0708-1300/Homework Assignment 3

0708-1300/Navigation Panel   Add your name / see who's in! # Week of... Links Fall Semester 1 Sep 10 About, Tue, Thu 2 Sep 17 Tue, HW1, Thu 3 Sep 24 Tue, Photo, Thu 4 Oct 1 Questionnaire, Tue, HW2, Thu 5 Oct 8 Thanksgiving, Tue, Thu 6 Oct 15 Tue, HW3, Thu 7 Oct 22 Tue, Thu 8 Oct 29 Tue, HW4, Thu, Hilbert sphere 9 Nov 5 Tue,Thu, TE1 10 Nov 12 Tue, Thu 11 Nov 19 Tue, Thu, HW5 12 Nov 26 Tue, Thu 13 Dec 3 Tue, Thu, HW6 Spring Semester 14 Jan 7 Tue, Thu, HW7 15 Jan 14 Tue, Thu 16 Jan 21 Tue, Thu, HW8 17 Jan 28 Tue, Thu 18 Feb 4 Tue 19 Feb 11 TE2, Tue, HW9, Thu, Feb 17: last chance to drop class R Feb 18 Reading week 20 Feb 25 Tue, Thu, HW10 21 Mar 3 Tue, Thu 22 Mar 10 Tue, Thu, HW11 23 Mar 17 Tue, Thu 24 Mar 24 Tue, HW12, Thu 25 Mar 31 Referendum,Tue, Thu 26 Apr 7 Tue, Thu R Apr 14 Office hours R Apr 21 Office hours F Apr 28 Office hours, Final (Fri, May 2) Register of Good Deeds Errata to Bredon's Book

Announcements go here

Reading

Read sections 8-10 of chapter II of Bredon's book three times:

• First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.
• Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.
• And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.

Also, read section 12 of chapter I of Bredon's book, but you can be a little less careful here.

Doing

Solve the following problems from Bredon's book, but submit only the solutions of the problems marked with an "S":

problems	on page(s)
S1, S2, 3, S4, S5	88
S1, 2, 3, S4, 5	89

Note that these problems largely concern with material that we will not cover in class.

Due Date

This assignment is due in class on Thursday November 1, 2007.

Just for Fun

• Trace the proof of the Whitney embedding theorem to find an embedding of the two dimensional real projective plane, ${\mathbb {R} }{\mathbb {P} }^{2}=S^{2}/(p=-p)$, inside ${\mathbb {R} }^{5}$. Do not do anything explicitly; just convince yourself that indeed you can find a small atlas (how small?), use it to embed ${\mathbb {R} }{\mathbb {P} }^{2}$ in some large ${\mathbb {R} }^{N}$ (how large?), and figure out how many times you will need to use Sard's theorem before you're down to the target, ${\mathbb {R} }^{5}$.
• Now see if you can come up with some cleverer way of viewing ${\mathbb {R} }{\mathbb {P} }^{2}$, that will allow you to explicitly embed it in ${\mathbb {R} }^{5}$.