Thanks for the reply, and with that being said, can you tell me what comes after differential equations? I just want to plan for my future classes in college.
A very-generalized undergraduate math program is of the following:
Calculus & Analytical Geometry I
Calculus & Analytical Geometry II
Calculus & Analytical Geometry III
After that, the aim is to give you a background on doing proofs of higher mathematics with...
Analysis I,II or Real Analysis I,II or Advanced Calculus I,II
Abstract Algebra I, II
Now depending on your "emphasis", the number of Analysis and Abstract Algebra courses will vary. If you are planning to go into pure math and/or graduate study in math, then more likely you will have to take Analysis/Real Analysis I & II AND Abstract Algebra I & II. If you plan on doing applied math or math/CS then you will only take Analysis/Real Analysis I and Abstract Algebra I or just one ONE of those courses. Just about NO math department will let you out of there without at least one course in either Analysis or Algebra...regardless of your emphasis.
Note: because of the intensity of these theoretical courses, more and more schools are NOW offering a "Transition to Higher Math & Proofs" course to take after Diff Eq to prep you for the rigors or Analysis/Real Analysis and Abstract Algebra. I would suggest taking that course so that you know how to do good proofs without having to "learn it on the fly" while trying to digest Analysis/Real Analysis/Abstract Algebra at the same time (like us old math majors had to do).
After those courses, then you will get into your math electives that will form your emphasis. Here are some examples....
- Partial Diff Eqs
- Numerical Analysis
- Advanced Vector/Tensor analysis
- Numerical Analysis
- Numerical Linear Algebra
- Combinatorics (jr/sr level class...more advanced than discrete math as sophomore)
- Graph Theory (jr/sr level class...more advanced than discrete math as sophomore)
- Selected CS courses
- Optimization/Mathematical Programming
- Operations Research
- Stochastic Processes
- Probability (separate class...not the combined Prob & Stats course for engineers)
- Statistics (separate class...not the combined Prob & Stats course for engineers)
- Experimental Design
- etc, etc