MA 542 - Spring 2003 - Home Page
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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
- 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
- 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
- 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
- Fri, Jan. 31
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
- Fri, Feb. 14
- Ch. 15: 51,59,63
- Ch. 16: 1,3,9
Week 6
- Tue, Feb. 18 (Substitute Monday)
- Wed, Feb. 19
- Fri, Feb. 21
Week 7
- Mon, Feb. 24
- Ch. 16: all odd numbered problems
- Wed, Feb. 26
- 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
- Fri, Mar. 7
- Ch. 17: 29,31
- Ch. 15-18 Supplementary Exercises: 7,9,11,13,15,19,32
Week 9
- Mon, Mar. 17
- Wed, Mar. 19
- Fri, Mar. 21
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
- Fri, Mar. 28
Week 11
- Mon, Mar. 31
- Wed, Apr. 2
- Fri, Apr. 4
Week 12
- Mon, Apr. 7
- Wed, Apr. 9
- Ch. 21: 3,5,7,8,9,10,14,15
- Fri, Apr. 11
Week 13
- Mon, Apr. 14
- Same as on Apr. 9 (keep going with it)
- Wed, Apr. 16
- Fri, Apr. 18
- Ch. 19-23 Supplementary Exercises: 1,5,7,8
Week 14
- Mon, Apr. 21
- Wed, Apr. 23
- Fri, Apr. 25
Week 15
- Mon, Apr. 28
- Wed, Apr. 30
Homework Assignments (Turn In!)
- #1. Assigned - Wed. Jan. 22 (Due Fri. Jan. 24)
- #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 ar=0 for some r>1.
- Note: If ar=0 then as=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)=xp is very important in finite field theory.
- #5. Assigned - Wed. Feb. 26 (Due Fri. Feb. 28)
- #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
:R
R.
- 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)
- #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 a
F then F(a)=F.
Miscellany (Look here for additional materials!)
- Exam 2 Key
- Some worked out exercises (all very computational in nature) [PDF format]
- The ring that is a PID but not a Euclidean domain.
- American Mathemtical Monthly, Vol. 95, Issue 9, (11/1988) PP. 868-871