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Uli Walther

Math 746, 494-1959

walther@math.purdue.edu

teaching Math 453 Spring 2011

TTh 9:00-10:15, REC121

Office hours: Tue 2:30-3:00, Th 1:30-2:30.

Grader's email: cho41 AT math DOT purdue DOT edu

Book: Contemporary Abstract Algeba by J. Gallian (Editions 6 and 7 are
fine, but be careful with the homework numbering!)
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The syllabus

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The Midterm

Day and time: Th Feb 24, in class. (This is week 7; the
midterm will cover all material we discuss from the part on "groups".)

Midterm solutions

You can bring HW solutions and your notes. No textbooks, instant
messaging, or outside consultants.

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The Final

Day and time: ??.

The location is: ??.

### Homework assignments due

(Due every Thursday in class or in my office by 3:30.)

These are the numbers for edition 6. The numbers for edition 7 are
here.

Week 1-Jan 13: nothing due.

Week 2-Jan 20 (In[tro]duction, 0): Ch 0: 25, 24, 7, 14, 19, 21

Week 3-Jan 27 (Groups, 1+5): Ch 1: 6, 13. Ch 5: 6,8, 19, 43.

Week 4-Feb 3 (Sub-, cyclic, solvable groups, 3+4+32): Ch3:
4,8,9,38,40. Ch4: 9,19,61

Week 5-Feb 10 (Cosets, 6+7): Ch6: 7,22,35(hint: R_90 in D_4). Ch7:
7,10. Question 1 from file

Week 6-Feb 17 (Morphisms, 9+10): Ch9: 7,11. Ch10: 7,24,31,32. Question
2 from file

Week 7-Feb 24 (Products, 8): Ch8: 2,8,28,34,37,52, Question 3 from file.

---> Midterm on Feb 24

Week 8-Mar 3 Nothing due.

Week 9-Mar 10 (Rings, 12+13): Ch12: 2,20. Ch13: 5,6,10,28.(Hint:
identify the group structure. Then wonder what this says about multiplication.)

---> Spring break Mar 17

Week 10-Mar 24 (Ideals, 14+15): Ch13: 41,54. Ch14: 6,26. Ch15: 33,54.

Week 11-Mar 31 (Division, 16): Ch16: 12,13,16,22,32,34,49.

Week 12-Apr 7 (UFD's, 17+18): Ch17: 4,6,7,10,21. Question 4 from file

Week 13-Apr 14 (Fields, 20): Ch20: 1,29,31,5,19,21,25.

Week 14-Apr 21 (Fields, 21): Ch21: 8,14,16,24,33,30.

Week 16-Apr 28 (Finite fields, 22)Ch22: 1,2,4,10,30, Question 5
from file.

Recommended exercises on Ch23 (Geometry, 23) Ch23: 13,14,16,18.and Question
2 from file.
### Extra credit

Ch4: 51.
Ch17: 29.(Hint: x^4+1 = (x^2+i)(x^2-i)
= (x^2-sqrt(-2)x-1)(x^2+sqrt(-2)x-1)
= (x^2-sqrt(2)x+1)(x^2+sqrt(2)x+1).
Find out under what circumstances -1, 2 or -2 have square roots modulo p.)

### Homework Solutions

Comments to *
walther@math.purdue.edu*