Class Information:
Handouts:
- Some basic number theory facts
Student notes from Fall 2013 (thanks Sam!):
- Notes from Fall 2013
More Resources:
- David Stapleton's Math 100a course has more practice problems are here with solutions.
Study guides:
Test solutions:
Homework:
1.1 |
# 5,8,11,12,25,28 - Extra solution to 28 |
1.2 |
1(b,c), 4
A) Compute the group table for D_6 and D_8.
B) Find the inverse of r^2 in D_6, r in D_8, r^2 in D_8, and sr in D_8. What is the inverse of r in D_2n? What is the inverse of sr^i in D_2n? C) In D_8, simplify the following products: s r^2 s r^3 and r s r^(-2).
|
4550 HW |
Do these problems from MATH 4550: HW 1 - 1, 4, 5, 7, 12, 14 |
1.3 |
1, 2, 4(a)
- Sam's solutions |
4550 HW |
Do these problems from MATH 4550: HW 3: 1, 2, 4, 5 |
1.6 |
1, 2, 3, 4, 5, 6, 13, 15
- Sam's solutions - Extra solutions to 1,3,4,5,6,15 are here. Extra solutions to 2 and 13 are here. |
1.7 |
14, 15, 16, 17, 18
- Sam's solutions - Extra solutions to 14, 15, 16 are here. Extra solutions to 17 and 18 are here. |
4550 HW |
Do these problems from MATH 4550: HW 5: 1, 2, 3 |
2.1 |
1(b), 2(a), 3(b), 10(a), 11, 12(b), 14
- Sam's solutions - Extra solution to 11 is here. Extra solutions to the problems except for 11 are here. |
2.2 |
2, 5(a), 6, 7, 11
- Sam's solutions - Other solutions are here. |
2.3 |
11, 12, 13, 26 Note: For #26, in the book for this problem, Z_n denotes an abstract cyclic group of order n. So the notation x^n does not mean multiplication in the group Z_n = {0,1, ..., n - 1}, it means multiplication in the abstract cyclic group. Also, do:
- Sam's solutions - Other solutions are here. |
4550 HW |
Do these problems from MATH 4550: HW 2: 1, 2 (not U3), 4, 6, 11, 12, 13, 14 |
TEST 1 covers everything above | |
3.1 |
1, 3, 4, 5, 20, 22(a), 36
|
3.2 |
4, 5, 8, 16
- Sam's solutions - Extra solutions for the problems (except for 5) are here. Extra answer to 5 is here. |
3.3 |
For A and B, find groups that the following are isomorphic to and use the first isomorphism theorem to prove it: C) Let G and G' be groups, and let H and H' be normal subgroups of G and G', respectively. Let f be a homomorphism from G to G'. Show that f induces a natural homomorphism
- Sam's solutions - Extra solutions here |
3.5 |
2
- Sam's solutions - Extra solutions here |
4550 HW |
Do these problems from MATH 4550: HW 6: 1, 2, 3, 4 |
TEST 2 covers up to this point |
|
4.3 |
2(a), 4, 8
- Sam's solutions - Extra solutions here (Note: there is a typo in the solution for #8 at the very end. It should say sigma o tau /= tau o sigma. Right now it has sigma o tau = tau o sigma.) |
4.4 |
2, 15
- Sam's solutions - Extra solutions here |
4.5 |
5, 13, 30 Hint for 5: Show that <r^{n/p^k}> is the unique Sylow p-group of size p^k if p is odd and 2n = 2p^k * m (where p does not divide m).
- Sam's solutions - Extra solutions for 5 and 30 are here. Extra answers to 13 are here |
5.2 |
A) Let G be a finite abelian group. Prove that G is simple if and only if G is isomophic to Z_p for some prime p. B) Find all abelian groups of size 36. Find all abelian groups of size 540.
- Sam's solutions - Extra solution to A is here |
5.4 |
A) Classify all groups of size 5^2 * 7
- Sam's solutions - Extra solution here |
Lecture notes: (we didn't start taking pictures until 9/19)
- Thursday, 9/19
- Tuesday, 9/24
- Thursday, 9/26
- Tuesday, 10/1
- Thursday, 10/3
- Tuesday, 10/8 - Test 1
- Thursday, 10/10
- Tuesday, 10/15
- Thursday, 10/17
- Tuesday, 10/22
- Thursday, 10/24
- Tuesday, 10/29
- Thursday, 10/31
- Tuesday, 11/5
- Thursday, 11/7
- Tuesday, 11/12 - Test 2
- Thursday, 11/14
- Tuesday, 11/19
- Thursday, 11/21
- Tuesday, 12/3
- Thursday, 12/5
- Thursday, 12/12 - Final exam, 5pm--7pm