Jan 9 
1.1 
Introduction. Rings: examples and basic properties. 
Jan 12 
1.1–1.2 
Isomorphic rings. Integral domains and fields. 
Jan 16 
1.2 
Integral domains and fields, field of fractions 
Jan 19 
1.3 
Ideals and quotient rings 
Jan 23 
1.3, 1.4 
Maximal ideals, ring homomorphisms 
Jan 26 
1.4 
First Isomorphism Theorem, Chinese Remainder Theorem. 
Jan 30 
2.1 
Polynomial rings 
Feb 2 
2.1 
The division algorithm, evaluation and roots of polynomials 
Feb 6 
2.2 
Irreducible polynomials, factoring polynomials over the real and complex numbers 
Feb 9 
2.2 
Gauss' Lemma, Modular Irreducibility Test, Eisenstein Criterion, gcd of polynomials 
Feb 13 
2.2 
Euclidean algorithm, unique factorization of polynomials 
Feb 16 
2.3 
Quotient rings of polynomials over a field 
Feb 19–23 
Reading week 
Feb 27 
3.1 
Unique factorization domains 
Mar 2 
1.1–2.3 
Midterm test 
Mar 6 
3.1 
Unique factorization domains 
Mar 9 
3.1–3.2 
Unique factorization domains, principal ideal domains 
Mar 13 
3.2–3.3 
Principal ideal domains, euclidean domains 
Mar 16 
4.1–4.2 
Review of vector spaces, field extensions 
Mar 20 
4.2 
Field extensions, minimal polynomials 
Mar 23 
4.2 
Field extensions, the Multiplication Theorem 
Mar 27 
4.3 
Splitting fields 
Apr 3 
4.3 
Splitting fields, algebraic closures 
Apr 6 
4.4 
Finite fields 
Apr 10 
Review 
