HW1
Read Logic (Class Handout)
Do problems in section 8.
HW2
Read Chapter 0, Preliminaries up to page 12.
Pay particular attention to the Division and Euclidean Algorithms.
Do problems 1, 2, 3, 4, 6, 8, 9, 11, 13, 14, 16
Proof Notebook: Modify the proof of Theorem 0.2 to prove the Corollary on page 5. (Your proof should not reference the result of Theorem 0.2.)
HW3
Read Chapter 0, Preliminaries, again!.
Learn how to do modular arithmetic.
Do Computer problems 1, 2, 3, 4, 5, 6
HW4
Read Chapter 0, Induction, Equivalence relations and functions.
Problems 22, 23, 24, 26, and 30 can all be done by mathematical induction. Choose 2 of them to hand in. Also Do #53, 54, 57.
HW5
Read Chapter 1, Introduction to Groups.
- Learn to multiply in D3 and D4.
- Identify symmetry groups of logos.
Do problems 1, 2, 3, 11, 13, 16, 20, 22
In the table for D3, put the symmetries in the order R0 R120 R240 F1 F2 F3
HW6
Read Chapter 2, Groups.
Do problems 1, 2, 3, 4, 5, 7
HW7
Read Chapter 2 again.
Do problems 24, 25, 26, 27, 30, 33
HW8
Read Chapter 3, Finite Groups and Subgroups.
Learn to use the One-Step, Two-Step, and Finite subgroup tests.
Do problems Computer exercises 1, 2, 3
Do problems 1, 2, 3, 4, 5
HW9
Read Chapter 3, Finite Groups and Subgroups.
Find the Center of a group
Find the Centralizer of every element of a group.
Do problems 12, 14, 17, 23, 28
HW10
Read Chapter 4, Cyclic Groups.
Do Problems 1, 2, 6, 8, 12, 14, 32, 38
HW11
Read Chapter 5, Permutation Groups.
Do problems 3, 4, 8, 9, 17, 18, 23, 26, 30
Challenge: 52
HW12
Read Chapter 6, Isomorphisms.
Do problems 1, 6, 7, 10, 16, 24, 26
HW13
Read Chapter 7, Cosets and Lagrange's theorem.
Do problems 2, 5, 6, 14, 17, 31, 42
Last Update: December 12, 2009
Ronald K. Smith
Graceland University
Lamoni, IA 50140
rsmith@graceland.edu