Preparation materials for math subject test
Preparation materials for math subject test
I have already taken my subject GRE test. My score is 850. Now I am planning to retake it. I think I have some lacking in Algebra and additional topics parts. Is there any good resource that will help me in this case?

 Posts: 7
 Joined: Thu Mar 23, 2023 1:48 pm
Re: Preparation materials for math subject test
Isn't that around an 85%ile? That's a really good score imo, beyond 80%ile I found that it gets hard to increase your score and I've heard admissions officers don't care much about your score past 80%ile. Below I've listed some tips and resources I used to improve my score from ~65%ile to ~90%ile.
Helpful Links, many with practice GRE style problems, sometimes grouped by subject:
https://math.uchicago.edu/~min/GRE/
https://web.math.ucsb.edu/~padraic/ucsb ... w2015.html
https://sites.math.rutgers.edu/~iacoley/greprep.html
https://www.mathsub.com/resources/
http://rambotutoring.com/mathgre/
I found the following post on this forum to be EXTREMELY helpful, I definitely recommend checking it out!! Definitely helped
viewtopic.php?t=4577
The exam gets pretty repetitive so make note of the types of questions in the officially released exams. Also note that they released a new exam (GR3768) this year but nobody has made a solution guide yet. https://www.ets.org/pdfs/gre/practicebookmath.pdf. Also remember that this is a test against the clock. If a question format appears almost every year, it can be worthwhile to memorize what the answer is in a generalized form. If that saves you an extra couple minutes, then that's a couple minutes that can go into a more difficult problem.
Some tips/resources:
Linear & Abstract Algebra: I found Schuam's outlines super helpful, especially for linear algebra. For abstract algebra, identify every single question you've gotten wrong on the practice tests and figure out what concepts in particular you're struggling with. For me, that was ring theory and ideals, so I did targeted review on that stuff. Review Sylow's theorems and its consequences, orbitstabilizer theorem, center, conjugacy classes, etc. Wikipedia can be a good resource ngl. Number theory is my field of study so I don't have any advice on that, sorry.
Real Analysis and Topology: The most difficult part of the exam for me, I always struggle with it. I used Schuam's outlines and similarly targeted concepts I struggled with. There are some concepts that are recurring, identify those and know them inandout. Princeton Review is NOT a good resource for this. Check out this link: viewtopic.php?t=4691. Try to memorize some common sums and sequences as well as common Taylor series. Memorize a bunch of random properties. In studying, I ended up with a page full of just random properties and it def helped me a lot. Unfortunately I got one real analysis and one topology question wrong on my actual exam :/
Graph theory, logic, and algorithms: You're probably going to have about one question about each. Super basic stuff, almost always the same type of question, Princeton Review suffices for this.
Complex Analysis: Almost always either a CauchyRiemann equations question (ux = vy, uy = vx) or contour integration (residue theorem). Princeton Review mostly suffices.
Combinatorics, probability, and statistics: Princeton Review should mostly suffice. Memorize some other random formulas and properties as you see fit during your practice. Review both versions of stars and bars and review statistics on random samples/observations as they aren't covered in Princeton Review. The questions in this group range from easy to difficult depending on the exam, I got a really tough probability question on my exam and got it wrong :/
Numerical Analysis: Review questions of the type "order these numbers" in past and practice exams. I got it wrong on my actual exam :/
I hope this helps! If anyone has any further resources, they should share them.
Helpful Links, many with practice GRE style problems, sometimes grouped by subject:
https://math.uchicago.edu/~min/GRE/
https://web.math.ucsb.edu/~padraic/ucsb ... w2015.html
https://sites.math.rutgers.edu/~iacoley/greprep.html
https://www.mathsub.com/resources/
http://rambotutoring.com/mathgre/
I found the following post on this forum to be EXTREMELY helpful, I definitely recommend checking it out!! Definitely helped
viewtopic.php?t=4577
The exam gets pretty repetitive so make note of the types of questions in the officially released exams. Also note that they released a new exam (GR3768) this year but nobody has made a solution guide yet. https://www.ets.org/pdfs/gre/practicebookmath.pdf. Also remember that this is a test against the clock. If a question format appears almost every year, it can be worthwhile to memorize what the answer is in a generalized form. If that saves you an extra couple minutes, then that's a couple minutes that can go into a more difficult problem.
Some tips/resources:
Linear & Abstract Algebra: I found Schuam's outlines super helpful, especially for linear algebra. For abstract algebra, identify every single question you've gotten wrong on the practice tests and figure out what concepts in particular you're struggling with. For me, that was ring theory and ideals, so I did targeted review on that stuff. Review Sylow's theorems and its consequences, orbitstabilizer theorem, center, conjugacy classes, etc. Wikipedia can be a good resource ngl. Number theory is my field of study so I don't have any advice on that, sorry.
Real Analysis and Topology: The most difficult part of the exam for me, I always struggle with it. I used Schuam's outlines and similarly targeted concepts I struggled with. There are some concepts that are recurring, identify those and know them inandout. Princeton Review is NOT a good resource for this. Check out this link: viewtopic.php?t=4691. Try to memorize some common sums and sequences as well as common Taylor series. Memorize a bunch of random properties. In studying, I ended up with a page full of just random properties and it def helped me a lot. Unfortunately I got one real analysis and one topology question wrong on my actual exam :/
Graph theory, logic, and algorithms: You're probably going to have about one question about each. Super basic stuff, almost always the same type of question, Princeton Review suffices for this.
Complex Analysis: Almost always either a CauchyRiemann equations question (ux = vy, uy = vx) or contour integration (residue theorem). Princeton Review mostly suffices.
Combinatorics, probability, and statistics: Princeton Review should mostly suffice. Memorize some other random formulas and properties as you see fit during your practice. Review both versions of stars and bars and review statistics on random samples/observations as they aren't covered in Princeton Review. The questions in this group range from easy to difficult depending on the exam, I got a really tough probability question on my exam and got it wrong :/
Numerical Analysis: Review questions of the type "order these numbers" in past and practice exams. I got it wrong on my actual exam :/
I hope this helps! If anyone has any further resources, they should share them.

