Real Analysis or Intro to CS: Which Class Should I Take?

[PieceOfPi]

Hi all,

I'm starting my second year at my uni pretty soon, and I'm trying to make a final decision about the classes that I'm going to take. I still haven't figured out what I want to do in future yet, but I'm thinking of along either academics (not necessarily math, but math is one of my options), or becoming an applied mathematician (I don't know if this is a common position, though) and work in some field that uses applied math to some extent (finance, science, engineering, medicine, etc.)

But either way, I'm hoping to study good amount of math, including both pure and applied, since I find both of them pretty interesting. I personally want to take both real analysis and intro to computer science, but they're both offered at the same time, so I won't be able to take both. If I decided to take real analysis, I might take another applied math course (either stats or advanced ODE), or take something that counts toward my graduation requirement. On the other hand, if I decided to take CS, I'm probably going to take abstract algebra because I do want to gain some mathematical maturity before becoming a junior (and abstract algebra sounds fun, too!). Note that I don't necessary have to take a math course this year, but I'd personally like to squeeze many math classes as possible, so I'm hoping to take at least one math class each quarter.

I personally think they're both important classes, since many applied math comes from analysis (DiffEq, statistics, etc), but I also think I need to know something about programming.

Let me know if you have any suggestions, questions, or comments.

Thanks!

EDIT: I'm mainly having a hard time making this decision because
(i) I'm more interested in algebra than analysis, since I personally liked linear algebra a lot. However, I took a class in elementary analysis, and thought the subject was somehow exciting.
(ii) I'd like to be more well-rounded in other subject areas before becoming a junior or senior, and that's why I'd like to learn something about computer science earlier (who knows, I might enjoy CS).

So it looks like I should pick CS, however, if I took analysis this year instead, I can save some time in future by finishing my requirement. (Note that I'm not planning to take both analysis and algebra, because that seems like a little too much for me right now. Also, I do want to take at least one math course if I decided to take CS).

 

[Jaunty]

Hi PieceOfPi,

These are both really useful classes if you're planning on using a lot of applied math in your future - you should definitely take both eventually. I assume the CS class you're talking about is more of a programming course than a course on say complexity theory. If so, then I would recommend taking it first just because it may open up some possibilities to do some undergrad research in applied mathematics if you're interested (not that analysis won't help, but in my experience a lot of the undergrad research jobs involve a healthy amount of coding). Plus, real applied mathematicians do tons of modeling and numerical work that requires a good deal of programming knowledge.

If you're dead-set on taking a lot of more advanced math classes though, then the analysis course might be better for you. As you mentioned, it will open up a lot of higher-level courses on differential equations, measure theory, wavelets, statistics, etc. Although there are plenty of upper-level math courses you can take that are independent of analysis.

Anyway, I always liked taking a technical course or so each semester that was somewhat outside my area of expertise (physics). One of my favorites turned out to be an algorithm analysis class I took in the CS dept my senior year. Undergrad is still a good time to get some breadth in areas you won't go on to specialize in.

 

[PieceOfPi]

Jaunty,

Thanks for your reply. Right now, I'm signed up for real analysis and advanced ODE (I don't know much about this course, but apparently it will cover materials like stability theory, Liapunov's second method, periodic solutions, and chaos). But I'm still thinking about real analysis and CS, but I can also take another CS course in a different quarter, so right now I'm leaning more toward analysis.

BTW, what kind of research is available in applied math (Or math in general)?

 

[Jaunty]

As I mentioned, both classes will be very useful to you - take whichever one you prefer at the moment (ODEs are also a good choice btw). As for research in applied mathematics (and pure math as well), it's a huge field and your best bet is to just check your department's webpage for a list of active research areas. At my old university these ranged from engineering-esque things like numerical fluid dynamics and population modeling to more pure math areas like chaos and general DiffEq research.