Assignment #1 (5 points) - due Fri. Jan. 20 in class.
Read Sections 1.1, 1.2
Write up the exercise which appears in the text at the top of page 7 (proof of
Thales' theorem).
Assignment #2 (35 points) - due Fri. Jan. 27 at the beginning of class.
Read Sections 1.4, 1.5 (do the reading of 1.4 by Mon. Jan. 23)
Write up exercises 1.41, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48 to turn in.
Assignment #3 ( 35 points) - due Mon. Feb. 6 at the beginning of
class.
Read Sections 1.6, 2.1, 2.2
Write up exercises 1.5.8, 1.5.9, 1.5.10 (5 points each) and the lab report from
Section 1.7 (20 points).
For the lab report from Section 1.7, you should summarize what you did in the lab. Include some detail, including sketches. You should focus on what the lab shows you about the similarities and differences between Euclidean and hyperbolic geometry, and include exercise 1.7.1 (b) and (d) (but not (a) and (c)).
The sample lab report which was handed out can give you an idea of how much detail to include. I'm not expecting any outside research, though.
It is important to do the first half of the lab from Section 1.3 also, but you do not need to turn in any report on this work.
Assignment #4 (50 points) - due Wed. Feb. 15 at the beginning of
class
Write up exercises 1.6.8-1.6.11, 2.1.1, 2.1.2, 2.1.7-2.1.10
(10 exercises total)
Note: 1.6.7 has been removed from
the assignment.
Assignment #5 (25 points) - due Fri. Feb. 24 at the beginning of
class.
Read Sections 2.2, 2.5
Write up exercises 2.2.7, 2.2.10, 2.5.1, 2.5.4, 2.5.5
Assignment #6 (35 points) - due Monday March 6 at the beginning of
class
Read Sections 5.1, 5.2
Write up exercises 5.1.2, 5.1.4, 5.1.5, 5.1.6, 5.1.9, 5.2.3, 5.2.4
Notes:
1. On 5.1.5, there are two things to prove: given a circle C1, show
there is another circle C2 of the same radius so that all of the points of C1 go
to points of C2. Then show that the isometry maps C1 onto C2.
You may use the inverse of the isometry.
2. For 5.1.9, explain your answers in addition to answering "yes" or "no".
Assignment #7 (30 points) - due Friday March 17.
Read Sections 5.3, 5.4, 5.6 (understand the theorems but you do not need to read
the proofs of the theorems)
Write up exercises 5.3.4 (use Corollary 5.10), 5.6.4, 5.6.5, 5.6.7, 5.6.9,
5.6.10
Notes:
1. For 5.3.4, use Corollary 5.10.
2. In 5.6.4, you can set up the coordinates so that the line of reflection
is the x-axis. What is the formula for the glide reflection in terms of (x,y)-coordinates?
3. For 5.6.5, use Theorem 5.17 and problem 5.3.4.
4. There is a typo in the sentence immediately before problem 5.6.6.
It should be "the second condition is true for all collections of isometries."
5. Notice that the definition of group of symmetries is exactly the
group axioms which you studied in Section 1.4, page 24.
6. To show that a set of isometries is a group, you need to show
that all four properties are true. To show it is not a group, just
show that one of the properties is false. You can use any of the
properties we've developed in class. If you're uncertain about how much
detail to include, discuss with me.
Due date for project topic - Friday, March 31
See
http://www.math.uiuc.edu/~kmortens/402/project.html for details on the
project assignment.
Assignment #8 (35 points) - due Wednesday April 5
Read Sections 7.1, 7.3, 7.4
Write up exercises 7.3.1 (for Poincare model instead of Klein), 7.3.2 (for
Poincare model instead of Klein), 7.3.3
Write up a lab report for Section 7.4, describing what you did in lab and
including exercises 7.4.1 and 7.4.2
Assignment #9 (30 points) - due Friday April 21
Read Sections 7.5, 7.6
Write up exercises 7.5.1, 7.5.2, 7.5.4, 7.5.6, 7.5.9, 7.5.11
Assignment #10 (20 points) - due Wed. May 3 (or sooner if you'd like
it back before the final exam)
Read Sections 7.7, 7.8. Turn in the write up from lab
on April 17.