Week	Lecture Day	Topic	Suggested Reading	Additional Suggested Exercises
1	January 5 January 7	Rings: definition and first examples; zero divisors, units; integral domains, fields Ring homomorphisms; subrings; ideals and quotient rings	§7.1 §7.3	§7.1: 11, 13, 15, 26 §7.3: 3, 4, 10, 11, 19, 26, 30
2	January 12 January 14	Isomorphism theorems for rings; more examples of rings Ideal generated by a set, principal ideals; maximal ideals, prime ideals	§7.3(end);§7.2 §7.4	§7.2: 1, 3 §7.4: 9, 11, 12, 19, 26, 31
3	January 19 January 21	Operations on ideals; the Chinese Remainder Theorem Euclidean domains; the Euclidean algorithm	§7.6 §8.1	§7.6: 1, 4, 7 §8.1: 1, 3, 4
4	January 26 January 28	Principal Ideal Domains (PIDs) Unique Factorization Domains (UFDs)	§8.2 §8.3	§8.2: 1, 5 §8.3: 2, 8
5	February 2 February 4	Ring of fractions Review	§7.5 -	§7.5: 3, 4 -
6	February 9 February 11	Midterm Polynomial rings over fields	- §9.2	- §9.2: 1, 2, 3, 5, 7, 8
7	February 16 February 18	Polynomial rings over UFDs Irreducibility criteria	§9.3 §9.4	§9.3: 1, 2 §9.4: 2, 7, 8, 16, 19
8	February 23 February 25	Modules, submodules, and module homomorhisms Quotient modules; generators, direct sums, and free modules	§10.1 §10.2; §10.3	§10.1: 7, 8, 11, 13 §10.2: 4, 8, 10, 13; §10.3: 4, 5, 6, 7, 9, 12, 13
9	March 2 March 4	Structure Theorem for finitely generated modules over PIDs Application I: Rational Canonical Form	§12.1 §12.2
10	March 9 March 11	Application II: Jordan Canonical Form Review	§12.3 -