My input for test taking Strategy

Forum for the GRE subject test in mathematics.
JonMLTR
Posts: 27
Joined: Sun Nov 11, 2012 10:17 am

My input for test taking Strategy

Postby JonMLTR » Mon Dec 10, 2012 5:17 am

I am someone who does NOT have a major/minor in mathematics, never have taken Complex analysis, Number theory, Abstract Algebra, Topology. I have studied for the test for about 1.5 months including studying two books on Abstract Algebra, Topology. I have just received my score and unfortunately %85 which is quite below for my target schools(yes I was aiming for 900 which also put me in a lot of stress and unfortunately with this score I doubt I will have any chance at all)

It is really sad because I could have answered every question perfectly yet the timing issue ,having no previous experience and high expectations caused me to mess things up.

But I think I may give some feedback for the new students who are aiming for high scores which is something that is missing from this forum.

The study strategy is quite simple yet I have seen that the same rookie mistakes is being made by everyone. DON'T rely on reivew books for this test, DON'T. Use the review books, like cracking the GRE subject Math, as a GUIDE for your review.

1. The exam is very much Calculus heavy and it takes a lot of time. Try to solve at least half of the questions in your calculus book while reviewing the subjects. It is easier than you think but when you time yourself it is very rewarding especially in eliminating your stupid errors.

2. Solve as many questions as you can in basic analysis (Rudin), basic topology, Abstract algebra. Those questions are placed in the second part of the exam hence you won't be very fresh, the more familiar you are with the question the faster and more accurately you can understand and solve them.

3. If you have not taken some fundamental courses like me then please add an additional month to study 2-3 books(even more depending on the situation).

4. There are 4-5 practice tests I have seen and definitely solve them (but not all at once try to correct your weaknesses before solving a new one, you don't want to waste them)

5. If possible take the test more than once, by just solving the practice tests it is hard to get the feel of the real thing( If I had the opportunity I would have taken the exam in October too which would have helped me for eliminating my stupid mistakes). I have seen people taken it 3 or more times so I can say that it is "fair" to take it more than once.

WHILE TAKING THE TEST:

1- Sleep well, I haven't slept before the exam and it was torture towards the end, I found it extremely hard to focus towards the end (which probably contrubuted to my mistakes).

2- Time , time is not on your side. Timing is extremely crucial in this test. While studying you should be able to set your internal clock to about 2-2.5 minutes per question. When you do that it will prevent you from spending too much time on a question.

3- Learn when to skip a question. Yes the questions may be easy but it is also easy to get carried away while trying not to miss a question. I did that in a question (which I believe the question itself was wrong) and because of that I missed 3 easy questions that I could have answered easily(would have made a big difference).

4- Don't put stress on yourself by thinking about your target score, it will just drag you down.


Finally this test does not really measure how smart you are but I believe it is a good indicator about your undergraduate background(courses not research or intelligence).

Though most of you will not be gaining a lot by getting a score of 900 if I can get above 800 easily in 1.5 months without taking any courses in several fundamental topics then anyone with a proper background and some luck can get 900 by studying around 2 months(Of course if you are fresh or better at thesubjects you can do it much more quickly).

I sincerely hope you all do great in the coming exams.

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Re: My input for test taking Strategy

Postby Legendre » Mon Dec 10, 2012 9:57 am

JonMLTR wrote:
The study strategy is quite simple yet I have seen that the same rookie mistakes is being made by everyone. DON'T rely on reivew books for this test, DON'T. Use the review books, like cracking the GRE subject Math, as a GUIDE for your review.



I actually thought the best strategy is to rely on Princeton Review because the test doesn't actually tests your maths ability, but rather your ability to do the test. Princeton Review maybe outdated but it is based on the test, and a few rare questions in the book actually appeared in the test (in a similar form, not exact).

When I tried to study from textbooks I ran out of time and learn a whole bunch of irrelevant stuff. E.g. The Graph Theory on the test is actually more computer science than actual Graph Theory. Someone gave a very good advise to focus on engineering and computer science texts rather than mathematics text.

