Math 7752. Algebra-II.

Algebra-II. Math 7752. Spring 2010.

ThTh 11am-12:15 pm, Kerchof 317.

Main Text: Abstract Algebra, David Dummit and Richard Foote.

Course outline

Prerequisites: Math 751 and an undergraduate courses in linear algebra comparable in level to UVa 551.

Course content: The first half of the semester (up to the spring break) will be devoted to modules and multilinear algebra. The material we will cover is mostly contained in Chapters 10-12 of Dummit and Foote. Sections 11.1-11.3 will only be briefly reviewed as they contain material covered in standard undergraduate linear algebra courses. In the second half of the course we will study fields and Galois theory. The material we will cover is mostly discussed in Chapters 13-14 of Dummit and Foote, though the order of my exposition will be quite different and closer to Lang's book ``Algebra''. Time permitting, at the end of the course (the last two or three classes) we will discuss an additional topic, e.g. the proof of Hilbert's Nullstellensatz.

Exams and homework: There will be weekly homework and three exams -- two midterms (both take-home) and the final (format TBD). Tentative dates for exams are as follows:



Homework will be assigned weekly and will usually be due on Thursdays. Each assignment will contain 6-8 problems, and your lowest score (on each assignment) will be dropped. You are allowed and encouraged to submit your homework electronically (as a .tex file) or orally to get a more efficient feedback.

Collaboration policy.