ChapterZero

Ha ha! I just finished my comment for the student evaluation survey for CDS202, the course I’ve been complaining about for way too long. I spent 45 minutes crafting this, because I’m sure he’s heard essentially the same complaints the entire time he’s been teaching the course, and yet, from what I can determine, has done nothing to address them. Hopefully I got my message across.

I struggled with this course, almost entirely due to the choice of text: for several reasons, MTA was a bad choice.

MTA’s most egregious deficiency, given the introductory nature of the course, is that the intuition behind the definitions and theorems are unexamined, making it hard to integrate the new concepts. While Marsden did an excellent job of motivating what concepts he covered in class, there was too much material for him to provide such context for most of the reading– that made it a bitch trying to absorb the 80 or so new pages of material each week.

Also, MTA provides more generality (e.g. splitting subspaces and other infinite-dimensional considerations) than is optimal given the pace and length of the course– ultimately, I ended up referring to several of the recommended texts to get a handle on the ideas, and only looking in MTA for the notation conventions and the homeworks.

I really can’t stress how much of a chore it was to read MTA; the combination of high generality, absence of intuition, and brevity of exposition– which make for a good encyclopedic reference– made it a monotonous, unrewarding choice as an introductory text.

If Marsden wrote a book that captured the same kind of intuition that made his lectures a pleasure to attend, it would be a good choice for the course text. Until then, I think MTA should be relegated to a supplementary role; students would better gain an appreciation for and facility with differential geometry from a more introductory book, such as Warner’s.