<p>@geo: have you even ever taken an upper level math class?</p>
<p>As far as undergraduate courses are concerned, abstract algebra and real analysis have no formal prerequisites beyond experience with proofs and basic high school material. Depending on your particular school, these classes might require some linear algebra or might teach you linear algebra. In either case, calculus classes don’t teach linear algebra properly anyway. Differential equations will only show up in a differential geometry class as an undergraduate in things like showing uniqueness of curves, and even then you only need a few basic results that will take at most a week to learn on your own. Complex analysis and topology usually just require real analysis, or not even that. PDEs are like the only undergraduate course that may require calculus background.</p>
<p>So yea, please enlighten me as to why calculus 1,2,3 and diff eq are generally prerequisites for higher-level math. </p>
<p>The calculus sequence is designed to gather all the math necessary for engineers into one sequence. It has no relevance whatsoever to a math major.</p>