Lectures
Office Hours
T 1:15-2:15pm (Math 430 Priority)
W 3:15-4:15pm (General)
F 11:20am-12:20pm (General)
Textbook
| Instructor: Robert Ellis | Office: E1 Bldg, Rm 105C | Email:
|
|
Lectures |
MW 1:50-3:05pm | E1 Bldg. 027 |
|
Office Hours |
M 3:15-4:15pm (Math 152 Priority) T 1:15-2:15pm (Math 430 Priority) W 3:15-4:15pm (General) F 11:20am-12:20pm (General) |
Office phone 567-5336 |
| Appointments and emailed questions are welcome | ||
|
Textbook |
Gallian, Contemporary Abstract Algebra, 6th edition, Houghton Mifflin | |
First day handout (pdf) (course contract & exam schedule)
IIT Math 454 sections schedule
Exam Keys: Exam 1
Exam 2
Exam 3
| Due Date | Assignment | Optional (recommended) problems not to turn in |
|---|---|---|
| W 9/6 | Ch. 0, p23: 2, 6, 7, 10, 18, 31, 34, 50 Comp. Ex. p26: 4 |
Ch. 0, p23: 4, 7, 11, 14, 17, 20, 22, 30, 48, 49, 51, 53 Comp. Ex. p26: 1, 2, 3 |
| M 9/11 | Ch. 1, p37: 5, 6, 8, 9, 12, 19, 22 | Ch. 1, p37: 14, 15, 16, 23 (amusing) |
| M 9/18 | Note: I am looking for explicit formal proofs, but many of these have a
small number of steps. Give line-by-line justification, such as "by
associativity", or "by cancellation", or "by definition of inverses", etc. Ch. 2, p53: 4, 6, 8, 14, 18, 24, 26 (Hints: For 6, we have discussed a possible group. For 8 and 24, see Example 11.) p57, Computer Exercise #2 Ch. 3, p67: 2, 4, 14 |
Ch. 2, p53: 1, 2, 3, 5 Ch. 3, p67: 1, 3, 5, 7 |
| M 9/25 | Ch.3, p67: 6, 10, 16, 20, 30, 38, 40, 52, 54 (Hint: reduce #20 to a previously assigned problem) | |
| M 10/2 | Ch.3, Computer Exercises p71: 1, 2, 3 Ch.4, p83: 2, 8, 14, 16, 28 Ch.4, Computer Exercises p86: 2 |
|
| M 10/8 | Supplementary Exercises Ch1-4, p90: 1, 2, 3, 12, 22 (Hint: #12 generate all
possible
Cayley tables; #22 {a,a^2,a^3,e} is a subgroup, and the order of the group is not 6) Ch.5, p112: 4ab, 6 Ch.5, Computer Exercises p116: 1 |
Supplementary Exercises Ch1-4, p90: 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15 |
| T 10/16 | Ch.5, p112: 8, 12, 18, 20 (model...), 34 Ch.6, p132:6, 18, 22, 24 |
Ch.5, p112: 1, 3, 5, 7, 9, 11,16, 17, 21, 23, 25, 29, 41 Ch.6, p132: 1, 3, 5, 7, 9, 17, 19, 25, 27 |
| M 10/23 | Ch.6, p132: 13 (see 31, 39, recommended problems), 14, 26, 28, 38, 40 Also: Find a group that is isomorphic to Aut(D4) (see #13) |
Ch.6, p132: 29, 31, 35, 39 |
| M 10/30 |
(A) Prove the comment after the definition on the
top of
page 144, namely, stab_G(i)<= G. (B) Prove that A_4 has no subgroup of order 4. Ch.7, p148: 4, 6, 8, 10, 14, 20, 30, 40, 44 (Many of these are quick -- consult lecture notes, e.g.) |
Ch.7, p148: 1, 3, 5, 7, 9, 11, 12, 16, 18, 25, 31, 33 |
| F 11/10 |
Ch.8, p164: 6, 12, 16, 20, 22, 30, 42, 50 Computer Exercise Ch.8, p168: 2 |
Ch.8, p164: 1, 3, 5, 7, 13, 19, 21, 25, 29 (nice example), 33, 37, 47, 51, 59 |
| W 11/15 | Ch.9, p190: 4, 8, 10, 16, 18 | Ch.9, p190: 1, 5, 7, 9, 11, 15, 17, 19, 21 |
| W 11/29 |
Ch.9, p190: 30, 34, 52, 54 and: (i) Prove or disprove the following: Let n = 2 mod 4, where n>6. Then the dihedral group D_n is equal to the internal direct product of H and K, where H is isomporphic to D_{n/2} and K is an order 2 subgroup. (ii) Verify that the candidate isomorphism of the proof of Theorem 9.6 is 1-1 and onto Ch.10, p210: 1, 4, 6, 14, 16 |
Ch.9, p190: 49, 51, 53, 57, 59, 61 Ch.10, p210: 2, 3, 5, 7, 9, 11, 13 |
| F 12/8 2pm (to E1 105C or mailbox) |
Ch.10, p210: 20, 24, 30, 52
If you are going to graduate school, prove 39&40 (not to turn in). Ch.11, p225: 2, 6, 16, 24 Ch.12, p240: 4, 6, 8 |
Ch.10, p210: 15, 19, 21, 25, 31, 35, 37, 43, 53
Ch.11, p225: 1, 3, 5, 7, 11, 13, 19, 25 Ch.12, p240: 1, 3, 7, 9, 13, 17 |
page maintained by Robert Ellis / http://math.iit.edu/~rellis/