JonMLTR wrote:
5. If possible take the test more than once, by just solving the practice tests it is hard to get the feel of the real thing( If I had the opportunity I would have taken the exam in October too which would have helped me for eliminating my stupid mistakes). I have seen people taken it 3 or more times so I can say that it is "fair" to take it more than once.



I would say taking the test 3 times (April, Oct, Nov) was the most helpful thing I have done. I actually tried the test a few years before during my undergrad. I was able to reproduce around 55+ questions on each test, and this gave me 3 sets of very good notes and practice materials for the Nov test. (they are all destroyed and forgotten, and it is illegal to discuss test content, so please do not message me to ask for them)

c3adv
Posts: 12
Joined: Fri Apr 06, 2012 8:34 pm

Re: My input for test taking Strategy

Postby c3adv » Mon Dec 10, 2012 11:06 am

I appreciate your emphasis on feedback and a straightforward study strategy. I was under the impression that the 85th percentile was enough even for Berkeley, but I could be wrong. I think something I would like to eventually add would be a breakdown of sample study plans to give others an outline of how they could potentially budget their time. The REA book mentioned that studying for an hour a day for 12 weeks should be sufficient for preparing around anyone's busy schedule, but that can be shortened considerably for someone who knows the material well. For those who have gaps, it may be harder to extrapolate how much time is needed, but it seems that about 2 months is good enough. How often did you study? Every day or primarily on weekends? Roughly speaking, since you are not a math major/minor, did you study for 4 to 10 hours a day? Did you focus on specific topics? Can you mention a sample scenario concerning a concept you had previously never studied before?

Although it does not seem to be mentioned often, if at all, I would suggest looking into textbooks with hints or brief answers in the back. Mastering Rudin, Dummit and Foote, Lang, etc. is definitely better preparation for graduate courses overall, but for this test, some immediate feedback can help streamline study time while making the transition into the standard upper-level textbooks much smoother.

As such, I have a few study suggestions. First, review and memorize all the precalculus, algebra, and trigonometry theorems and any major geometry proofs from high school. For example, be able to recall double angle formulas and all the values from the unit circle. The very basics of vectors, partial fraction decomposition, and complex numbers (especially modulus, De Moivre's Theorem, and powers/roots of complex numbers) are taught in many standard high school textbooks, but it seems they are retaught, respectively, in calculus, introductory real and complex analysis, and linear algebra textbooks time after time. The same is true for set theory and the basic rules for functions, which get repeated too often (I hate it when a class spends even a single lecture going over this stuff when everyone in the class has seen it three times already, or more, only to rush through the more complicated topics later on).

The calculations needed for most problems on Stewart and other standard calculus textbooks are basic enough, so speed is the only thing that needs to be improved upon. The AP Calculus questions somewhat overlap with the ones on this test, so those can provide extra timed practice on standardized questions, and if I am not mistaken, they are also written by ETS. Some of the standard calculus/analysis proofs could be found in the solutions manuals. Student solutions manuals are not usually available, however, for higher-level courses. So, if you have not taken the classes before or if your professors skipped many key topics/problems, you are currently not enrolled in school, and/or you are all alone except for help on the forum and a few helpful textbooks, then it can seem daunting. Nonetheless, I have found problem books in analysis and linear algebra to be very useful in reviewing techniques I had forgotten or never fully mastered. The ones I have used so far are:

A Problem Book in Real Analysis by Aksov;
Problems in Mathematical Analysis 1, 2, and 3 by Kaczor;
Linear Algebra Problem Book by Halmos;
Problems in Real and Complex Analysis by Gelbaum;
and Problems and Solutions for Undergraduate Analysis by Shakarchi.

I am curious as to whether problem books exist for Abstract (Modern) Algebra and the other subjects; I have used and looked into the ones for functional analysis and algebraic number theory, but those aren't needed for the GRE subject test. I know Gallian and Pinter have some hints for introductory abstract algebra, and Ross is good for basic probability, but Grimmett's books on probability have some worked-out solutions if you are stuck or want to check your work. Boyce and DiPrima or Nagle cover basic ODE. Burton for Number Theory is easy enough for someone who has never taken a course in the subject before. For topology, I have not looked beyond Munkres as of yet. Definitely, look into Brown and Churchill or Wunsch for the basics of Complex Variables.

