Math 451 -- Fall 2009
Tues, Thurs: 10:10-11:25, Malott Hall 203
from the text
On reserve in Mathematics Library:
Homework:
27 Aug - 1 Sept:
Read "Introductory Handout"
Read Chapter 3 of Crocheting Adventures With Hyperbolic Planes (this chapter is a much expanded (with lots of photos) version of Chapter 0 of Experiencing Geometry.
Read Chapters 1, 2, and first part of 4 of Experiencing Geometry and work on (but do not hand in) Problems 1.1, 2.1, 4.1a.
3 Sept:
Read Chapter 3 and page 59-67 of Chapter 5.
Write and hand-in to my door (MT403) before 11am on Monday (see "Introductory Handout").
3.1 and 3.2 for plane, sphere, cylinder, and cones
Make (bring to class but do not turn in) a paper annular hyperbolic plane (AHP) as described on pages 62-63 and using at least 4 annular strips from the template handed out in class or here
5.1 based on your experiences in class Thursday and on your experiences with your paper AHP.
10 Sept:
Read Chapter 5.
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 5.2 , 5.3, and 5.4ac (not bd)
Second priority: finish (respond to comments) 3.1 , 3.2, and 5.1abc
15 Sept: class summary
17 Sept: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 6.2ab(not c), and 6.4
Second priority: finish (respond to comments) previous work
22 Sept: class summary
24 Sept: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 6.5, and 7.1abc
Second priority: finish (respond to comments) previous work
29 Sept: class summary
1 Oct: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 7.3ab, and 8.1ab
Second priority: finish 6.4, 6.5
Third piority: Finish previous work
6 Oct: class summary
8 Oct: class summary
Write and hand-in to my door (MT403) before 11am on Wednesday:
First priority: 8.2, and 8.3abc (Hint: use symmetry and Chapter 7)
Second priority: finish 6.4, 6.5, 7.1, 7.3
Third piority: Finish previous work
15 Oct: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 11.2, and 11.3a Use hints in book
Second priority: finish 6.5, 8.1, 8.2, 8.3
Third piority: Finish previous work
20 Oct: class summary
22 Oct: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 11.3abcde, and 11.5abc Use hints in book
Second priority: finish 11.2
Third piority: Finish previous work
27 Oct: class summary
29 Oct: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 12.1ab, 12.2abcd, and 12.3ab (Use hints in book)
Second priority: finish 11.2, 11.3, 11.5
Third piority: Finish previous work
03 Nov: class summary
05 Nov: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 13.1, 13.2, and 13.4a (For 13.2, use your favorite proof of the Pythagorean Theorem but show it by dissection)
Second priority: finish 12.1, 12.2, 12.3
Third piority: Finish previous work
10 Nov: class summary
12 Nov: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 20.1ab, 20.2abc, and 20.3ab (For 20.2, look at the Summary of 10 Nov. For 20.3, look at the summary for 12 Nov.)
Second priority: finish 13.1, 13.2, 13.4
Third piority: Finish previous work
17 Nov: class summary
19 Nov: class summary
Write and hand-in to my door (MT403) before 11am on Monday:
First priority: 18.1abc, and an assignment that will count as 2 problems! It is basically 18.6 and you can use that as a basis.
18.6': How can an intrinsic 2-d bug tell which geometric 2-manifold it is on?
Two cases:
1. the bug can walk everywehere and lay down markers and can have friends help.
2. The bug can not walk and can only look very far along geodesics.
Consider the 10 manifolds that we discussed in class:
E2, S2, H2, infinite cylinder, projective plane, flat torus, flat Klein Bottle, hexagonal torus, psuedosphere, octagonal 2-holed torus.
