ChapterZero

This is the end of the third week of CDS202, the geometry course based on MTA, being taught by Marsden. So far the class hasn’t been exactly what I’d hoped for: the lectures are superficial to the point of being useless, while the assignments cover more material than I can absorb in a week.

The first week, which focused on topology, covered the entirety of Chapter 1– not so taxing if you’ve seen topology before (I didn’t do have to do much reading), but I imagine the students with a less structured mathematical background had it hard. The second week covered multilinear algebra, functional analysis (banach and hilbert spaces, the three important theorems of functional analysis, and other miscellany), and differentiation in normed spaces, including taylor’s theorem and the converse, the implicit and inverse function theorems, and the calculus of variations in function spaces. Did I mention there are only two lectures a week? Consequently, Marsden doesn’t even have time to state all the theorems, much less give anything beyond a very broad stroke overview of the material. The third week covered manifolds, tangent bundles, vector bundles, submersions, immersions, tranversality, and Sard’s and Smale’s theorems.

So this course is insane. Fun, in a desperate not to fall behind way, but insane.

Possibly relevant posts:

• Differential Geometry (9/16/2004)
• Differential Geometry (5/31/2003)
• The implicit and inverse function theorems (9/12/2006)