SF2729 Groups and Rings

Plan

	Part I - Groups
Jan 27	Groups	I 1-4	Jan 28	Exercises
Feb 2	Subgroups, cyclic groups and Cayley digraphs	I 5-7	Feb 4	Exercises
Feb 9	Permutations	II 8-9	Feb 11	Exercises
Feb 16	Lagrange's Theorem and finitely generated abelian groups	II 10-12	Feb 18	Exercises
Feb 23	Homomorphisms and factor groups	III 13-15	Feb 25	Exercises
Mar 2	Group actions	III 16-17.	Mar 4	Exercises
Mar 9	Free groups and group presentations	VII 34, 38-40	Mar 11	Exercises
	Part II - Rings
Mar 23	Rings and fields, integral domains and Fermat's theorem	IV 18-20	Mar 25	Exercises
Mar 30	Fields of quotients and rings of polynomials	IV 21-23	Apr 1	Exercises
Apr 13	Factor rings and ideals	V 26-27
Apr 20	Gröbner bases	V 28	Apr 22	Exercises
Apr 27	Unique factorization domains and Euclidean domains	IX 45-47	Apr 29	Exercises
			May 4	Exercises
May 6	Vector spaces and algebraic extensions	VII 29-31	May 11	Exercises
May 18	Finite fields	VII 32-33	May 20	Exercises

Chapter numbers refer to chapters in the book: "A first course in Abstract Algebra" by J.B. Fraleigh.