Syllabus for Roster(s):
- 15F MATH 3354-002 (CGAS)
In the UVaCollab course site: 15F MATH 3354-002 (CGAS)
Course Description
This course introduces basic structures of modern algebra: groups, rings and fields. Approximately first 4 weeks of the course will be devoted to elementary number-theoretic topics (Chapter 2 of the book): greatest common divisor, unique factorization theorem, congruences etc. You should be familiar with most of these from high school, but we will study them at a more sophisticated level. The core part of the course (about 7 weeks) is concerned with group theory (Chapters 3 and 4). In the last 3 weeks we will discuss selected topics from ring theory (Chapters 5 and 6) and (if time allows) some additional topics, possibly not covered by the book (in the latter case, additional references or online notes will be provided). I will assume basic familiarity with material of Chapter 1 (mostly set theory). You should read this chapter on your own in the first couple of weeks and ask me questions about unclear points.