Algebra

Administrivia

The course meets at 12:30 MWF in Doherty Hall 231A. Office hours are by appointment only, please send email to jcumming@andrew.cmu.edu to arrange an appointment. Homework will be set most Fridays and will be due on the following Friday. Late homework will not be accepted under any circumstances, but the two lowest homework scores will be dropped. I encourage submission of homework by email in TeX, PostScript, PDF or RTF, but will not accept Microsoft Word documents.

Prerequisites, text and syllabus

Prerequisites: A basic knowledge of groups, rings and fields as covered in the "Algebraic structures" course. Knowledge of linear algebra is helpful but not essential.

Text: Rotman "Advanced modern algebra".

Tentative syllabus:

1. Groups: Group actions, Sylow theorems, finite p-groups, Jordan-Holder theorem, solvable and nilpotent groups, examples of simple groups.
2. Rings and modules: Noetherian rings and modules, Basissatz, structure of fg modules over a PID, localisation, integrality, rings of integers in number fields.
3. Fields: Structure of field extensions, Galois group, fundamental theorem of Galois theory, unsolvability of the quintic, symmetric poynomials, transcendence of e and pi, transcendence degree, Steinitz' theorem.

Exams, HW and grading policy

There will be a midterm and a final. Grades will be assigned according to a formula in which (roughly speaking) homework counts 35 percent, the midterm counts 30 percent and the final counts 35 percent.

Homework sets and exams

1. Homework 1 in PostScript and PDF.
2. Homework 2 in PostScript and PDF.
3. Homework 3 in PostScript and PDF.
4. Midtern in PostScript and PDF.
5. Homework 6 in PostScript and PDF.
6. Final in PostScript and PDF.

Homework solutions

Handouts