Choosing a class: CS vs. ODE vs. stats.

[PieceOfPi]

I am an incoming sophomore that is majoring in math and having a potential interest in studying physics along side. Right now, I'm trying to take one more class alongside of physics (first year), abstract algebra, and history (for grad requirement). So far, I found these three courses to be interesting, so I'd like to know which would be the best.

1. Computer Science I
The first sequence of the first-year computer science course that mainly teaches programming using Java. I have a very little experience w/ programming, and I always wanted to know a little bit about it. And it also sounds useful if I'm studying math and/or physics, but I don't know if Java is the right language, after reading some people's recommendations (e.g. FORTRAN, C++).

2. Ordinary Differential Equations
I've taken the "Introduction to Differential Equation" course already, but I'm assuming this course is going to be more advanced than the introductory course (since it has Elementary Analysis or Honors Calculus as a prerequisite). I don't know what this course really covers, so I emailed the professor who's teaching this course to get some idea. But besides that, I think this might be an interesting and a useful course to take, especially if I want to study physics, but again, I might be wrong.

3. Intro to Statistics
A stat course for people who have taken single-var calculus. Since I don't know much about stats and probability, I thought this might be a good course to take.

Let me know if you have any suggestion.

Thanks!

 

[will.c]

All three are great classes, but I'd take ODE, and then Stats would be my second choice. Programming is something that you can always pick up as you need it, whereas manipulating differential equations is a huge part of physics and applied mathematics.

 

[PieceOfPi]

Thanks for your reply! BTW, here's a short description of the ODE class that I found on my school website: "Ordinary differential equations. General and initial value problems. Explicit, numerical, graphical solutions; phase portraits. Existence, uniqueness, stability. Power series methods. Gradient flow; periodic solutions." And I agree diff eq. seems to have a lot of important applications in many areas.

Any other suggestion is appreciated.

 

[tmc]

All three courses seem exceptionally useful.

Computer Science is something that everyone in math or physics needs to learn, period. It doesn't really matter what you end up going into, you will at some point be writing code, period. While the course teaches Java, if it's anything decent, it will focus on the concepts which themselves apply to most other languages, and simply uses Java to teach them (which a large number of universities do).

ODE might overlap with Intro to DE, especially if it doesn't list it as a prerequisite. DE is obviously extremely useful, but if you've already seen 75% of the material, it may not really be worth it.

As for stats, I'm quite surprised that's not a compulsory class for a math major...

Overall, I'd really suggest finding a way of taking all the courses (maybe not at the same time, but you have many years still until you graduate). Would you be able to fit two of these this semester?

 

[PieceOfPi]

Yeah, I'm surprised that stat is not a mandatory course too, but I'm certainly planning to take it someday.

What else from ODE should I be familiar with, besides finding solutions to first order equations (linear, separable, autonomous, exact, etc), second and higher order linear equations (homogeneous /nonhomogeneous), and systems of first order linear equations? In my introduction class, we've covered Chapters 2, 3, 4, and 7 on Boyce/Di Prima textbook (which are the stuff I listed above), but I wonder if any other chapters are important. Also, that ODE course uses Boyce/Di Prima textbook, so it's possible there may be some overlaps.

I'm personally more interested in taking PDE/Fourier Analysis, but that class is not offered until Winter Quarter. And that ODE course is not a prerequisite for that class (Intro to DE is).

I can take two of those classes this quarter if I give up abstract algebra, which is little sad b/c pure math has started to interest me, but again, I still have time to take it in future (and who knows? I might find out physics is more interesting this year).

 

[PieceOfPi]

Since this is an old thread, I'm not so sure if I'll be getting any reply, but I just got a reply from the professor who's teaching that ODE class. And here's the list of what he's going to cover in class:

-Systems of first order linear differential equations
-Fundamental matrices and eigenvalues
-Existence and uniqueness
-Stability and the phase plane
-Autonomous system and stability
-Almost linear systems
-Liapunov's second method
-Periodic solutions and limit cycles
-Chaos

So it looks like most of the topics will be from chapter 9 of Boyce/DiPrima text. Do you think these topics are worth studying in class?