)

I am currently a math teacher (up to calc AB). I want to eventually go for my masters in applied math, but because I have a bachelors in business, I haven't taken many math courses... I've only taken precalc, calc 1-3, linear algebra, and discrete structures at the college level. What classes would you recommend taking so that I can get a decent score on this test (I will hopefully take it by the end of this year, so I have time to take a few more classes). I have been studying quite a bit (mainly from Cracking the GRE math subject test) but many of the concepts are new to me. Thank you!

Answer 1

This is not in particular for the GRE but is good knowledge to have when you start your masters in applied mathematics.

I am not sure what calc 1-3 exactly includes but to do applied maths at Masters level you will need a good knowledge of the following :

• Ordinary differential equations, all 1st order, the theory behind linear ODE
• Some knowledge on numerical solution to differential equations would be very nice (Euler's method, Runge-Kutta methods to start with)
• Differentiation of all kind of functions, integration methods.
• Complex analysis. Mainly stuff around the Residue Theorem.
• Basic knowledge in fluids could help, depending on what kind of applied you do.
• Dynamics. Again, depends on the type of applied.
• Basic knowledge of PDE, transport equation, heat equation, wave equation, Laplace equation form a good start.
• Knowledge of one type of mathematics language certainly helps! Matlab, Maple, Mathematica, ...
• Fourier transforms, z-transforms and other similar methods.
• General multi-variable calculus

Certainly this list is not complete but if you master these then you will surely have a better knowledge than a lot of people doing a similar masters. Regarding books, Mathematical techniques is a good place to look at as it includes most of the above.

Answer 2

I have taken the GRE subject test and my score is 850. This is not very high, as I only achieved 88 percentile. So you should take my advice with a grain of salt.

I think you should review the basics using a standard calculus textbook like Stewart, because most of the test problems are similar to homework problems there. Other subjects you should review, but not included in your list are abstract algebra, complex analysis, point set topology, elementary probability and statistics. I suppose a standard review book (like Princeton's review) should have a list. But all such lists are not adequate, because they change the content every year, and the test is becoming more difficult over the years.

Also, there are sample test online(4 or 5). You should be able to know roughly what they are testing and how much you do not know after you finish the sample test. You should aim high (I thought I would score around 900, but I only get 850) and prepare to the best of your ability. This does have a huge impact on the grad school admission process.