What are some tips for a Pure Math major?

[samspotting]

Hi, I have just finished first year in general math and am going to choose the pure math major at my university (uwaterloo). I have a few questions about undergraduate math education.

I wish to do research in math before I graduate, what should I be doing? I am currently learning analysis through rudin, and linear algebra through friedberg on my own. Should I focus my education on the core areas of Pure Math? Or should I be trying to get through some papers now of a field of interest?

What strategy should I take for choosing courses. Should I try and max out on pure math courses, and eventually in my 3rd and 4th year choose hard upper level courses like functional analysis, topology, measure theory, ... or choose a few and spend more time learning outside the classroom.

I am looking for a second major, I like computer science but am also interested in the applied math area. I would need to take a few physics courses and a couple courses in differential equations (ode, pde). Would applied math more than cs? CS would get me more and better coop jobs, while applied math seems more true to a mathematics education. For cs, I would have room for only the minimum needed to graduate with a cs second major.

 

[lax1113]

I am in no way a mathematician or even majoring in math, but just from reading your post it appears you might have answered your own question.

Computer science for a better career outlook

Applied math to be more of a mathematician

 

[samspotting]

True, that was a minor question, I guess I was trying to ask how important are differential equations to upper mathematics? There are no diff eq courses included in my pure math major option. I am seeing them mentioned everywhere though.

 

[ralphhumacho]

For sophomores, most universities make you take one or two courses from each branch of Mathematics (Algebra, Analysis, Number Theory, Prob/Stats etc). Figure out which field (or two) you could see yourself doing research in, and then load up of those courses Junior/Senior year. Don't worry about research until you've taken some upper level classes.

Statistics is a great second major, as is Computer Science. Both are very employable.