01/06 Lecture 1. Review of the properties of the integers. See Harron's notes for a more precise treatment.
01/09 Lecture 2. Divisibility.
01/11 Lecture 3. Primes.
01/13 Lecture 4. Fundamental Theorem of Arithmetic.
01/18 Lecture 5. Congruence mod n: definitions.
01/20 Lecture 6. Units and zero-divisors mod n.
01/23 Lecture 7. Fermat's little theorem.
01/25 Lecture 8. Chinese remainder theorem.
01/27 Lecture 9. Rings.
01/30 Lecture 10. Integral domains and fields.
02/01 Lecture 11. The polynomial ring.
02/03 Lecture 12. Irreducibility.
02/06 Lecture 13. Homomorphisms.
02/08 Midterm I.
02/10 Lecture 14. Isomorphisms.
02/13 Lecture 15. Euclidean domains: polynomial rings.
02/15 Lecture 16. Euclidean domains: Gaussian integers.
02/17 Lecture 17. The Euclidean algorithm.
02/20 Lecture 18. Factorization into irreducibles.
02/22 Lecture 19. Primes and unique factorization.
02/24 Lecture 20. Factorization in F[x].
02/27 Lecture 21. Irreducibility in C[x] and R[x].
03/01 Lecture 22. Irreducibility in Q[x]: rational roots.
03/03 Lecture 23. Irreducibility in Q[x]: reducing mod p.
03/13 Lecture 24. Ideals.
03/15 Lecture 25. Quotient rings.
03/17 Lecture 26. Quotient homomorphisms.
03/20 Lecture 27. Some finite fields.
03/22 Midterm II.
03/24 Lecture 28. Irreducibles in the Gaussian integers.
03/27 Lecture 29. Irreducibles in other quadratic rings.
03/29 Lecture 30. The first isomorphism theorem I.
03/31 Lecture 31. The first isomorphism theorem II.
04/03 Lecture 32. Quotients of Euclidean domains.
04/05 Lecture 33. Prime and maximal ideals.
04/07 Lecture 34. Minimal polynomials.
04/10 Lecture 35. Finite-dimensional field extensions.
04/12 Lecture 36. Bases and dimension.
04/14 Lecture 37. Existence of bases.
04/17 Lecture 38. Multiplicativity of degree.