What's Next After Linear Algebra for an Advanced Math Student?

[beeftrax]

I'm a high school senior, and I've taken Multivariable Calculus and Differential Equations at the local community college. This semester I'm pursuing an independent study in Linear Algebra (because there's nothing else for me to take at the college). What is a typical course for a math major to take following these courses that I could study independently next semester?

 

[quartodeciman]

Here is a guess. You will probably be advised to take solid courses in general topology and abstract algebra. This is considered necessary background for any specialty you might pursue later. Since you have completed MC and DE, real analysis and complex analysis (usually taught separately) might be on your recommended list too. Finally, a course in mathematical logic might be recommended. Past this, the course work would become dependent on your interest.

 

[superman]

did you take any calculus courses in high school to go to mc and de? or do you need to? I was thinking about going to my community college to take some classes after senior year even though i shouldve before it. instead i spent the summer with a book i bought studying by myself. i think time at a college would have been more productive.

 

[Cod]

Here's the order from my university:

Precalculus
Calculus I
Calculus II
Calculus III
Ordinary Differential Equations
Discrete Mathematics
Introduction to Advanced Mathematics
Linear Algebra
The Real Line
Functions of a Real Variable
Calculus and Linear Algebra
Abstract Algebra
Applications of Mathematics

Keep in mind, a lot of the courses above can be taken during the same semester. For example, you can talk Calc I and Discrete Math during the same semester since both have the same prerequisites.

The course sequence differs from school to school somewhat, but for the most part you'll end up taking the same classes to earn your degree. Once you decided on a school and get accepted, you should contact/visit the mathematics department. They can give you all the information you need.

Hope I helped you at least a little.

 

[beeftrax]

thanks for the info, cod and quartdeciman!

superman: I studied calculus on my own the summer after my sophomore year. I agree that a regular class is generally better. I mainly did it this way so that I could dual enroll and thus take college level math classes for free.