Differential Geometry without Analysis?

[ROLEX4life]

Hi

I am a 2nd year Pure Mathematics undergraduate student. I have always coveted Differential Geometry as it seems extremely interesting but I do not know much about it. The prerequisites for this class are MAT 208 (Linear Algebra) and MAT 314 (Intermediate Analysis I). I am in Linear Algebra right now and I already passed (my grade is high enough so I am exempt from the final) so that is not a problem. The problem is that MAT 420 (Differential Geometry) is being offered next quarter and I haven't taken Analysis yet. I am signed up for it next quarter. Differential Geometry is only offered during Winter quarters on alternating years so the next time it would be offered would be in Winter 2010 (My senior year). I would have no problem with waiting but the College of Science at our school is in the midst of a budget crisis and some classes will be cut and there is a very realistic possibility that this next quarter will be the last opportunity I will have to take it. The other problem is that my schedule is already pretty rough so adding MAT 420 would only make it rougher. This is what I am signed up for right now:

MAT 314 (Intermediate Analysis I)
MAT 325 (Number Theory)
MAT 418 (Modern Algebra II)
MU 100 (Introduction to Music...my one easy class)

The good news is that MAT 420 does not conflict with any of my other classes in terms of schedule and times. Also, I have a friend who is a graduate student who is signed up for the class and he is willing to drop the class and give his spot to me. He also said he'd help me petition to waive the MAT 314 requirement so they would let me sign up for it.

Now my question is this. Is Analysis really THAT important for Differential Geometry or is it doable while concurrently taking Analysis? Also, if I do take Differential Geometry, I would probably drop either MAT 325 or MU 100. If I swapped MAT 420 for either of those classes, would that be way too hard of a schedule? I don't say this to brag but my professors always tell me to take as much as possible because they are in awe of the fact that I am just a sophomore taking [Modern] Algebra. According to them, I have progressed faster than almost any other math student at the school. I started college in Fall 2006 just beginning in Single Variable Calculus. I say this because I feel that they are just in love with the fact that I am progressing so fast that they forget to stop and think for a minute what would be best for me.

Thanks for your advice.

 

[mathwonk]

the only person who can advise you competently is the instructor. even then he may not be able to give good advice. i have had both experiences in the past. once a professor said all i needed for his class was such and such, i learned it and did fine. another time the prof said i only needed what i could learn by quickly reaDING A CERTAIN SMALL BOOK, BUT THAT BOOK COntained essentially a years worth of material and i did terrible. in general if they say something is required you should assume they are correct. also you seem to have a lot on your plate.

 

[zhentil]

It depends on the level of the course. If it's DG for physics majors, I wouldn't sweat it. But if it's rigorous and you've never taken topology or analysis, I wouldn't rate your chances very highly.