Math 3593H Honors Mathematics II Spring Semester 2004
Assignment 10 - Due Thursday 4/8/2004
Read: Hubbard and Hubbard Sections 6.3 and 6.4.
Section 6.3 (pages 588-590): 1, 2, 3, 4, 5, 6*, 7, 8*, 9, 10*, 11, 14, 15*, 17a.
Section 6.4 (pages 601-602): 1*, 2, 3, 4*, 5, 6, 7, 9a.
I calculate that if we do about 2 sections per week from now on we will get to the end of Chapter 6 comfortably. The trouble is that the sections are uneven in the demands they place on you. I am inclined to think that getting through both of sections 6.3 and 6.4 this week is a little optimistic, but we can do more than just 6.3. Some of this material is theoretical, like the proof of Theorem 6.4.10 that integrals over oriented manifolds are independent of the parametrization, provided it is orientation-preserving. You can probably believe this anyway, otherwise we wouldn't be doing these integrals, and move straight on to the homework questions which you may be able to do using your intuition. The difference between this class and other undergraduate classes is that we say precisely what we mean by an orientation, whereas the other classes leave this to intuition. If the other classes can do it using intuition, then you probably can too!
Julian: What do oceans do when they meet?
Peter: I don't know. Say, 'It's great to sea you?'
Julian: No, they merely wave.