MA 541 - Fall 2002 - Home Page

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
  • none
• Fri, Sep. 6
  • none

  Week 2

• Mon, Sep. 9
  • Ch.0 : 1,3,4,9,17,47
• Wed, Sep. 11
  • Ch. 4: 13,19,21,25,31,33,41,45,49,51,53,54
  • Turn in #1
• Fri, Sep. 13
  • Ch. 2: 1,3,7,11,15,17,19

  Week 3

• Mon, Sep. 16
  • Ch. 2: 25,27,29
  • Also, work out group table(s?) for G={e,a,b}
• Wed, Sep. 18
  • Ch. 2: 31,37
  • Ch. 3: 1,3,29
  • Turn in #2
• 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
  • Ch. 3: 33,35,49,51
  • Turn in #3
• Fri, Sep. 27
  • Work out the group table for D₄ as in class.

  Week 5

• Mon, Sep. 30
  • Ch. 4: 1,3,5,7,9,11
• 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
  • study, study, study!
• Fri, Oct. 11
  • Exam #1

  Week 7

• Tue, Oct. 15 (Substitute Monday)
  • Ch.5 (see above)
• 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
  • none

  Week 8

• Mon, Oct. 21
  • Ch. 10: 1,3,8,33
• Wed, Oct. 23
  • Turn in #6
  • See below for a worked out solution to Turn in #5
• 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
  • Ch. 6: 4,5,26,28
  • Turn in #7
• 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(S_n)=Inn(S_n) for n3 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
  • Ch. 8: 1,3,5,7,9,11
• Wed, Nov. 13
  • Ch. 8: 13-19 odd, 23-31 odd, 35
  • Turn in #9 Due MONDAY
• Fri, Nov. 15
  • Ch. 8: 14,16,41,43,51

  Week 12

• Mon, Nov. 18
  • none
• Wed, Nov. 20
  • none
• Fri, Nov. 22
  • Exam #2

  Week 13

• Mon, Nov. 25
  • Ch.9: 1,9,11,13,15,17,21,22,23,27,31,35,37,39
• Wed, Nov. 27
  • No Class - Thanksgiving
• Fri, Nov. 29
  • No Class - Thanksgiving

  Week 14

• Mon, Dec. 2
  • Ch. 9: 41,43,45,47,50,53,55,61
• Wed, Dec. 4
  • none (just work on Ch. 9 stuff above)
  • Turn in #10
• Fri, Dec. 6
  • Ch. 10: 9,13,21,47,53

  Week 15

• Mon, Dec. 9
  • none
• Wed, Dec. 11
  • last class

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)
  • Ch. 3: #14
• #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)
  • Ch. 9: #36

• Ch.0 #47 NEW!
• Ch.2 #15
• Ch.2 #17
• Ch.2 #27
• Ch.2 #29
• Ch.4 #25
• Ch.4 #33
• Ch.4 #40
• Ch.4 #41
• Ch.5 #46 (Turn in #5)
• Ch.5 #7
• Ch. 5-8 Supplementary Exercises #2 (aka Turnin in #8)
• Exam 1 Answer Key
• Note, you need Adobe Acroread to read these PDF files.

• 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).