Math 6122, Abstract Algebra II

Spring 2006

• Instructor: Matt Baker
• Time and place: MWF 10:05 P.M. - 10:55 P.M, Skiles 108A
• E-mail: mbaker@math.gatech.edu
• Office: Skiles 263
• Office Hours: Monday 2-3, Wednesday 3-4

If you haven't already done so, please fill out the Online Course Survey.

Tentative exam schedule:

• Midterm #1: Hand out Wed. 2/15, due Wed. 2/22
• Midterm #2: Hand out Wed. 3/29, due Wed. 4/5
• Final Exam: Hand out Wed. 4/26, due Wed. 5/3

Eighth homework assignment:

• Click here to download.

Seventh homework assignment:

• Section 14.6 #29,30,31,32
• Section 14.7 #10,11

Sixth homework assignment:

• Section 14.5 #2,5,7,10,11,12

Fifth homework assignment:

• Section 14.2 #13,17,18,31
• Section 14.3 #6
• Section 14.4 #1,2

Fourth homework assignment:

• Section 14.2 #3,5,11,14,15,29,30

Third homework assignment:

• Section 14.1 #1,4,5,7,8,9,10

Second homework assignment:

• Section 12.2 #4,8,9,17
• Section 12.3 #9,17,18,24

First homework assignment:

• Section 10.1 #8
• Section 10.2 #11,12
• Section 10.3 #2,6,7
• Section 12.1 #6,11,12

Course outline:

This graduate-level course in abstract algebra is the second in a two-course sequence which also includes Math 6121. Topics to be covered will include:

• Module theory:

  Submodules and quotient modules, homomorphisms, free modules, finitely generated modules over a principal ideal domain, determinants, rational and Jordan canonical forms via module theory. (Relevant sections: 10.1-10.3, 11.4, 12.1-12.3)

• Field extensions:

  Existence and uniqueness of splitting fields and algebraic closures, inseparable extensions, perfect fields, classical straightedge and compass constructions. (Relevant sections: 13.2-13.5)

• Galois theory:

  Normal extensions, Galois groups, the Galois correspondence, Galois theory of finite fields, composite extensions, simple extensions, abelian extensions, Galois groups of polynomials, solvable and radical extensions, insolvability of the quintic, computation of Galois groups, transcendental extensions. (Relevant sections: 14.1-14.9)

• Representation theory of finite groups:

  Modules over a group ring, Maschke's theorem, Wedderburn's theorem, class functions, character theory, orthogonality relations, characters of groups of small order, theorems of Burnside and Hall. (Relevant sections: 18.1-18.3, 19.1-19.2)

• Computational ring theory:

  Polynomials in several variables over a field, Grobner bases. (Relevant sections: 9.6)

Prerequisites:

Math 6121, or permission of instructor.

Exams:

There will be 2 midterm exams during the course of the semester, plus an in-class final exam at the end of the course.

Homework:

Homework will be assigned on a regular basis.

Grading Policy:

The two midterm exams will each count for 25% of your grade, the final will count 40%, and homework will count 10%.

Collaboration:

On the homework sets, collaboration is both allowed and encouraged. However, you must write up yourself and understand your own homework solutions. Any academic dishonesty on the midterm or final exams, if detected, will result in a score of zero for that exam.