Undergrad Math Electives (with an eye on Grad School)?

[DarrenM]

Hello there,

I'm currently an undergrad working towards a B.S. in Mathematics. I'm not too far along; I've completed the Calculus sequence and a couple classes after that. I'm currently in the equivalent of an "Intro to Proofs" class, required by my school. I work full-time, so during Spring and Fall semesters I can usually take one or two classes at the very most. As such, I try to take as many classes as possible (or feasible) over the summer. It is my intention to apply to a doctoral program eventually, so I am trying to pick my math electives with that in mind.

I'll definitely be taking the first Linear Algebra course this summer. Where I'm having a bit of difficulty is the electives; I'm required to take three math electives, only one of which can be at the 300 level. (Undergrad classes are given a course number of 1xx, 2xx, 3xx, or 4xx, roughly corresponding to the difficulty of the class.) Oddly enough, Diff. Eq and Partial Diff. Eq are not required courses, but a 300 and 400 level elective. I will definitely be taking those.

The required major courses (that I still need to complete) are:
Intro Linear Algebra
Linear Algebra
Modern Algebra I
Analysis I
Analysis II
Mathematical Statistics I
Three Math Electives (Two 400 level, one 300 level)

I have read that "For grad school in math, linear algebra, real analysis and abstract algebra are absolutely essential." And "Other valuable classes would include a second course in linear algebra, complex analysis, advanced calculus and topology."

At this point, I believe that I will have to try to take some graduate classes at my undergrad institution prior to applying to grad school elsewhere, if only to have some of those classes (e.g. topology) under my belt, since there is no undergrad equivalent here.

I'm getting a bit far afield, so I'll bring this to a close and summarize my concerns in two questions:

1) What electives would it be wise for me to try to take? (For example, from everything I've read not taking differential equations and partial differential equations would be insane if my goal is math grad school.) There is a 400 "College Geometry" class offered this summer, and I was considering taking that, and/or a 400 level "Intro to Statistical Methods" class (which is not the same as the required "Math Stat" class.)

2) Are there any classes not listed under the "required major courses" above that are, nevertheless, "essential" for a math major with an eye on grad school?

Thanks, in advance, for any assistance.

 

[wilsont23274]

Thank you for your questions. To answer your first question, I would suggest taking the differential equation and partial differential equation classes as they are essential for math grad school. As for your second question, I would recommend taking classes such as complex analysis, advanced calculus, and topology if they are offered at your institution. Taking these classes will give you a better understanding of advanced mathematics and prepare you well for graduate school.