MA 542 - Spring 2003 - Home Page

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Click HERE to see course syllabus (in MS-Word format).

Click HERE to see course syllabus (in Adobe PDF format).

OFFICE HOURS: M,W 3-5 in Room MCS 235

Important Dates

Classes Begin - Jan. 13

Days Off

Monday January 20
Monday February 17 (substitute monday on Tuesday February 18!)
Monday March 10 - Friday March 14 (spring break)

Exams

Exam 1 - Friday Feb. 21
Exam 2 - Friday Apr. 11
Final Exam - Friday May 9, 2:00-4:00 PM
EXAM INFORMATION (in PDF format)

Last Day to Withdraw (without a 'W') - Friday February 14
Last Day to Withdraw (with a 'W' grade) - Friday March 7

Homework Assignments (Non turn-in)

Week 1

Mon, Jan. 13
- none
Wed, Jan. 15
- Ch. 12: 1,3,9,12,13,17,19
Fri, Jan. 17
- Ch. 12: 22,23,25,29,31,41,47
- for #41, think of some sample elements of the ring
- Click here for a discussion of the M₂(Z[x]) vs. M₂(Z)[x] question.
Week 2
Mon, Jan. 20
- (no class)
Wed, Jan. 22
- Turn in #1
- Ch. 12: 24,25,37,39
- Ch. 13: 4,7,9,10,11,13
Fri, Jan. 24
- Ch. 13: 15,16,19,21,25,31
Week 3
Mon, Jan. 27
- Ch. 13: 15,16,17,19,20,31,41,44,59
Wed, Jan. 29
- Ch. 14: 5,7,10,11,12,13
- Turn in #2
Fri, Jan. 31
- Ch. 14: 23,25,27,29,39
Week 4
Mon, Feb. 3
- Ch. 14: 29,31,33,35,37,51
Wed, Feb. 5
- Turn in #3
- Ch. 14: 38,39,40,41,43,44
- Ch. 12-14 Supplementary Exercises: 7,9,15,18,25,31,37,41
Fri, Feb. 7
- Continue with homework from Feb. 5
Week 5
Mon, Feb. 10
- Ch. 15: 5,8,11,12,13,19,21,22,27
Wed, Feb. 12
- Turn in #4
- Ch. 15: 36,37,39,45,47
Fri, Feb. 14
- Ch. 15: 51,59,63
- Ch. 16: 1,3,9
Week 6
Tue, Feb. 18 (Substitute Monday)
- SNOW!!!
Wed, Feb. 19
- none
Fri, Feb. 21
- Exam #1
Week 7
Mon, Feb. 24
- Ch. 16: all odd numbered problems
Wed, Feb. 26
- Turn in #5
Fri, Feb. 28
- Continue with Ch. 16 problems.
Week 8
Mon, Mar. 3
- Ch. 17: 3,5,9,11,13,14,15
- Click here for a discussion of Turn in #5
Wed, Mar. 5
- Turn in #6
- Ch. 17: #21,23,25
Fri, Mar. 7
- Ch. 17: 29,31
- Ch. 15-18 Supplementary Exercises: 7,9,11,13,15,19,32
Week 9
Mon, Mar. 17
- Ch. 18: 1,3,5
Wed, Mar. 19
- Ch.18: 13,14,15,17,21,23,37
- Turn in #7
Fri, Mar. 21
- Ch. 18: 19,25,27,33
Week 10
Mon, Mar. 24
- Ch. 18: 6,7,8,9,11
- Reference for article describing the PID that is not a ED.
Wed, Mar. 26
- Turn in #8
- Ch. 19: 1-15 odd
Fri, Mar. 28
- Ch. 19: 17-31 odd
Week 11
Mon, Mar. 31
- none
Wed, Apr. 2
- Ch. 20: 1,3,5,7,13,14,19,23
- Turn in #9
Fri, Apr. 4
- Ch. 20: 27,29,31,35
Week 12
Mon, Apr. 7
- none
Wed, Apr. 9
- Ch. 21: 3,5,7,8,9,10,14,15
Fri, Apr. 11
- Exam #2
Week 13
Mon, Apr. 14
- Same as on Apr. 9 (keep going with it)
Wed, Apr. 16
- Ch. 21: 17,19,23,34
Fri, Apr. 18
- Ch. 19-23 Supplementary Exercises: 1,5,7,8
Week 14
Mon, Apr. 21
- no class
Wed, Apr. 23
- Answer Key for Exam 2
- Turn in #10
- Ch. 21: 31,33,35
Fri, Apr. 25
Week 15
Mon, Apr. 28
- none
Wed, Apr. 30

Homework Assignments (Turn In!)

#1. Assigned - Wed. Jan. 22 (Due Fri. Jan. 24)
- Ch. 12: #34
#2. Assigned - Wed. Jan. 29 (Due Fri. Jan. 31)
- Ch. 13: #42
- See #13 for definition of nilpotent.
- Setup: Assume charR=p (for some prime p > 1) and that a^r=0 for some r>1.
- Note: If a^r=0 then a^s=0 for any s>r.
#3. Assigned - Wed. Feb. 5 (Due Fri. Feb. 7)
- Ch.12-14 Supplementary Exercises: #48
#4. Assigned - Wed. Feb. 12 (Due Fri. Feb. 14)
- Ch. 15: #38
- The Frobenius map f(x)=x^p is very important in finite field theory.
#5. Assigned - Wed. Feb. 26 (Due Fri. Feb. 28)
- Ch. 15: #50
#6. Assigned - Wed. Mar. 5 (Due Fri. Mar. 7)
- Ch.15-18 Supplementary Exercises #2
- Recall that an automorphism of a ring R is an isomorphism :RR.
- Show also that Aut(Q(2)) is a (finite) group under composition and determine which group it is.
- This idea will be very important later on.
#7. Assigned - Wed. Mar. 19 (Due Fri. Mar. 21)
- Ch.15-18 Supplementary Exercises #20
#8. Assigned - Wed. Mar. 26 (Due Fri. Mar. 28)
- Ch. 18: #38
#9. Assigned - Wed. Apr. 2 (Due Fri. Apr. 4)
- Ch. 20: #20
- Show both containments, F(c)F(ac+b) and vice versa.
#10. Assigned - Wed. Apr. 16 (Due Fri. Apr. 18)
- Ch. 21: #28
- Hint: Write r as a/b and then consider the possible cases depending on whether
- this number is positive, negative or zero.
- Also, observe that if aF then F(a)=F.