Advice For Undergrad Sophomore

Forum for the GRE subject test in mathematics.
d3dx3
Posts: 4
Joined: Wed Jan 03, 2018 3:54 pm

Advice For Undergrad Sophomore

Postby d3dx3 » Wed Jan 03, 2018 5:06 pm

Hi everyone, as the title says I'm currently a sophomore in undergrad. I am planning on getting a pure math phD after I graduate (2020), not really sure specifically what I want to study but maybe number theory or topology. In terms of career I want to go into research.
Basically I am looking for any tips or advice on what I can do now so I can be a competitive applicant. If there are any mistakes, regrets, things I should avoid, please let me know those as well.
I think my dream schools are Cornell, Berkeley, and U of Chicago. I have read on their websites about their programs but not done any deep research about their faculty and specializations and such. As I said before I myself am not sure about what exactly I want research, but I wanted to list them just to give an idea the level of competitiveness I am aiming for.

Here is some information about me:

Undergrad Institution: Small, unknown, liberal arts
Major(s): Math and computer science double major
Minor(s): Japanese
GPA: 3.8 (3.6 math)
Type of Student: Domestic, white, nonbinary. Also have autism, maybe get some diversity points

Have not taken the GRE yet.

other:
- I do not really have research experience besides meritorious winner in COMAP's MCM. Hoping to do an REU this summer and the next, or BSM.
- I graded for a stats class and tutored a high school student for the SAT, but besides that no real relevant work experience.
- Math department is small so I have gotten to know most of the professors; I think I will get good letters.
- I slacked off my first semester but I have a better work ethic now and am confident I can raise both GPAs.

Some questions I have:
- Is the mGRE more important than the GRE? Or does it depend on the school? I ask because I think I could only afford to retake one of them.
- When should I take the GRE/mGRE? I was thinking this summer or during my junior year, because I want time to retake if needed, but I am sure having more time to study would be beneficial as well...I also don't have a lot of money to spare so the senior year discount is appealing.
- I live in Chicago and was thinking of reaching out to the departments at U of Chicago and Northwestern to learn about their programs. Is this a good idea/is there a good way to do this? I am afraid I'd be annoying but I would like to learn what its like to be a phD student and make connections and such. Any other schools that would be good to check out in the Chicago area?
- Any other good websites I should check out that are helpful for looking for grad schools and such? I was really glad to find this one, it looks so useful!

Thanks for reading my long post and for any advice!!!

kieroda
Posts: 28
Joined: Thu Feb 16, 2017 8:45 pm

Re: Advice For Undergrad Sophomore

Postby kieroda » Wed Jan 03, 2018 5:45 pm

Your profile looks fine so far. Here are some bullet point answers:
  • Research experience isn't too important, but if you can get an REU it's a good place to make connections and it does look good.
  • Letters of recommendation are arguably the most important part of the application, so try and get to know a few professors.
  • The math subject GRE is far more important than the general GRE, I'm pretty sure most schools don't care about the general GRE at all. Take the subject GRE whenever you can find time to study and do the practice tests beforehand.

d3dx3
Posts: 4
Joined: Wed Jan 03, 2018 3:54 pm

Re: Advice For Undergrad Sophomore

Postby d3dx3 » Wed Jan 03, 2018 9:23 pm

kieroda wrote:Your profile looks fine so far. Here are some bullet point answers:
  • Research experience isn't too important, but if you can get an REU it's a good place to make connections and it does look good.
  • Letters of recommendation are arguably the most important part of the application, so try and get to know a few professors.
  • The math subject GRE is far more important than the general GRE, I'm pretty sure most schools don't care about the general GRE at all. Take the subject GRE whenever you can find time to study and do the practice tests beforehand.


Very helpful, thank you!

djysyed
Posts: 224
Joined: Sat Oct 28, 2017 9:59 pm

Re: Advice For Undergrad Sophomore

Postby djysyed » Wed Jan 03, 2018 9:50 pm

I've reached out to Northwestern and UChicago since I am a student at UIC (Top 30 Graduate Program so definitely apply here as well). Based on the responses I've received from Northwestern faculty, you'd want to do as many guided readings and REUs as possible since you don't have access to graduate courses. In addition, keep your MGRE as high as possible (preferably 90%). Many of the incoming students don't have previous graduate study. Unlike Northwestern, UChicago is a top 5 program so they expect you to have seen a fairly large amount of math and possess the ability to pass their first year sequence, which is very very intense.

I'd recommend checking out r/math on reddit since the math community there is much larger and quite a few PhD students from Top 10 institutions lurk there.
Last edited by djysyed on Wed Jan 03, 2018 11:27 pm, edited 1 time in total.