Can anyone expand on or provide corrections to what I have written so far?

JonMLTR
Posts: 27
Joined: Sun Nov 11, 2012 10:17 am

Re: My input for test taking Strategy

Postby JonMLTR » Mon Dec 10, 2012 3:49 pm

@c3adv:

You and Legendre have made a lot of good points, I am quite busy right now but I will try to add more explanation in the following days when I have the time.

As for %85, my situation is unfortunately highly irregular and I needed 900 not for a top school like Berkeley, (still a respectable University but not in math and this would have guaranteed an admission, it was rather unexpected, I was also on the verge of publishing a paper that's why I didn't have a lot of time to study). For Berkeley or any other top school, I strongly believe there is little difference between %85 and %99. The resolution of this test is really really low on the higher end of the scores. Experience, luck, your motivation and focus on the day of the exam makes a big difference. I really wished that the exam contained much harder questions and was longer so that the spread between good students were meaningful but right it is very prone to noise. This exam is more like a confirmation that you have an acceptable grasp on the undergraduate subjects since undergraduate grades depend on the university and your classmates a lot and bear little information. In short I didn't mean to imply that 900 is the ticket for Berkeley.

I had several friends who were really good math majors and what I saw was medals in IMO and exams like Putnam make a "big" difference, another thing that I observed was publications/research also made a great impact on the application. All of these FAR outweight the Gre Subject test. Again Subject test is like a necessity rather than sufficiency.

rmg512
Posts: 97
Joined: Sat Nov 12, 2011 8:15 pm

Re: My input for test taking Strategy

Postby rmg512 » Mon Dec 10, 2012 9:33 pm

I think the mods need to put a sticky on this thread. It's some of the best content this forum has ever seen, in my opinion.

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

Re: My input for test taking Strategy

Postby Legendre » Tue Dec 11, 2012 10:17 am

rmg512 wrote:I think the mods need to put a sticky on this thread. It's some of the best content this forum has ever seen, in my opinion.


I concur.

Also, the thread starter (or a moderator) should change the title of this thread to something like "Compilation of Preparation Strategies/Guides". Then, others can contribute their own versions.

waiting512
Posts: 61
Joined: Sat Dec 10, 2011 10:41 pm

Re: My input for test taking Strategy

Postby waiting512 » Tue Dec 11, 2012 12:12 pm

I think the best preparation can begin you sophomore year by taking some of those courses which you may not take until after the test (e.g. Complex Analysis etc.). Those questions tend to be very easy if you have had the subject and moderately difficult otherwise. Also, for us domestic folk it might behoove students to sit in on a Calc. III and DE course for a quick refresher.

Also, "sleep well" is not good advice DURING the test, haha.

c3adv
Posts: 12
Joined: Fri Apr 06, 2012 8:34 pm

Re: My input for test taking Strategy

Postby c3adv » Wed Dec 12, 2012 1:54 am

@JonMLTR
Yes, sorry, I was not being precise. I agree with your comment regarding necessity and not sufficiency.

@waiting512
You make a valid point. I did not realize how much multivariable calculus I had forgotten until I was helping out some students recently. Right now, I have a shortlist of concepts that I know I have to review briefly before the exam. I think graduate-level courses and tutoring really showed me that I needed to review my old books methodically and rederive and memorize key results that I thought I knew pretty well. I remember the main points, but speed and some details may be missing.
Taking some of the upper-level classes during sophomore year can be hard. My undergraduate department only offered complex variables and abstract algebra once every three years. I could only take them during my senior year as electives, but they were two of my favorite classes.

