What classes should I take for a pure maths program?

[abiyo]

Hi everyone,

I am a rising junior in college. I was in Engineering program before I switched to Maths this semester.

My main reason was that I was not intellectually involved in the program that much. So basically I am behind the average Maths major in my school. Right now I am planning my classes for Fall 2010 and beyond. I really like maths and with few maths classes I have taken, I have done quite well. More than the grade, I really have tried to learn the concepts.
For example when I took my probability class, I used Feller for self study although that was not required as a text. I really want to go into Maths Grad school. My main interest is logic and foundations of mathematics but frankly I don't know a lot on the area. My GPA as of now is 4.3. I have taken multi-variable calculus, differential equations and probability. So my question is

1. What classes do you recommend me take for a pure maths program?

2. Do you think I have a good shot of grad school given that I have only two years and the number of my maths classes will not be that many?

Any other advices

Thanks a lot
Abiyo

 

[hitmeoff]

Hi everyone,

I am a rising junior in college. I was in Engineering program before I switched to Maths this semester.

My main reason was that I was not intellectually involved in the program that much. So basically I am behind the average Maths major in my school. Right now I am planning my classes for Fall 2010 and beyond. I really like maths and with few maths classes I have taken, I have done quite well. More than the grade, I really have tried to learn the concepts.
For example when I took my probability class, I used Feller for self study although that was not required as a text. I really want to go into Maths Grad school. My main interest is logic and foundations of mathematics but frankly I don't know a lot on the area. My GPA as of now is 4.3. I have taken multi-variable calculus, differential equations and probability. So my question is

1. What classes do you recommend me take for a pure maths program?

2. Do you think I have a good shot of grad school given that I have only two years and the number of my maths classes will not be that many?

Any other advices

Thanks a lot
Abiyo

I would say that at the very minimum you will have to take the core math classes:
2 semesters/quarters of Linear Algebra
2 semesters/3quarters of Abstract Algebra
2 semesters/quarters of Analysis

Outside of that I am not sure. For pure math, classes like Number Theory, Complex Analysis, Differential Geometry, Topology, etc would be likely electives. For applied math, upper division classes in Partial Differential Equations, Numerical Analysis, Fourier Series, cryptography, probability etc would be in order

 

[owlpride]

The core courses/sequences for a pure math major are real analysis, abstract algebra and topology. The introductory graduate courses in any selective program will assume that you have taken all three. (Adding that missing linear algebra class goes without saying.)

Given your interests and time constraints, the most relevant electives might be Discrete Math, Theory of Computation (might be taught in the CS department), and whatever logic courses your school offers. UCLA and Carnegie Mellon run NSF-funded summer programs in logic in case that's something you are interested in.

 

[abiyo]

Thanks hitmeoff and owlpride for your advice. I will consider the logic summer program. It is something I am really interested in. Does the plan below make sense?

Junior year
Fall Real Analysis, Topology, Linear Algebra
Spring Functional Analysis, Complex Analysis, Logic

Senior Year
Fall Abstract Algebra 1 Elective 1 Elective 2
Spring Abstract Algebra 2 elective 3 Elective 4

I am doing 1 non-maths class every semester. I am taking only 3 to ensure I master the material rather than over burdening myself. My only worry is that if I take Abstract Algebra senior year, would it affect my grad school application? Thanks a lot people.

 

[hitmeoff]

Thanks hitmeoff and owlpride for your advice. I will consider the logic summer program. It is something I am really interested in. Does the plan below make sense?

Junior year
Fall Real Analysis, Topology, Linear Algebra
Spring Functional Analysis, Complex Analysis, Logic

Senior Year
Fall Abstract Algebra 1 Elective 1 Elective 2
Spring Abstract Algebra 2 elective 3 Elective 4

I am doing 1 non-maths class every semester. I am taking only 3 to ensure I master the material rather than over burdening myself. My only worry is that if I take Abstract Algebra senior year, would it affect my grad school application? Thanks a lot people.

Not sure what the pre-reqs for topology are in your school, but at my school you need 1 analysis class before you are allowed to take topology. I am also not sure how this translates into the semester system, but again Real Analysis (including multi-variable analysis) is at least a year long course (at my school single variable analysis is 2 quarters and multivariate analysis is another 2 quarters so that's a year and a quarter). We also typically do 2 quarters (20 weeks) of Linear Algebra, so I am not sure if at semester schools they squeeze in what would 20 weeks worth of linear algebra into the typical 16 week semester. But if your school offers a "Lin Algebra 2" you might really want to take a look at that.

So other than squeezing in another Real Analysis semester in there (maybe in lieu of the logic), I think you pretty much covered the basics of what you are expected to know going into a grad program.

Also, if your school has grad classes in math you might consider taking a few. I wouldn't take any this upcoming year since it would be your first exposure to axiomatic and proof oriented math (believe me, upper division math is a completely different monster than freshman and sophomore level Calc/Lin Alg/Diff Eq). But, depending on how confidant you feel about your performance in classes like Analysis and linear algebra, you might want to consider taking the Algebra series at the grad level. Doing well in grad level courses always looks phenomenal to grad schools. Its not a must, but if you've got the work ethic and talent, you might want to give it a go.

 

[abiyo]

Thanks hitmeoff once again. You are right. Linear algebra is squashed to 16 weeks here and I need to take the extra real analysis course. Maybe I will push Topology after taking analysis 1. I am planning to take grad classes senior year. Hopefully my mathematical maturity will be good by then. Once again thanks.