What topics should I focus on for self-studying mathematics?

[naele]

I'm a biochemistry major who's interested in continuing my studies of mathematics on my own time, mainly for time and monetary reasons (school's getting more expensive) and because I think competence in math can be helpful in other areas. At my university I'm required to go through a full year of calculus and of my own choice I will be taking a linear algebra course and most likely a course in differential equations to prepare myself for the quantum mechanics requirement.

With that said, I'm looking for advice on a list of topics that I can study one at a time in an order that makes sense.

My order so far goes like this:
1 year calculus course
Intro Linear Algebra
ODEs

Thanks for any help.

 

[jacksonpeeble]

I know that the University of Michigan offers a class called "Mathematical Methods in Chemical Engineering." A course like that would probably be beneficial to you, and the resources are pretty readily available online.

Course Description: "Linear algebra, ordinary and partial differential equations, integral equations with chemical engineering applications. Analytical techniques and preliminaries for numerical methods, including: spectral analysis, orthogonal polynomials, Green's functions, separation of variables, existence and uniqueness of solutions."

 

[naele]

There's a course similar like that at my university "Mathematical Methods for Chemists" which uses McQuarrie's Mathematical Methods for Scientists and Engineers book. Ultimately the main reason I'm interested is because I think that a mind used to thinking inside a mathematical framework would be beneficial to my field. That's why I want to continue learning into higher mathematics.

 

[statdad]

Unless your 1-year calculus course includes multi-variable calculus, you may need some of that before differential equations

 

[naele]

Unless your 1-year calculus course includes multi-variable calculus, you may need some of that before differential equations

It most certainly does. Functions of several variables, geometry of space, etc. A pretty typical calc 3 course IIRC.

I drafted a preliminary list based on some of the classes offered at my university:
Analysis
Discrete math
Number theory
Abstract algebra
Complex/Functional analysis
-more stuff if i have time-

But then again, that's just from looking at a course list and seeing what requirements for which class were what. Given that I would be doing it one at a time there might be a better order.

 

[statdad]

Real analysis in place of number theory? (He says at the risk is annoying all the number theorists) - I can't see a lot of use for number theory in your area, but can definitely see analysis used, and it will be needed before complex and functional analysis.

 

[naele]

So a more revised list:
Discrete math
Real analysis
Abstract Algebra
Complex/Functional analysis
-other things like number theory-

While I'm at it, does anybody have suggestions for good books with lots of problems and worked examples?