Instructor: Adam S. Sikora
115 Math Bldg, Email: asikora at buffalo.edu
Office hours: Tu 3:30-4:30, Th 1-2pm, or by appointment.
Class meets: Tu,Th 11:00-12:20, 250 Math
Recitations for 419: Tu 8-8:50am, Mth250, (There
are no recitations for Mth519)
TA: Michael Rosas, Office: 140 Math Bldg, Phone:
645-8825,
Email: marosas at buffalo dot edu
TA's office hours: M,Tu,Th: 12:30-1:30 and Math Help Center, Rm
107/110. M,W: 11-12
Prerequisite: Mth 309, Recommended: Math 311.
Text: T.W. Judson, Abstract Algebra Theory and Applications, free pdf book.
Preliminary Test Schedule: Feb 21, Apr 5, Apr 26.
You are
required to know the material in the lectures, and in the homework. Only
non-graphing, non-programmable calculators are permitted on exams/quizzes.
You are expected to attend each test as scheduled, unless you have a
documented medical or other valid excuse. IDs will be checked. Contact me
before taking an exam if you are seriously ill.
Quizzes (for Mth419): There will be a short quiz in each
recitation on the recent
material. No makeups will be given, but the 2 lowest marks will be
dropped without penalty.
Additionally, there may be some simple quizzes during lectures.
Homework: due in Tu class. No late homework will be accepted, but
the
2 lowest marks will be dropped without penalty. Each homework assignment will
consist of a large number of problems, of which only some problems (not
specified beforehand) will be graded.
Final grade in MTh419 will be based on HW (and in-class quizzes
if they are given), 100pts, and the best of
| Class Date | Class contents and HW | Due |
|---|---|---|
| Jan 17,19 | Ch 3 #2,8,14,15,25,30,31 | Jan 31 |
| Jan 24,26 | Ch 4 #1abc, 2abce, Problem: Find all subgroups of Z_60. (What theorem do you use?) Problem: Is U(30) cyclic?, #18abc, Problem: Compute #18f without expanding the 12th power, #24, #31 | Feb 7 |
| Jan 31,Feb 2 | Ch 5 1, 2(a),(b),(c), (j),(o), 3(a),(b), 7,13,20,23. | Feb 14 |
| Feb 7,9 | Ch 5: 18, 29, Ch 6: 1,5,6,7,8,9,11 | Feb 21 |
| Feb 14,16 | Ch 6: 17,18 Ch 9: 1,2,3,5,6,7 | Feb 28 |
| Feb 21,23 | Ch 9: #10, Give an example of 3 non-isomorphic abelian groups of order 8 (Prove that they are non-isomorphic), Prove that the quaternion group is not isomorphic to D_4 (Hint: count elts of order 2), #12, #13, #16(a,b,c),#25 | Mar 6 |
| Feb 28 | Test 1: Ch 3,4,5. | |
| Mar 1 | Ch 9: #28,45, Ch 10: 1bde,2,4,7,9 (Hint for 7&9: No. Try G=D_4) | Mar 20 |
| Mar 6,8 | Ch 10: 10, 13(1st part only: show that C(g) is subgroup), 14abc, Ch 11: 2,3, Pr: Find all homomorphisms Z_6->Z_9 (Hint: Follow the example in class. Each homo h is determined by the value of h(1).) | Mar 27 |
| Mar 13,15 | Spring Break | -- |
| Mar 20,22 | Ch 11 #7,15,17 Ch 12 2,3ac,10,11, Prove that the group of orientation preserving isometries of R^2 is generated by translations and rotations wrt the origin. | Apr 3 |
| Mar 27,29 | Ch 13: 1, Ch 16: 1(justify those which are not rings), 2,3acde, Prove that for every d in Q^*, Q[sqrt(d)]={a+b*sqrt(d): a, b in Q} is a field. | Apr 10 |
| Apr 3 | Ch 16: 16,19,20,25,26,27,38 | Apr 17 |
| Apr 5 | Test 2: Ch 6,9,10,11 (1st Isom Thm) | Apr 17 |
| Apr 10,12 | Ch 16: 4a,c(Hint: use the fact proved in class that every nonzero principal ideal in M_2(R) is M_2(R)),e, 5b,7,10, Prove that the principal ideal (2) in Z[x] is prime but not maximal. | Apr 24 |
| Apr 17,19 | Ch 17: #3b,#7,#8d (Hint: use a result in Sec 17.3), Prove that x^3+2x^2+3x+4 is irreducible in Q[x] (Hint: use another result in Sec 17.3), #9,#13. | suggested due date: Apr 26, but not later than Apr 30 |
| Apr 24 | Review | -- |
| Apr 26 | Test 3: Ch 12,13,16,17 | -- |