Took DiffEq Over 5 Weeks and Didn't Learn Anything; Retake?

[nickadams]

Two summers ago back when I was a lazy and all-around poor student, I took DiffEq at a community college in 5 weeks because I had heard it was easier than during the regular semester.

It was easy, but I didn't end up learning anything (mostly my own stupid fault), and now I'm wondering if I should take DiffEq again this spring at my 4-year university? I am a much more serious student now but I can't decide if it would even be beneficial for me to take DiffEq at this point seeing as it's a purely computational course at my school (no proofs) and I like to think I've reached the point where I only take proof-based classes.

I'm signed up to take intro to real analysis and intro to abstract algebra next semester and since I don't like taking more than 3 math courses per semester, it has come down to choosing between DiffEq and intro to number theory (all proofs). I realize DiffEq is an important subject (probably far more valuable to math majors than intro to number theory) so I was thinking if I don't take it in the spring I could self-study it this coming summer with the theory.Advice?

 

[nickadams]

Edit: Or I could take the honors diff Eq which still uses boyce + diprima but goes into a lot more theory...

This morning when I made this thread I was leaning toward intro number theory over diffEq but i looked at the book used for the intro number theory class and it seems wayyyy more suitable to self-study than diffEq. Also, I've already taken 1 intro number theory class and a discrete math class that covered a lot of basic number theory so it's starting to seem like differential equation would be the right choice.

thoughts?

 

[micromass]

i looked at the book used for the intro number theory class and it seems wayyyy more suitable to self-study than diffEq.

Why does it seem that way?? Does the number theory look easier than the ODE book?? That's weird...

Anyway, if you're a pure math major, then I'd say number theory is much more important than differential equations. That doesn't mean that differential equations are not important, but they don't really pop up much if you don't do applied math.
If you're a physicist or applied math major, then differential equations is of much more importance.

 

[nickadams]

Why does it seem that way?? Does the number theory look easier than the ODE book?? That's weird...

Well it is intro to number theory; intended as a transition course to get students used to a little more rigor in preparation for abstract algebra and real analysis. And I've decided if I take diffEq, I would take the honors section which means more theory and less computation.

Anyway, if you're a pure math major, then I'd say number theory is much more important than differential equations. That doesn't mean that differential equations are not important, but they don't really pop up much if you don't do applied math.
If you're a physicist or applied math major, then differential equations is of much more importance.

Well crap, now you have me reconsidering all over again! I want to get a taste of as broad a range of math topics as possible while i still can, and seeing as I've already taken 1 semester of intro to number theory, I thought it might be good to see what diffEq is like.
Also, I forgot to mention but the intro to number theory class is not an official class but rather a for-credit conference course where me and 3 other students meet with a professor for one hour a week and the professor tells us what to try to prove that week and we go over results from last week...

Help me decide what to do! Intro to number theory (part 2) conference course, or diffEQ honors?
The only reason I'm a little scared to do diffEq honors is because it will be very time consuming and that takes time away from intro abstract alg and intro real analysis which are extremely important classes to prepare me for the meat and potatoes of a math degree...

 

[bcrowell]

I remember differential equations as a cookbook class. I remember essentially nothing from the bag of tricks I learned. Hasn't hurt me a bit. (I'm a physicist.)

 

[Robert1986]

Can you just audit the ODE class?

 

[nickadams]

I guess that depends on your major. Kinda curious though, were there no test in the course making sure you understood the material?

im a pure math major. But back when i took differential equation the first time I was an extremely lazy engineering major and I just memorized how to do homework problems and the test was exactly like them.

Can you just audit the ODE class?

good idea, but if I don't enroll in the course I'm going to have to take 2 other nonmath classes to make up the hours and that seems like a waste

i will consider it though...

 

[AlephZero]

Just my 2 cents worth:

A cookbook course in how to solve DEs is fairly useless on its own. Nobody employs people to do that stuff, when Mathematica can do it faster and without making careless mistakes.

A course on the "theory" of DEs (theorems about the existence and uniqueness of solutions, for example) would be more interesting mathematically. In a sense, it's bridging the gap between analysis and geometry.

A good course on numerical methods for solving DEs would also be interesting mathematically, but judging from the sort of questions that are asked on PF, these courses seem to be more like learning 50-year-old recipes from a cookbook than doing mathematics, or even learning modern cookery.