GENERAL PROCEDURES

Each quiz is worth 5 points. The number of HW points will vary with the assignment. Unless permitted by the instructor, the quizzes must be taken in class when they are given, and the HW is due before the beginning of class on the due date, or earlier. If external cicrumstances make it necessary to postpone a quiz or a HW, the student must contact the instructor as soon as possible.

Two lowest quiz grades will be dropped. Two HWs may be resubmitted without penalty. The quizzes are worth 20% of the total score, the HW is for 10%. 


Quizzes and Homework Assignments

HW 1
Due: Jan 16
Appendix D 1,3,8,9,10,12,16.
Maximum 15 points (one for each question asked)

Quiz 1
Date: Jan 18
The set S is the set of integers. Prove that the following relation is an equivalence relation: x~y iff 5|(2x+3y)
Grading Notes: 1pt for definition, 1 pt for being  reflexive, 2 pts for symmetric, 1 pt for transitive.

HW 2
Due: Jan 23
2.1 3,10,14;
2.2 3,8;
2.3 2,4;
3.1 1,2,5,9,23
7.1 1,4,16

Quiz 2
Date: Jan 23
For each element of the group S_3 find its inverse (in a notation of your choice).

HW 3
Due: Jan 30
3.2 1,2,5,7,13
4.1 1,3a,5a,6


Quiz 3
Find all units and zero divisors in Z/(12Z).

HW 4
Due: Feb 4
6.1. 1,2,8,13,14,15a,17,18

Quiz 4
R_1 is a subring of R_2, I is an ideal of R_2.
a) (3 pts) Prove that if I is prime, then the intersection of I and R is a prime ideal
b) If I is maximal, does the intersection have to be maximal?

HW 5
Due: Feb 11
6.2. 1,2,4,5,7,11,12
6.3 1,2,4,6,7,11

Quiz 5
Find all subgroups of S_3

HW 6
Due: Feb 27
7.2 1,3,4,7,21,22,23,27,28
7.3 1,2,3a,4,8,25,26,31,32,33
7.4 1,6,10,11,17,24,25

Quiz 6
Prove that the center of any group is a normal subroup in it.

HW 7
Due: Mar 5
7.5 4,5,9,11,14,17,19
7.6 5,6,9,16,20,29
7.7 1,2,8,10,14,17,23

Quiz 7
Prove that all groups of order 5 are isomorphic to Z/5Z.