<p>
</p>
<p>A very-generalized undergraduate math program is of the following:</p>
<p>–starting foundation–
Calculus & Analytical Geometry I
Calculus & Analytical Geometry II
Calculus & Analytical Geometry III
Linear Algebra
Differential Equations</p>
<p>After that, the aim is to give you a background on doing proofs of higher mathematics with…</p>
<p>Analysis I,II or Real Analysis I,II or Advanced Calculus I,II
Abstract Algebra I, II</p>
<p>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.</p>
<p>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).</p>
<p>After those courses, then you will get into your math electives that will form your emphasis. Here are some examples…</p>
<p>Applied Math
- Partial Diff Eqs
- Numerical Analysis
- Advanced Vector/Tensor analysis</p>
<p>Computational Math
- 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</p>
<p>Optimization/Operations Research
- Optimization/Mathematical Programming
- Operations Research
- Stochastic Processes</p>
<p>Statistics
- Probability (separate class…not the combined Prob & Stats course for engineers)
- Statistics (separate class…not the combined Prob & Stats course for engineers)
- Regression
- Experimental Design
- etc, etc</p>