GRE Mathematics Subject Test

mrb

I am a math major at a third rate school who's a year away from graduating. I'm planning on going to grad school for possibly math or biomathematics.

I've known for a while now that my math classes are extremely lightweight, and I've been trying to supplement them with my own study. I did most of this fun non-Euclidean geometry book, and I just bought Spivak's Calculus and am on Chapter 2 now. My actual classes are basically a joke. Everything is strictly "plug and chug;" all tests and homework consist of solving problems exactly like those the professor just showed us how to solve. I have not been required to find a proof for anything. In any class. (Is this as strange as it seems to me?) On the bright side, at least everything is extremely easy (is this really a bright side?...)

Anyway, I will be taking the GRE and possibly the GRE Math Subject test in presumably November. So I just looked at the practice GRE Math Subject test on the ETS web site. Wow. I am nowhere near prepared for it. Many of the questions I don't even understand. Others I just have no idea how to approach. Only a very few do I feel more or less OK about. I feel like I now have to spend the next few months teaching myself all the stuff I should have been learning in my college career already.

I guess I'm just looking for some encouraging words or some pointers or something...

xaos

its my understanding that until youve had a strong course in topology you will not be ready for the subject test. and only at the most advanced programmes will see topology at the undergraduate level.

hubris

At least you are aware of your relative strength.
When I was in my grad program, one of the students had a mental break down due to the fact they got crushed by the coursework and had no idea how flimsy their background was. On paper it sounded impressive, but ouch. Not pretty.

However, you have a good idea what you need to do. So, just learn what you can.

tmc

It's a common understanding that one shouldn't be able to have a degree in mathematics without a course in topology.

Also, yes, a math program without proofs is extremely strange, and at most universities, the tests are about applying the knowledge that you learned into a totally new setting (and, hopefully, also learning something new while writing the test, making it fun and interesting as well as a good measure of one's learning).

Honestly, if you have trouble understanding many of the GRE questions, then you're not currently ready for grad school. Thankfully, you still have a year before that begins, so you should have time to prepare. My advice would be to study hard for the GRE, where you'll need a good score for grad school applications, and once that's done, keep self-studying other parts of mathematics that you feel you should have learned (i.e., redo everything more thoroughly). So take a very light courseload (if possible), and use the extra-time to self-study.

While getting a bad grade on the GRE would be bad, getting accepted into grad school without being ready and subsequently failing courses would be much, much worse. So once you've managed to catch up to the GRE material (you have many months, and if you enjoy math as much as you appear to, this really shouldn't be as hard as it may appear), keep going.

mrb

Thank you for the replies.

After I calmed down from my initial shock things aren't so bad as they appeared at first. Once I looked up some things (reminded myself what vector subspaces are, learned what it means to compare cardinality of sets with infinitely many members, etc), there's really little or nothing on the test that I don't understand at all.

However there is still quite a bit that I don't really know how to approach, especially on a timed test, so I do have a lot of work to do. Just preparing for a test when I don't know almost exactly what will be on it will be pretty much a new experience (I wonder what that says for my college education...). I wish I had seen this practice test a year ago and had started preparing then.

Regarding topology, unfortunately I won't be able to take it. It's not required and only offered every other year in the fall. It is offered this fall but it conflicts with a "Math Seminar" which I AM required to take and this will be the only time I can take it. (I would probably have been able to fit it in somewhere except that I am finishing this undergrad stuff in 2.5 years so my schedule is always packed.)

rodigee

It is VERY strange that you haven't had to do any proofs . Just out of curiosity, what math classes have you taken?

mrb

I've had: Calc 1 through 3, Diff Eq, Linear Algebra, Intro to Modern Algebra, Geometry, and Operations Research. I've also had Discrete Math but that is called computer science.

It's not exactly that we haven't seen a proof. The modern alg class actually did a few of them, but the professor gave us all of them and had us memorize them rather than ever having us try to find one on our own. (By the way... that class started with rings and we never got to groups. It seems like groups may be the more important concept?)

Geometry could have had proofs but... that class was a mess. I had the same professor for OR as for Geometry, and in OR he came in 20 minutes late the first day and told us directly that he didn't care about the class or the subject. He proceeded to demonstrate that very clearly the rest of the semester. He actually enjoyed geometry but... he was a mess. He would come in and announce that he didn't know what we should do today. Then he would end up lecturing on some random, inappropriate topic (he gave us this huge lecture on models of hyperbolic geometry when nobody in the class knew what hyperbolic geometry was). Anyway, we didn't really DO much in the class, except regurgitate exactly what was in his lectures back onto the take-home tests.

uman

Wow. What school do you go to?

tmc

So you've had a total of eight math courses?

The reason you haven't done any proofs is because you haven't had any upper-level math courses. From your courses you listed, you've covered about 3 semesters of a normal math major, so up to half their sophomore year.

morphism

I don't really mean to be discouraging, but if you need to remind yourself what vector spaces are, if you don't know what groups are, and if you don't have any real experience with producing proofs, then you aren't ready for advanced undergraduate coursework, let alone graduate school, in math.

