MA 541 - Fall 2002 - Home Page
Click HERE to see course syllabus (in HTML).
Click HERE to see course syllabus (in Adobe PDF format).
OFFICE HOURS: M,W: 3-5 and, by appointment
Important Dates
Classes Begin - Sep. 3
Days Off
- Monday October 14 (substitute monday on Tuesday October 15!)
- Wednesday November 27 - Friday November 29 (Thanksgiving break)
Exams
- Exam 1 - Friday October 11
- Exam 2 - Friday November 22
- Final Exam - Monday December 16 [12:30-2:30 PM]
Important: The final exam will be in Room COM 217, not the usual classroom!
Extra Office Hours:
- Wed (12/11): 3,5
- Thu (12/12): 3,5
- Fri (12/13): 3,5
- Monday: Before the exam, I will be in my office.
Homework Assignments
Week 1
- Wed, Sep. 4
- Fri, Sep. 6
Week 2
- Mon, Sep. 9
- Wed, Sep. 11
- Ch. 4: 13,19,21,25,31,33,41,45,49,51,53,54
- Turn in #1
- Fri, Sep. 13
Week 3
- Mon, Sep. 16
- Ch. 2: 25,27,29
- Also, work out group table(s?) for G={e,a,b}
- Wed, Sep. 18
- Fri, Sep. 20
- Do more problems from Ch.2
- I will be typing up some and posting them in .pdf format.
Week 4
- Mon, Sep. 23
- Ch. 3: 1,3,5,9,13,15,21,23,29,31,37,41,43,47
- Look below for written out answers to some of the problems from Ch. 2.
- Wed, Sep. 25
- Fri, Sep. 27
- Work out the group table for D4 as in class.
Week 5
- Mon, Sep. 30
- Wed, Oct. 2
- Ch. 4: 13,19,21, 25,31,33,41,45,49 (see 41), 51, 53, 54
- Turn in #4
- Fri, Oct. 4
- Ch. 1-4 Supplementary Exercises: 1,5,11,17,21
Week 6
- Mon, Oct. 7
- Ch. 5: 1-11 odd,17,21
- See below for worked out solutions to some problems in the text.
- Wed, Oct. 9
- Fri, Oct. 11
Week 7
- Tue, Oct. 15 (Substitute Monday)
- Wed, Oct. 16
- Ch. 5: 23,26,27,28,31,33,39,45
- Turn in #5
- See below for worked out solutions the questions on Exam 1.
- Fri, Oct. 18
Week 8
- Mon, Oct. 21
- Wed, Oct. 23
- Fri, Oct. 25
- none (Turn in #6 on Monday.)
Week 9
- Mon, Oct. 28
- Ch. 6: 1,3,5,7,22,23,25 <- for this, suppose there were an isomorphism from Z to Q and find a contradiction.
- Also see below for a site which lists the number of groups of a given order n up to 2019
- Wed, Oct. 30
- Fri, Nov. 1
- Ch. 5-8 Supplementary Exercises: 1,3,6,13,29,41,43,45
Week 10
- Mon, Nov. 4
- Ch. 7: 1,2,3,5,7,9,11,12,13
- Wed, Nov. 6
- Ch. 7 homework (above)
- See below for a number of resources related to the discussion
- in class regarding how Aut(Sn)=Inn(Sn) for n
3 but n
6
- Turn in #8
- Fri, Nov. 8
- Ch. 7 homework (above)
- See below for a reference to encryption based on Fermat's/Euler's Theorem
Week 11
- Mon, Nov. 11
- Wed, Nov. 13
- Ch. 8: 13-19 odd, 23-31 odd, 35
- Turn in #9 Due MONDAY
- Fri, Nov. 15
Week 12
- Mon, Nov. 18
- Wed, Nov. 20
- Fri, Nov. 22
Week 13
- Mon, Nov. 25
- Ch.9: 1,9,11,13,15,17,21,22,23,27,31,35,37,39
- Wed, Nov. 27
- Fri, Nov. 29
Week 14
- Mon, Dec. 2
- Ch. 9: 41,43,45,47,50,53,55,61
- Wed, Dec. 4
- Fri, Dec. 6
Week 15
- Mon, Dec. 9
- Wed, Dec. 11
Homework Assignments (Turn In!)
- #1. Assigned - Wed. Sep. 11 (Due Fri. Sep. 13)
- Ch. 0: Do either #26 (a statement requiring induction) or #28 (a congruence problem)
- Note, n3 mod 6 = n mod 6 is equivalent to n3=n (mod 6)
- #2. Assigned - Wed. Sep. 18 (Due Fri. Sep. 20)
- Ch. 2: #34
- Check all the group axioms and determine whether this group is abelian or not.
- This example is a good example (amongst many!) of the applications of group theory.
- #3. Assigned - Wed. Sep. 25 (Due Fri. Sep. 27)
- #4. Assigned - Wed. Oct. 2 (Due Fri. Oct. 4)
- Ch. 4: #40
- You may wish to experiment with different m and n to see what's happening.
- However, you should give an answer that works for any m and n.
- #5. Assigned - Wed. Oct. 16 (Due Fri. Oct. 18)
- Ch. 5: #46
- Note:
=
, the identity permutation.
- #6. Assigned - Wed. Oct. 23 (Due Fri. Oct. 25)
- Ch. 5-8 Supplementary Exercises #16
- #7. Assigned - Wed. Oct. 30 (Due Fri. Nov. 1)
- Ch. 6: #22 (Look at #4,5 for practice.)
- #8. Assigned - Wed. Nov. 6 (Due Fri. Nov. 8)
- Ch. 5-8 Supplementary Exercise #2
- Refer to question 1 for the relevant definition.
- Also recall that
(N)=N means N
(N) and
(N)
N but does not mean that
(n)=n
n in N
- #9. Assigned - Wed. Nov. 13 (Due Mon. Nov. 18)
- Ch. 5-8 Supplementary Exercises: # 34
- #10. Assigned - Wed. Dec. 4 (Due Fri. De. 6)
Miscellany (Look here for additional materials!)
- Gallian's Web Page
- History Web Page mentioned in Gallian's Book
- Table with Number of Isomorphism Classes of Groups
- Note, to read this table, say to find the number of groups of order 132, go to the row that's marked 120+ then go over to the
- column marked +12 (i.e. 120+12=132) and look at the entry to find N(132) = 10
- Here are a number of links regarding the peculiarities of S6
- From the website of the mathematical physicist John Baez
- A really short! note (see me if you want further explanation)
- In the library, look up the article Outer Automorphisms of S6 by Janusz and Rotman in the American Mathematical Monthly Vol. 89, No. 6, pp. 407-410
- Here is a page describing how RSA public key encryption works.
- In particular it shows how it comes from Fermat's and Euler's theorem(s) which themselves are consequences of Lagrange's Theorem applied to the group U(n).