Can I Pass the GRE Math Subject Test with a Lightweight Math Education?

[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]

However if just looking at my transcript is going to make a grad school reject me, that's another story.

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.

How different are the requirements for a math degree at other schools?

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

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?

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]

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...

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?

 

[tmc]

so after two years, if you've spent 6 courses per semester and 4 in summer, that's 32 courses total.
8 of those were math, so 1/4 of your courses.
What happened? You said you were filling your schedule with whatever seemed interesting, and obviously these weren't math classes. So what does interest you?

Bottom line is, you've spent 2 years at the university, and you know about as much math as someone who has spent 2 years doing math at university, out of a 4-year program. Just because your university so happens to give out degrees preemptively, doesn't mean you'll be ready for grad school after completing the requirements.

Now since you can take 6 courses at a time and maintain a GPA close to a 4.0, then hey, you're probably not the problem. Choose your courses differently if possible (i.e., fill as much math as you can), and strongly consider staying an extra year to take more advanced classes, as well as gain more research experience.

 

[mrb]

so after two years, if you've spent 6 courses per semester and 4 in summer, that's 32 courses total.
8 of those were math, so 1/4 of your courses.
What happened? You said you were filling your schedule with whatever seemed interesting, and obviously these weren't math classes. So what does interest you?

It's not really quite 2 years. I started in Jan of 2007. So I've had 3 semesters and I'm almost finished with my 2nd summer. So 26 courses. A lot of those extra courses of course went to filling the ~42 hours (14 courses, although I'm not quite done with all of them yet) of random general ed requirements. Then my math major also requires 11 hours of science which I didn't mention. Then another chunk for my CS minor. And yes I do have other interests. I took a trip this summer for credit related one of my interests. I love math too. I was under the impression that this was what one did at a university; it never even occurred to me that the school's requirements for a math degree would not be considered a sufficient undergrad math education.

 

[tmc]

Oh okay.
So you've taken 3 semesters
And as I said in I think my first post in this thread, you have about the math knowledge of someone with 3 semesters under his belt.

I'm not quite sure I see the problem. Take the other 5 semesters, keep learning, and then go to grad school. No point finishing 1.5 years early if you haven't learned 3 semesters worth of material.

You're doing nothing wrong with respect to enjoying your university experience. You're simply lying to yourself that you can have the same math education that everyone else does in 4 years, but in only 2.5 years. Get over it and do the last three semesters like everyone else. You're not behind, you're exactly on time.

 

[mrb]

This fall I will be a 2nd semester Junior. You can call it 3 semesters if you want but I have the credit hours of someone who has taken 5 semesters. I can't just stay at the school for 5 additional semesters; they penalize you if you take more than I think 6 hours over what you need to graduate. What may be an option is for me to just not take anything next summer and instead take classes the following fall when advanced math classes will presumably be offered (although topology won't be available; it is only alternate years). Of course that would delay my potential entry into grad school an entire year and I'm skeptical about how productive that would be from any standpoint except making my transcript look better.

Everyone's making it sound like there are tons of classes I'm lacking but I'm not clear on what they are. Topology, a better Algebra, and Analysis. What else?

 

[tmc]

I'll be clear then, because it seems like it will be helpful for you:
If you enter (or try to enter) grad school in mathematics without topology, abstract algebra and analysis, you'll be at least two years behind everyone else. These aren't extremely advanced topics that many people don't cover, these ARE what the mathematics degree is about. And you don't seem to have any of them. This isn't just a question of being able to understand the GRE question, but a question of not failing out of grad school because you're too far behind.

If you're not willing to spend an extra year just to take a few classes, and since your university is preventing you from taking more math classes (seriously, what kind of university is this), then my best advice would be to learn these things on your own before grad school. Be aware though that you'll have a good 5+ worth of courses to self-study, and that's really just to get the minimum required (ie, topology, analysis, some advanced algebra). So try to keep your schoolwork to a minimum if possible, and use the free time to self-study these advanced topics.

 

[mrb]

I really do appreciate your advice.

I just met with my undergrad advisor and discussed all this. She was very surprised that someone thought Topology would be necessary for grad school. She said the Advanced Calc classes I am taking the next 2 semesters are Analysis classes. And I am in fact going to be taking another Modern Algebra course this next semester. She thinks I am right on track to apply for grad school this winter.

Now maybe she is fooling herself, or maybe she is just aiming a lot lower than what I'm thinking. Or maybe you're wrong. I don't know.

My concern as far as taking these classes really is pretty much limited to preparing me for the GRE and looking good to a grad school, because as I said earlier I am extremely confident about my ability to learn these topics through self study over the next year in addition to my schoolwork, which at least up to now has required very little time outside of class.

In any case I'm now going to try to discuss the issue with the grad coordinator for yet another opinion. Ideally I will be able to do some kind of independent study of Topology for credit.

