Assignment #1 will be due on Wednesday, 9/10/2008

Chapter 0

Exercises

Chapter 1

Exercises

All assignments – preliminary list

Chapter 0

Exercises 4 6 18

Chapter 1

Exercises 2

Chapter 2

Exercises 2 6

Chapter 2

Exercises 12 18 21 28

Chapter 2

Exercises 20 (prove your assertion!) 22

Chapter 3

Exercise 4

Chapter 3

Exercise 10 12 14 18

Chapter 4

Exercise 2 8

Supplementary (pages 90–91)

Exercise 6 12

Chapter 4

Exercise 10 14 38 40

Supplementary (pages 90–93)

Exercises 26 30

Chapter 5 

Exercise 4 8 10 12

Chapter 6

Exercises 4 16

Chapter 6

Exercises 14 22 36

Chapter 7

Exercises 6 8 10 14

Chapter 8

Exercises 4 6 8

Chapter 9

Exercises 2

Problem (3) Let G be the set of all ordered triples (x,y,z) such that x is an element of Z₂, y is an element of Z₃, and z is an element of Z₅.

Let (x,y,z)+ (x’,y’,z’)= (x+x’,y+y’,z+z’) where the addition x+x’ is performed modulo 2, addition y+y’ is performed modulo 3 and addition y+y’,z+z’ is performed modulo 5. Prove that G is an Abelian group.