Math 412 and 512H Abstract Algebra II

Instructor: Ralf Schiffler
Office: LGRT 1342
Phone: (413) 545-2871
E-mail: schiffler at math dot umass dot edu
Office Hours: TuTh 10:30 - 11:30 or by appointment

Schedule: TuTh 2:30 - 3:45 in LGRC A201ı 512H also meets on Th 4:10-5:00 in LGRT 1322
Text: Algebra: Pure and Applied, Aigli Papantonopoulou, Prentice-Hall, Inc. 2002.

Make-up policy for exams

Exams:
Midterm 1: Tue, March 11, 2:30 - 3:45
Midterm 2: Thu, Apr 17, 2:30 - 3:45

Final exam

The final exam is a take home final. Hand in your solutions on Monday May 19 (or before).

Grading: Course Grade = Homework (30%) + Midterm 1 (20%) + Midterm 2 (20%) + Final (30%)

Description: This course is part of a 2 semester sequence on Abstract Algebra and its subject is the theory of rings and fields. The topics covered include rings, integral domains, homomorphisms, ideals, quotients, prime ideals, maximal ideals, ring of polynomials, fields, field extensions, splitting fields, and finite fields. If there is time enough, we will also dive into Galois theory.
People who take the 512 honors class will meet one additional hour per week (starting in the second week of the semester) and study algebras and their representations.

Homework

Homework 1 (due thu, feb 14)

6.1: # 8, 10, 12, 21
6.2: # 12, 14, 16
read sections 6.3 and 7.1

Homework 2 (due thu, feb 21)

6.3: # 3, 9, 14, 33, 35 (hint for 33: use Lagrange's theorem or one of its corollaries)
read section 7.2

Homework 3 (due thu, feb 28)

7.1: # 4, 9, 18, 19
7.2: # 4, 11, 15
read section 7.3

No Homework for thu Mar 6

Homework 4 (due thu, Mar 13)

7.2: # 17, 22, 23, 33
7.3: # 16
8.1: # 8, 9
read sections 8.2 and 8.3

Homework 5 (due tue, Apr 1 (no joke))

8.1: # 17, 23
8.2: # 3, 5
read section 8.4
Math 512H only: Pick 4 problems of exercise #3 in chapter II. (You may drop the underlined problems from the regular homework)

Homework 6 (due thu, Apr 3)

8.1: # 15
8.2: # 6, 10ı [forı #6, use the Euclidean algorithm explained in Theorem 8.2.9 and Example 8.2.11]
8.3: # 7, 15
read section 8.6.

Homework 7 (due thu, Apr 10)

8.4: # 8, 9,19, 20
8.6: # 1, 2, 10, 12
Math 512H only: chapter II # 15, 17(a). (You may drop the underlined problems from the regular homework)

Homework 8 (due thu, Apr 17)

8.7: # 4, 10, 15 [Hint: Use exercise 29 of 8.4 without proof], 22, 29, 36
read section 10.1

No homework for Thu Apr 24

Homework 9 (due thu, May 1)

10.2: # 7, 11, 18, 22, 25
10.3 # 1, 4, 22
read sections 10.3 and 10.4