Do you think my classes "Advanced Single Variable Calculus" and "Advanced Multi-Variable Calculus" are sufficient for Analysis or should I look into another class as well?

 

[tmc]

It really depends on how the analysis courses are taught (though if you have an outline of the courses, we can tell you if they're good). If they're like your previous courses and contain no proofs, they'll be pretty worthless. If they're taught like regular analysis courses, then 2 semesters of analysis should help a lot. So will the other semester in modern algebra.

Topology isn't really necessary, but it's definitely the norm to have taken it, and it will probably be frowned upon not to have it. Topology is pretty much the basis of a lot of mathematics, and touches on just about every subject, so the large majority of universities make it a compulsory course. For example, pure math majors at my university tend to have taken three upper-year topology courses by the time they graduate (as well as three analysis courses and at least 3 upper-year modern algebra courses).

That being said, preparing for the GRE really shouldn't be too hard. The GRE doesn't cover the more advanced topics, so you've probably seen most of what is covered, just not in a proper formal setting. If you're confident in your ability to learn, picking up a slightly more advanced book on subject matter you've already encountered should be fairly easy

 

[JasonJo]

To have a real shot at grad school, you really need to have taken a topology course, an analysis course and an abstract algebra course. Why? Think about it, those are your first year grad courses. If you haven't taken them at the undergrad level, it's going to be murder taking them for the first time at the grad level. Also keep in mind, a lot of kids in grad school have ALREADY taken grad topology, grad analysis, grad algebra at their undergrad institutions.

 

[mrb]

In case anyone cares about a followup...

I've decided to delay the GRE and grad school applications for a year. This is really disappointing for me but I have no choice; getting a satisfactory score on the GRE is just not going to happen right now. This will also mean I can slow down my ridiculous pace at school. 18 hours of freshman level classes was a cake walk; 18 hours of upper level classes is starting to get silly.

I still don't think the key is going to be taking more classes at this school. A poster said "... if you need to remind yourself what vector spaces are... then you aren't ready for advanced undergraduate coursework." Well, I took the Linear Algebra course, made an A, and didn't learn what vector spaces are. So I'm going to have to do it on my own.

Right now I'm taking the Analysis course I mentioned (Adv Calc), Abstact Alg, Topology, Calc 4, and non-math stuff. The math is still more lightweight than I would prefer but it has at least moved towards real math territory. We actually have to write proofs (sadly, a lot of students are having real trouble with this... they have had 2 or 3 years of paint by numbers style math and now are suddenly dropped into courses that require a little bit of sophistication and they don't know what to do).

This is all a little bewildering to me. I am not used to being unprepared. Anyway, this way I will have until November of next year to prepare for the GRE and until the following fall to prepare for grad school. Hopefully I will be able to get into a good school; I don't know how weak my undergrad stuff will look.

 

[ralphhumacho]

Yeah... you're making the smart decision. Even if you got in somewhere, it's better to wait a year and strengthen your background, otherwise you will drown in Grad School.

As for the GRE Subject Test, make sure you go over all the practice tests and get used to the format/timing/tricks. The first practice test I took, I got like 32/66 correct and was very discouraged. Then as I went through EACH problem and figured out why I did it wrong/didn't get it (lots of stupid mistakes, overlooking simple tricks), I took another practice test 2 weeks later and got 47/66 correct. It's all about getting into the "find a trick fast and solve fast" mindset. That, and you need a VERY strong understanding in the basics (Calc I-III, Diff EQ, Lin Alg, Abs. Algebra) and at least a basic understand of the other topics (Analysis, Topology, Complex Vars, Probability etc.)

Good luck. I think you made the right choice.

 

[jhicks]

Calc 1 - 4

Calc 4? Good lord, they have ill-prepared you for the pace of a regular university class.

 

[mrb]

I'm taking that to mean that you think it's unusual that the Calculus material is spread out over 4 semesters?

Yeah. Looking through other school's course catalogs, I haven't seen any others offering a Calc 4.

The class seems to be more or less a retread of Calc 3 with maybe a little bit more. In my case this is a very good thing as the Calc 4 prof seems to actually care that we learn. (I got through Calc 3 with an easy A... without knowing how to find a tangent plane or what Green's Theorem is or Curl and Div... notice a trend?)

 

[ralphhumacho]

I'm taking that to mean that you think it's unusual that the Calculus material is spread out over 4 semesters?

Yeah. Looking through other school's course catalogs, I haven't seen any others offering a Calc 4.

The class seems to be more or less a retread of Calc 3 with maybe a little bit more. In my case this is a very good thing as the Calc 4 prof seems to actually care that we learn. (I got through Calc 3 with an easy A... without knowing how to find a tangent plane or what Green's Theorem is or Curl and Div... notice a trend?)[/QUOTE

hmm - some schools still go by the old naming stanrad, that is, calc III is multivariable calc and calc IV is diff eq. is this true at your school maybe?

 

[mrb]

No. Diff Eq is a different class which I have taken already.