Grad level classes...

[xorbie]

So I'm contemplating taking some next semester, which would be the second semester of my junior year. (Although I'm actually only in my second year here, I just had enough AP credit to have sophomore standing.)

I'm just wondering if, for those who have taken them, particularly math classes, do you find them to be a lot harder? Or just more advanced?

My courseload this semester is pretty hardcore, and I want my next semester to be a bit easier so I can spend some time doing research on campus.

So basically, what are your experiences with grad level math classes, especially if you took any as an undergrad?

I'll probably post this at II too, but Goliath can't poster there...

[Roland98]

I can't speak to math classes, but I didn't really find the grad classes I took to be much harder, necessarily. I liked them much better than most of my undergrad survey courses, simply because they assumed so much previous knowledge and didn't waste so much time "catching you up" so everyone would be on the same page.

As an undergrad, I took a lot of graduate-level courses. Most were in epidemiology (since my university had a school of public health) but 2 were in history of medicine--and I wasn't a history major. I was always so much more excited to do work for them (even though the work load generally was greater) because it was more than simple papers and regurgitation of facts*; for example, in my infectious disease epi course, we actually wrote a grant proposal for a study, and got to do some real analysis; and for one of the hist. of medicine classes, we were granted access to some of the rare book library's treasures to use for a final paper. I have no idea if math ones would be as much fun, but the grad courses I took as an undergrad were just so much cooler than the majority of the undergrad ones.







*Yeah, I'm probably making my undergrad courses look a little easier and more boring than they actually were, but such is the power of selective memory. :)

[xorbie]

Cool, sounds basically like what I'm hoping for.

[Goliath]

Hmmm, well graduate courses in mathematics are definitely more advanced and move at a faster pace. But if you've taken most of the upper-division undergraduate courses, then a grad course would definitely be worth trying. It'll look great on your transcript (especially in your Junior year...wow! :eek: ) and if it ends up being a bit too much, then you can always drop the course within the first few weeks.

As to just how much faster a graduate course can go...when I took the 400-level Abstract Algebra course at NDSU, we spent a few weeks going over functions, binary operations, equivalence relations, divisibility properties of integers, etc, before dipping our toes into group theory.

Now, in the first day of the first 700 level Algebra course that I took, the instructor introduced himself, handed out the syllabus, made a few remarks about the syllabus, asked if there were any questions, and then started writing "Definition: A group is a non-empty set G along with a binary operation * satisfying....."

Oh, another thing to mention about graduate courses that you may not be aware of is the graduate grading scale:

"A" means "Adequate"
"B" means "Bad"
"C" means "Catastrophic"
"D" means "Dumbass!"
and "F" means "Fucking Retard! Get the hell out of here, before I beat you to death with my bare hands!!!"

Well...okay, maybe the last two were a bit of an exaggeration...:wink: But you get the idea. If you show up to class, hand in your assignments on time, and put in a lot of work, you should have no problem getting an A (of course, 99.9% of the time when someone doesn't get an A in a graduate course, it's probably because they didn't put in the necessary amount of work).

Oh, and one more thing: which graduate course were you looking at taking?

[xorbie]

Straight from the horses mouth:

Math 551: Dynamical Systems Theory (http://courses.uiuc.edu/cis/catalog/urbana/2004/Fall/MATH/551.html)

(MATH 467) Course is an introduction to the study of dynamical systems. Students who intend to do research in nonlinear dynamics are encouraged to take this course. Specific topics will be chosen to illustrate the theory and use of techniques from global analysis and nonlinear dynamics such as (1) discrete dynamical systems, (2) global theory of ordinary differential equations, (3) Hamiltonian systems, (4) KAM theory, (5) bifurcation and stability, (6) Hopf index theory of vector fields, (7) Morse theory of gradient vector fields, (8) Lyapunov theory, (9) infinite dimensional dynamical systems, (10) structural stability. Prerequisite: Consent of instructor.

Either that, or Math 554: Linear Analysis & Partial Dif Eq (http://courses.uiuc.edu/cis/catalog/urbana/2004/Fall/MATH/554.html)

(MATH 495) Course will provide students with the basic background in linear analysis associated with partial differential equations. The specific topics chosen will be largely up to the instructor, but will cover such areas as linear partial differential operators, distribution theory and test functions, Fourier transforms, Sobolev spaces, pseudodifferential operators, microlocal analysis, and applications of the above topics. Prerequisite: MATH 447, 489 or consent of instructor.

The thing is, I haven't taken all of the undergrad math classes yet; in fact I still have to take abstract algebra, complex analysis, differential geometry and a numerical analysis class. However, I'm thinking of doing systems type stuff for my PhD, and want to know now if it's my type of thing. Because if not, I certainly don't want to waste time taking all sorts of biology classes that, while interesting, won't do me good if I decide to go to grad school just for math.

[Goliath]

Straight from the horses mouth:

Math 551: Dynamical Systems Theory (http://courses.uiuc.edu/cis/catalog/urbana/2004/Fall/MATH/551.html)


Hmmm...well, I've never taken a course in Dynamical Systems, but there were quite a few Ergodic Theorists at NDSU when I was a graduate student. If I remember correctly, a Dynamical System is a measure space along with some kind of transformation from the space to itself.

My impression is that the graduate version of this course will be extremely difficult, and may be a bit too tough...then again, I don't know for sure, since I have had exposure to only some (at best) of the buzzwords mentioned in the course description, and since I don't know exactly what level you're at, mathematically.



Either that, or Math 554: Linear Analysis & Partial Dif Eq (http://courses.uiuc.edu/cis/catalog/urbana/2004/Fall/MATH/554.html)



Well...I haven't had a course in PDEs, either...however, this course sounds like it would be more doable for you (but keep in mind that this is coming from someone who never took a PDE course and whose only course in differential equations was a 200 level ODE course).



The thing is, I haven't taken all of the undergrad math classes yet; in fact I still have to take abstract algebra, complex analysis, differential geometry and a numerical analysis class. However, I'm thinking of doing systems type stuff for my PhD, and want to know now if it's my type of thing. Because if not, I certainly don't want to waste time taking all sorts of biology classes that, while interesting, won't do me good if I decide to go to grad school just for math.

Well, here's my advice, as best as I can give it: You can try to take one or two of these courses, if you'd like...however, you might not have the background for them (especially 551). However, Father Time is on your side...hell, you've still got shitloads of time left. So if I were you, I'd concentrate on my undergraduate coursework a bit more...get some exposure to algebra, complex analysis, real analysis, etc, so that you can have an even better idea as to which field you want to go into for graduate school.

[xorbie]

Yeah, I looked more into 551 and it doesn't look like that will happen. I am pretty set on taking 554 next fall I guess, because I already have the prerequisite courses (Advanced Real Analysis and Differential Equations II).

The problem with "shitloads of time" is that currently I'm not planning on going into grad school in math per se. I'm trying to get into systems biology, specifically the CSB program at MIT (see here (http://csbi.mit.edu/csbieducation)). In order to do that, I'll need to take a lot of biology classes, and I don't want to do that if I decide that I actually prefer topology (totally random example) and want a PhD in math.