FreddieBiddleBooty
Posts: 120
Joined: Sat Oct 28, 2017 5:38 pm

Re: Advice For Undergrad Sophomore

Postby FreddieBiddleBooty » Wed Jan 03, 2018 10:58 pm

djysyed wrote:I've reached out to Northwestern and UChicago since I am a student at UIC (Top 30 Graduate Program so definitely apply here as well). Based on the responses I've received from Northwestern faculty, you'd want to do as many guided readings and REUs as possible since you don't have access to graduate courses. In addition, keep your MGRE as high as possible (preferably 90%). Many of the incoming students don't have previous graduate study. Unlike Northwestern, UChicago is a top 5 program so they expect you to have seen a fairly large amount of math and possess the ability to pass their first year sequence, which is very very intense.


To get into a decent school:

I would say rec letters, research experience (just having some, not so much the quality), and grades are most important. Then comes test scores. As far as the MGRE goes, just make a decent score (this means get a score past low 600's at least - other than that the test isn't as important as the former things mentioned). Also make a decent score on the GRE. This isn't mentioned enough on this site. But GRE scores say something about a student.

To get into a great school:

Have great everything. But most importantly have great rec letters and research.

Of course I'm not on an admissions committee, but neither is anyone else on this site. This is just my personal opinion based on what I've seen and what my advisor has told me.

ArtinWedderburn
Posts: 23
Joined: Sat Jan 06, 2018 3:07 am

Re: Advice For Undergrad Sophomore

Postby ArtinWedderburn » Sun Jan 07, 2018 4:30 pm

Obviously I am not in the admission committee so I could be wrong, but the following are what I see and what I hear from others.

1. Yes. GRE mathematics is more important than GRE. In terms of the schools that you want to apply to, you should score at least 800 (around 80 percentile). Nevertheless, for less competitive schools, if the rest of your application is strong enough, you could get in with a score around 700 (around 60 percentile).

2. You should have taken both of the tests by October 2019 if you plan to apply for Fall 2020 programs.

3. You could search for REU programs offered by the schools that you are interested in. You could also take some classes from the local schools you are interested in.

As for your number theory and topology interest:
1. Deleted.

2. If you want to take topology, you should know some basic algebra, such as tensor products, resolutions, etc. If time permits, you can read Hatcher's "Algebraic Topology". You should pay some attention once your class starts to talk about homology/cohomology, which are important in many algebraic areas. However I think most topology classes would teach in a topological fashion so that the homological algebra you learn in topology may be fairly different from the homological algebra you will need in algebra. Again, I don't have any background in topology except taking the topology qual class (which is approximately what Hatcher covers in his book), so I cannot give you any good advice. You can probably consult some topology professors in your department. You can also do some reading courses with them if you are interested.

3. I talked to one of my professor, who worked in graduate admission for five consecutive years. He told me that many PhD programs do not expect you to have any interesting result if you are conducting research in theoretical mathematics. However, it is better if you try to do some research, for example, in REU programs.

Good luck!
Last edited by ArtinWedderburn on Tue Jan 09, 2018 12:07 pm, edited 1 time in total.

djysyed
Posts: 224
Joined: Sat Oct 28, 2017 9:59 pm

Re: Advice For Undergrad Sophomore

Postby djysyed » Sun Jan 07, 2018 8:34 pm

OP, will you have access to graduate level courses or faculty who can supervise graduate level independent studies?

kuz
Posts: 51
Joined: Wed Jan 18, 2012 3:32 am

Re: Advice For Undergrad Sophomore

Postby kuz » Tue Jan 09, 2018 10:55 am

ArtinWedderburn wrote:As for your number theory and topology interest:
1. If you want to take number theory (or any algebra class), you should take commutative algebra as soon as possible. A friendly introductory text is Atiyah's "Introduction to Commutative Algebra". If you want to study number theory, you should read through the first ten chapters and pay attention to topics in integral dependence, discrete valuation rings, Dedekind domains, and completions. If you want to study algebraic geometry, the first eight chapters should suffice (though chapter 11 contains something that will appear in Hartshorne chapter 1). Unfortunately, I don't know any number theory so I cannot give you any further advice.


I could not disagree more with this specific advice. I'm a number theorist who's never read a book or taken a course on commutative algebra (and never needed to!). Commutative algebra is handy for algebraic number theory, but far from necessary - most intro to algebraic number theory texts just prove the basic results needed along the way. Also, there is much more to number theory than algebraic number theory, and a number theory class may be very different from an algebra class!




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