 Posts: 2
 Joined: Sun Oct 01, 2023 5:09 pm
Re: Preparation materials for math subject test
Is there any way of knowing what questions we got wrong?

 Posts: 7
 Joined: Thu Mar 23, 2023 1:48 pm
Re: Preparation materials for math subject test
Unfortunately not, I just memorized a few questions I was dubious on and the answer choices I chose and I worked them out later, used a calculator, or looked them up.
Re: Preparation materials for math subject test
@boredmathguy thank you so much for your information. Yeah It is 85 percentile. Doesn’t admission commette really care about 85% or 90%+? Actually My university is top in my country but it’s not well known around the world. So I thought better score would help me if I try for Ivy League. Is my assumption correct?

 Posts: 7
 Joined: Thu Mar 23, 2023 1:48 pm
Re: Preparation materials for math subject test
@Kibria I'm glad to help, we're all in this together! I think this is a question best left to admissions officers tbh. I've personally heard that 80+%ile is regarded as the same but I hesitate to say anything definitively because 1. even if I mean well I am still an internet stranger who could unintentionally mislead you, and 2. it probably depends school to school and year to year.
I see this sentiment a lot: viewtopic.php?t=3847; I've been told by faculty that an 80+%ile proves you're willing to put in the work to do well on the exam and therefore are likely to put in the work to pass the prelim/qual exams.
I will however note a couple things: 1. Stanford (https://mathematics.stanford.edu/academ ... admissions) and UCLA (https://ww3.math.ucla.edu/admissions/) both note in their FAQ that admitted students typically have at least an 800 or an 80%ile respectively. At the very least, the evidence all suggests that you are in a good position with that mGRE score. 2. The Ivy league is a sports thing, and the universities within it can differ wildly. Harvard is ranked very differently than Dartmouth for math.
If you want to break into the top 10% of people who took the subject test and you have the time and money to put into it, you should definitely be able to do it. Ultimately I think you need to assess what the best use of time is for you. As your score gets better, you need to put in even more time and effort to raise it again. If you're applying to graduate school next year and are still in school, maybe a better use of your time is to take graduate classes or work on a research project. On the flip side, perhaps your grades are a little on the low side and you don't have flexibility for your next semester so getting a 90+%ile is the edge your application needs. Try talking to a faculty member at your university for personalized advice.
Best of luck, this internet stranger believes in you!
I see this sentiment a lot: viewtopic.php?t=3847; I've been told by faculty that an 80+%ile proves you're willing to put in the work to do well on the exam and therefore are likely to put in the work to pass the prelim/qual exams.
I will however note a couple things: 1. Stanford (https://mathematics.stanford.edu/academ ... admissions) and UCLA (https://ww3.math.ucla.edu/admissions/) both note in their FAQ that admitted students typically have at least an 800 or an 80%ile respectively. At the very least, the evidence all suggests that you are in a good position with that mGRE score. 2. The Ivy league is a sports thing, and the universities within it can differ wildly. Harvard is ranked very differently than Dartmouth for math.
If you want to break into the top 10% of people who took the subject test and you have the time and money to put into it, you should definitely be able to do it. Ultimately I think you need to assess what the best use of time is for you. As your score gets better, you need to put in even more time and effort to raise it again. If you're applying to graduate school next year and are still in school, maybe a better use of your time is to take graduate classes or work on a research project. On the flip side, perhaps your grades are a little on the low side and you don't have flexibility for your next semester so getting a 90+%ile is the edge your application needs. Try talking to a faculty member at your university for personalized advice.
Best of luck, this internet stranger believes in you!
Last edited by boredmathguy on Thu Dec 14, 2023 8:27 pm, edited 1 time in total.
Re: Preparation materials for math subject test
@Kibria I'm in the same boat as you! I didn't get as good a score as yours (830 / 80% Percentile). I will definitely retake but I'm not sure how much effort I should be putting in. If the UCLA website is accurate then I'm somewhere in the average of admitted students. I'm also just taking the test to have the option to apply to UCLA, Columbia, and Harvard (lol), as they are the only needs that require nowadays
Re: Preparation materials for math subject test
It means a lot for me. Thanks @ boredmathguy
Re: Preparation materials for math subject test
@ JerryM Questions from which sections did you find difficult?
Re: Preparation materials for math subject test
@Kibria There were 2 or 3 algebra questions that I didn't understand as I was still taking the class at the time. The few combinatorics questions were all quite challenging. And I also found the first half of the test to be easier and the second half to be harder than all practice material I've used, that probably caused my timing to mess up as I had to guess a couple questions towards the end due to time.