<p>There seems to be a large tree with many branches after calculus... put what should one take after calc? And several classes after that? What would be the highest undergraduate math course typically offered somewhere? Thanks</p>
<p>linear algebra?</p>
<p>I was thinking that but for instance at my local Community College Differential Equations follows Cal 3 and is the last math course offered.</p>
<p>At my school, I believe Number Theory is the highest undergraduate offering, though students who complete it can apply for a graduate permit to take Abstract Algebra.</p>
<p>Applied math like statistics is good.</p>
<p>Typically you would take differential equations and linear algebra or just diff and linear combined in one course in the semester system. From then on, it branches. You can upper div linear algebra or abstract algebra or real analysis. But real analysis is reputed to be the most difficult undergrad math course so you should save it after they take upper div abstract algebra and linear algebra. Then after real analysis, there is complex analysis. Other than that, I think everything comes separate branches consisting of electives.</p>
<p>It depends. Differential Equations, Linear Algebra, and Statistics probably have the most real-life applications.</p>
<p>There are three areas in pure math:</p>
<p>Algebra includes courses such as linear algebra, abstract algebra, (algebraic) number theory, combinatorics.</p>
<p>In the analysis section you could take differential equations, real analysis, complex analysis, (analytical) number theory.</p>
<p>Geometry and topology are not offered everywhere but might be worth a look to.</p>
<p>And then there are a lot of applied math courses that vary a lot from college to college.</p>
<p>linear algebra, ODE,PDE</p>
<p>The introductory part of mathematics consists of calculus (calc 1,2, and 3) and then differential equations. If you were planning on doing more applied things, you'd do a numerical kind of linear algebra class, statistics, probability, more diffEQs etc. If you were planning on doing pure math, you'd start off with a more theoretical linear algebra class, a basic analysis class, and then an algebra course.</p>
<p>The highest "undergrad" class you can take depends on the school. At my school, there's no restriction on undergrads taking graduate level courses.</p>