You said you're taking 2.5 years to finish your undergraduate degree. Can I ask why? Maybe you should spend another year or so, so you can at least strengthen your background. And if your school really is as bad as you make it appear, maybe you can try transferring to a better one.

xaos

tmc. yes i should agree although its a bit fuzzy Munkres' topology qualifies: "for seniors and first year graduates"

one idea is take a course in real or complex analysis. then you should see some application of topology on the real line or complex plane.

mrb

I guess I can be a little less anonymous and tell you what school this is. UNC Charlotte. Here is our web page:

http://uncc.edu/

Here is the MATH section of our course catalog:

http://www.provost.uncc.edu/Catalogs/2007-2009/MATH.htm

(note that the descriptions are not necessarily accurate.. for instance the Intro to Mod Alg class says it discusses "especially groups". Well, we didn't mention groups at all.)

The requirements to get a BS in Math are:
Calc 1 - 4
Advanced Single Variable Calc
Advanced Multi Variable Calc
Linear Alg
Diff Eq
Intro to Modern Alg
2 Math Awareness Seminars
One out of: Statistics, Mod Alg, Abstract Linear Alg, or Intro to Topology
3 other 3000 or 4000 level math courses

Plus a lot of General Ed requirements.

So yes, I've had 8 math classes and have 6 more to go.

Here's my situation: As a kid I was smart and did great in school, etc. In high school I got completely disillusioned with school - it seemed like the whole thing was a joke, I felt like I could have done all 4 years of high school in a couple months when I was 10, and here they are making me sit here through this tedious crap for hours every day. So I quit going. I barely graduated, went to college (this same college) for a month or so and then quit that too.

In around October of 2006 (I was 27 at this point) I applied for readmittance and started in Jan of 2007. I had finally gotten my head on straight, my love of learning was back in full force, etc. I knew that this univ was not an extremely good one, but it is in my city and I didn't think I could get in anywhere decent anyway. I had a great SAT but horrible GPA and nothing else worth mentioning.

I started as a Comp Sci major. After I took the first few CS classes and they seemed like they were designed for 3rd graders, I switched to math major/CS minor hoping I would actually learn something.

I am going through in 2.5 years because
1. I am older than most college students and I feel like I'm behind. Even at this rate I will be 29 when I'm done!
2. I'm not really learning anything here, or at least not at a reasonable pace. Drawing it out any further would make me want to kill myself.

So I'm taking 18 hours (6 classes) each semester and 12 hours (4 classes) each summer.

I'm not sure what to think now. As I said at the start, I knew my classes were pretty crappy. I am actually extremely confident about my ability to teach myself what I need to know to prepare for grad school. However if just looking at my transcript is going to make a grad school reject me, that's another story. I do have a good GPA. 3.9+, 4.0 in math classes.

How different are the requirements for a math degree at other schools? I will be going a Bioinformatics research project this fall semester; is there anything else I can do to make myself more appealing to a grad school?

uman

So, you're trying to finish a four-year degree in 2.5 years and are surprised that you haven't seen advanced topics? "There is no royal road to geometry", and just because you're older than the norm doesn't mean you magically don't have to spend as much time as everyone else...

morphism

The thing is, so far your transcript doesn't have any of the fundamental upper-level math courses on it. I'm assuming you're going to be taking these next year, right? Will you be taking any in the fall? If you do well, then this will make your transcript look better. So this should be your focus -- this and doing well on the GRE subject test.

It varies from school to school, but the better ones will probably require analysis (real and complex), topology and a solid course in algebra.

Will you be doing this under the supervision of a professor? If so, how well do you know him/her? If you'll be having a lot of contact him/him, it'll help if you could "dazzle him/her," so to speak. Maybe then he/she will write you a good letter or recommendation.

Good luck!

mrb

I really don't think that's the issue. Somehow if I sat on my butt all summer instead of taking classes I would be in more advanced classes? Granted there is the one scheduling conflict I mentioned with Intro to Topology, but that could have happened anyway. In general I've just been taking classes to fulfill the requirements for my major along with whatever seemed interesting. I never knew I should be doing anything else.

This is all very depressing. Despite the general crappiness of my school I was really excited to be there and felt like I was finally going somewhere after wasting the previous 10 years of my life. And I started to look forward to grad school too. Now I feel like it has turned out that the last 2 years were a waste of time too and maybe I will have to discard or dramatically lower my grad school expectations. I have no idea what to do.

uman

Why can't you transfer to another school and do your last two years there?

mrb

Re: the research, yes it is under a professor and I do indeed plan to dazzle him. It's really not so much "research" per se, I just need to write/update a program for them which shouldn't be a problem.

Transferring is something I'll think about.

I've just rearranged my fall schedule to drop Statistics which I guess isn't important and add Modern Algebra. Analysis and Intro to Topology won't fit but I'm going to set up a meeting with my advisor and see if there's anything I can work out with her. Maybe I can do some kind of independent study thing?