Exam+1

For each of the chapters and sections mentioned, students should add more content

Exam 1 will cover:


 * Chapter 2


 * Chapter 3, but not the section on lifts.


 * Lecture notes, including fixed points and groups. Familiarity with the group of isometries of the line, and the group of isometries of the plane.


 * Homework including Problems, but NOT PoMoHoWo.

Question: The inverse calculation Professor did in class, how is that different from the homework calculation? Is it just two different dimensions. The one in class was 2 dimensional and the one on the homework was 3 dimensional? Also does anybody know how he got from x^2-2x^2c+x^2c^2+c^2=1 to (x-1)^2c^2-2x^2c+(x^2-1)=0.

In class we were working on the unit circle (S 1 ) and for the homework we were working on the unit sphere (S 2 ).

x 2 – 2x 2 c + x 2 c 2 + c 2 = 1 x 2 – 2x 2 c + x 2 c 2 + c 2 – 1 = 0 Subtract 1 from both sides. x 2 c 2 + c 2 – 2x 2 c + x 2 – 1 = 0 Same statement, just reordered terms. c 2 (x 2 + 1) – 2x 2 c + x 2 – 1 = 0 Factor out a c 2 from the first two terms. (x 2 + 1)c 2 – 2x 2 c + (x 2 – 1) = 0 Reorder terms to obtain what was completed in lecture.

Anyone found any questions that would be good exercises?

Some questions I found on stereographic projection. They might be helpful: [|http://people.math.gatech.edu/~xchen/teach/comp_analysis/note-stereo-proj.pdf]

Also, the other (not required) text for the course, Geometry with an Introduction to Modern Topology (Hitchman), which can be found at the NYU Bookstore has exercises throughout the first 3 chapters that pertain to the material we've covered.

Are the exercises in that textbook good examples of what we did in class? Is it possible for you to post some of the questions onto the wiki?