I have been thinking about it for a while, but has anyone ever thought of making their own practice tests? I am not talking about rehashing/copying off the actual or practice subject tests nor the Princeton Review and REA guides, but creating "original" tests. I think those would be great for studying purposes, and they can be recycled when you are teaching a course one day or want a quick refresher. Typing them up in LaTex might take a few days, but it could be a fun project, theoretically.

waiting512
Posts: 61
Joined: Sat Dec 10, 2011 10:41 pm

Re: My input for test taking Strategy

Postby waiting512 » Wed Dec 12, 2012 8:02 pm

I would be interested in collaborating with some of the people on here to make one for future test-takers. My specialties are the fringe topics like combinatorics and graph theory, two areas that usually show up on the exam. We could probably also come up with some quick things to memorize for people in areas like probability and complex analysis where students have not had much exposure.

I certainly understand the lack of course offering. I also went to a liberal arts school where course selection was limited, but if you have the opportunity you should definitely try.

ReneMagritte
Posts: 19
Joined: Mon Sep 03, 2012 4:38 am

Re: My input for test taking Strategy

Postby ReneMagritte » Fri Dec 14, 2012 8:03 pm

Has anyone ever considered that in a situation like the GRE where the percentile score is what matters, that every ounce of good advice you give to strangers ultimately works against you?!

quinquenion
Posts: 57
Joined: Fri Nov 04, 2011 12:34 pm

Re: My input for test taking Strategy

Postby quinquenion » Fri Dec 14, 2012 9:00 pm

ReneMagritte wrote:Has anyone ever considered that in a situation like the GRE where the percentile score is what matters, that every ounce of good advice you give to strangers ultimately works against you?!


Two points:
  • If memory serves, ETS only adjusts percentiles once a year over the summer. So the advice one gives won't effect any changes until the following year's application season, during which, if all went well, the advice-giver will already have been accepted to a graduate school.
  • Depending on the school, it isn't necessarily percentile score that matters. Some schools list expected scores in percentiles (e.g. Berkeley), while others list expected scaled scores (e.g. UPenn).

Of course, this is not counting the fact that other people scoring higher will make them more attractive candidates, and that there are only a finite number of spots available in programs of interest. Those of us who are fortunate enough to already be enrolled have none of these qualms, of course.

More importantly though, helping others makes you happy. :D

korean
Posts: 14
Joined: Sun Dec 09, 2012 7:51 pm

Re: My input for test taking Strategy

Postby korean » Fri Dec 14, 2012 10:01 pm

@ReneMagritte I view it in a different angle. "We" are
against the people who do not care enough to make a research
about how to maximize their scores. Everyone who is
willing to do well, i.e. he makes such efforts as preparing his calculus skills
searching through the internet to find all the tips
available then he should have the opportunity to do well.
And by giving advice you are helping those kind of people.

ReneMagritte
Posts: 19
Joined: Mon Sep 03, 2012 4:38 am

Re: My input for test taking Strategy

Postby ReneMagritte » Sat Dec 15, 2012 3:21 pm

quinquenion wrote:Two points:


I agree with both!

korean wrote:@ReneMagritte I view it in a different angle. "We" are
against the people who do not care enough to make a research
about how to maximize their scores. Everyone who is
willing to do well, i.e. he makes such efforts as preparing his calculus skills
searching through the internet to find all the tips
available then he should have the opportunity to do well.
And by giving advice you are helping those kind of people.


I think that's overly harsh. Someone might be a bit flippant about the GRE because they want to spend their time doing stuff that actually seriously matters, like studying advanced mathematics or doing their own researches. I wouldn't be so quick to judge others.

korean
Posts: 14
Joined: Sun Dec 09, 2012 7:51 pm

Re: My input for test taking Strategy

Postby korean » Sun Dec 16, 2012 1:51 pm

@ReneMagritte I was only reffering to their will to do well on the
subject test examination not generally towards the goal to be a better mathematician.
I believe that the preparation for subject has nothing to with the previous.

DDswife
Posts: 58
Joined: Thu Aug 14, 2014 5:29 pm

Re: My input for test taking Strategy

Postby DDswife » Sat Aug 16, 2014 5:07 pm

I have a question. What kind of material can we use during the test? Calculator, ruler, compass and other Geometry tools?

Thanks for all the advice.




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