What steps should I take to prepare for a math PhD as an undergraduate?

[inknit]

So I'm pretty sure I want to get a PhD in math...what are the proper steps I need to take as an undergrad?

I'm currently a freshman in Calc II, planning on taking Calc III and linear algebra next semester. I currently know the stuff I'm learning right now inside and out...however I think I might end up with a B, because I missed the 2nd midterm. Would a B in a lower level math like calc II kill my chances at top math programs?


I've also heard that undergrad research is important. Now I could imagine doing undergrad research in chemistry, psychology, or bio...but how the heck am I supposed to get involved in math research?

Lastly, it seems like most math PhD programs require a reading knowledge of French, German, and/or Russian.

I can speak and write French at an intermediate level...but no way can I read French mathematical literature. Do you suggest I take upper level classes in French?


Thanks

 

[Wretchosoft]

So I'm pretty sure I want to get a PhD in math...what are the proper steps I need to take as an undergrad?

What makes you so sure at this point in your undergrad career? I'd recommend keeping your eyes open, as you may not like upper level math courses, or not do well in them, or any number of other things could go wrong...

I'm currently a freshman in Calc II, planning on taking Calc III and linear algebra next semester. I currently know the stuff I'm learning right now inside and out...however I think I might end up with a B, because I missed the 2nd midterm. Would a B in a lower level math like calc II kill my chances at top math programs?

Grad schools won't care too much about your grades in lower level classes, provided you make up for any poor performance by excelling in upper level classes.

I've also heard that undergrad research is important. Now I could imagine doing undergrad research in chemistry, psychology, or bio...but how the heck am I supposed to get involved in math research? [\quote]

Getting involved in pure mathematics research as an undergrad is much more difficult than in other sciences. I can't say much for applied math, but in pure math, getting research experience can involve quite a bit of luck. Here are some tips:

i) Does your college have math seminars for undergraduates, a math club, or something like those? Attending mathematical talks is a good start to scoping out potential projects, and these should be at a level understandable to someone without specialized training.

ii) If you live in the States, look into applying for Math REUs (Research Experience for Undergraduates) the summer of your sophomore or junior year. These programs are highly competitive to get in to, but they are focused exactly on the type of research an undergraduate in mathematics could do.

Lastly, it seems like most math PhD programs require a reading knowledge of French, German, and/or Russian.

I can speak and write French at an intermediate level...but no way can I read French mathematical literature. Do you suggest I take upper level classes in French?


Thanks

From what I've heard, this requirement is more a formality than anything. No program is going to deny you for lack of foreign language experience, and any program which has a language requirement will likely have classes to get you up to speed. In short, having a great understanding of French is nice, but by no means necessary.

 

[vcxp]

So I'm pretty sure I want to get a PhD in math...what are the proper steps I need to take as an undergrad?

I'm currently a freshman in Calc II, planning on taking Calc III and linear algebra next semester. I currently know the stuff I'm learning right now inside and out...however I think I might end up with a B, because I missed the 2nd midterm. Would a B in a lower level math like calc II kill my chances at top math programs?


I've also heard that undergrad research is important. Now I could imagine doing undergrad research in chemistry, psychology, or bio...but how the heck am I supposed to get involved in math research?

Lastly, it seems like most math PhD programs require a reading knowledge of French, German, and/or Russian.
I can speak and write French at an intermediate level...but no way can I read French mathematical literature. Do you suggest I take upper level classes in French?


Thanks

Hi! I'm in roughly the same position as yourself. I can't answer all of your questions, but maybe I can help with some of them.

For the research, assuming you live in the United States, check http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=5044" list to see if there's any place where you'd like to do research at (they will often provide housing, if it's too far away from where you live). Do you know a professor who would be willing to talk to you about research? Even if it's not listed on that page, or you're not in the US, your school might be able to help you out. Keep in mind, however, that you are expected to have some minimum math knowledge in order to do research. For example, I will have finished Calc I-III, Linear Algebra and a course on applied Abstract Algebra (along with several relevant CS courses) before applying to any research this summer. This is just a hair above the minimum requirements for this program, and this isn't even pure math research (it's cryptography). Which courses are you taking next semester?

As for the foreign language, I've talked with several grad students who've made it seem as if it isn't that much of a hard requirement as it once was (it sounds like Wretchosoft has heard the same thing). Regardless, I know of one math book in German that comes with an attached English/German dictionary in order to guide the reader through the book. It might be worth seeing if anything of a similar nature exists for French.

 

[inknit]

I'm at UVa btw. I'm taking Calc III, Elementary Linear Algebra, and Survey of Algebra next semester.

I can take two math classes max in my third semester which will probably be Real Analysis I, and Advanced Linear Algebra (or Intro to Abstract Algebra)

4th semester probably Real Analysis II, Ordinary Differential Equations, Advanced Linear (or intro to abstract algebra), complex variables?

So that's roughly what I plan on taking...

I think I could probably start taking a couple graduate level courses starting my 6th semester (junior year). So what is research in mathematics like?

 

[vcxp]

I'm at UVa btw. I'm taking Calc III, Elementary Linear Algebra, and Survey of Algebra next semester.

I can take two math classes max in my third semester which will probably be Real Analysis I, and Advanced Linear Algebra (or Intro to Abstract Algebra)

4th semester probably Real Analysis II, Ordinary Differential Equations, Advanced Linear (or intro to abstract algebra), complex variables?

So that's roughly what I plan on taking...

I think I could probably start taking a couple graduate level courses starting my 6th semester (junior year). So what is research in mathematics like?

In that case, I'd start calling some of those programs on that list that interest you. Try to get a feel for what it is they expect you to know going into the program. You might be able to find something you can do this summer, but failing that, next summer your chances will be better. It might be worth selecting your courses to fit the requirements of the research program if it interests you enough (for example, if it were me, I'd take intro to abstract algebra over advanced linear algebra, but you might want to do research in linear algebra).

I don't actually know what research is like, because if I get in this summer it will be my first summer of research. (: The program I'm applying for is still pending NSF funding renewal, and even if it does get renewed there's a good chance it won't give a large enough stipend (meaning I'd have to work a normal job instead of doing research).

I do know that the professors there have made it sound very informal. The students will be given, in my case, a problem in cryptography. Under the guidance of a professor, the students work on solving the problem (I'm not sure if the approach is entirely the production of the student, or if the professors will set students on the right path; I suspect the latter), and might even get a publishable paper out of the ordeal, with the possibility of presenting a conference.

Hopefully someone who's already finished an REU will comment.

 

[inknit]

Also, how important is a computer science background for someone who wants to do pure mathematics in grad school?

Right now, I know jack about comp sci/programming, but as part of my math major, I'll be required to take one programming class (which I'll probably take in my sophomore year).