<p>I’m currently a college Sophomore, and am double majoring in CS w/ minors in networking and applied math, and a major in mathematics for information systems.</p>
<p>I’m taking Calculus III this spring, and I’m wondering, what’s next? Is there an equivalent to Calculus IV ? I know differential equations usually come next, but what else is there?
I have a few classes that do require Calc III, such as Numerical Analysis. </p>
<p>I also have to take Abstract Algebra. It’s pre-reqs are linear algebra and advanced discrete math. What exactly is abstract algebra in the first place??</p>
<p>Lastly, is there even a point for me to take so many math courses when my career will revolve around computer science and software engineering? </p>
<p>Depends on what you want to do with CS for example Number Theory has a decent number of applications (encoding/decoding/factorization) as well as courses to do with markov models from what I understand.</p>
<p>That is a lot of interests crammed into your program. I would use a more general CS/Math route while assessing your interests as a junior/senior…then take the appropriate courses.</p>
<p>If you have interests that may lie in the areas of scientific computation, operations research, algorithm development or cryptology, you may want to take some additional applied math courses in those areas. If you are not planning to enter those areas then there would be no reason to take that much math. Here is a CS/Math plan which would satisfy your degree requirements while giving you options to evaluate your interests.</p>
<p>Freshman
Calculus I, Calculus II
Object-Oriented Programming I</p>
<p>Sophomore
Calculus III, Linear Algebra, Differential Equs
Object-Oriented Programming II, Discrete Math/Structures, Computer Organization</p>
<p>Assess your interests!! At this time, you have taken more than enough math for a CS major who does NOT plan to enter areas like scientific computation, operations research, algorithm development or cryptology.</p>
<p>Junior/Senior
Algorithms & Data Structures (may be a combined course or 2 separate courses)
Optional Math Electives
** If Cryptology then take Number Theory, Abstract Algebra, Info Coding Theory
** If Operations Research then take Probability, Stats, Stochastic Processes
** If Scientific Comp then take Numerical Analysis, Numerical Linear Algebra
** If Algorithm Dev then take Combinatorics, Graph Theory, Computational Complexity</p>
<p>Assess your interests again between Junior and Senior years and even during your internship.</p>
<p>To answer your earlier question…Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.</p>