differential geometry.... I am constantly being told that this is important stuff for undergradautes to know about and it is taught by the end of the secon year....however, I am not going to be seeing ANY of this stuff at all during undergraduate school. And there isn't even a class offered in differential geometry. However, I was told my the mcs chair that he would set up a directed study in differential geometry since many other students are very interested in it. Is this differential geometry THAT imporant in a ugrad physics curriculum, and if so, why doesn't my school require it???
It CAN be very important- much of relativity is based on differential geometry just as much of quantum physics is based on group theory. It is, however, fairly advanced- I would consider analysis and abstract geometry prerequisites. Typically small colleges do not have regular differential geometry courses. Generally, you can, if necessary make it up in graduate school. I'm not crazy about most "individual" or "directed" study classes since the interaction with other students is an important part of a class but if there are several students who would be taking it- go for it!
would calc 1-3, diffEQ, linear algebra, prob/stats, adv. calc and adv. eng. math (similar to mathematical physics) be sufficient to study differential geometry?
course names are not universal; as you indicate you university isn't teaching what you expected in other places, so why should these be any different? in order to stfy differential geometry you should have a sound knowledge of the basicas of analysis (limits, differentiation of vector fucntions, integration), vector spaces (say to the point where you understand that the dual space of a finite dimensional vector space is isomorphic [but unnaturally] to its dual space), and topology with perticular regard to metric spaces. for instance, a differential manifold is a topological space with an atlas, that is a collection of open subset U_a, for a in A (possibly a finite index , possibly infinite) such that each U_a is homeomorphic to a nieghbourhood of the origin R^n and such that it is well 'behaved on intesections' ot things like (U_a)n(U_b) {i don't think it helps to talk too much about this. we then can transfer the analytic properties of these nbds in R^n to the U_a by pullnig back via these maps. i would be surprised if anywhere in the US taught this before the 3/4th year of undergraduacy if at all. In the Uk I'd have it as a third year course, possibly a second year one depending on how much detail they did it in. eslewhere in europe it could well be in the second year.
Yea I just looked and at my school(in the US) it's a graduate course. I guess won't be taking it, or maybe I'll take it my last semester. I have a friend who did his undergraduate studies in Europe and he says it's alot more work. Is this the case in general?