• [Half-exactness of adjoint functors, Yoneda lemma] [pdf] ... (updated Wed, 09 Mar 05, 12:41 PM)
• [Cantor-Schroeder-Bernstein theorem] [pdf] ... (updated Wed, 17 Mar 04, 04:41 PM)
• [Simple algebras and involutions ] [pdf] ... (updated Sat, 12 Jan 02, 02:28 PM)
• [Poincare-Birkhoff-Witt theorem ] [pdf] ... (updated Fri, 08 Oct 04, 12:56 PM)
• [Cech vs. derived-functor sheaf cohomology] [pdf] ... (updated Mon, 07 Feb 00, 12:02 PM)
• [Homology and derived functors ] [pdf] ... (updated Tue, 18 Jun 02, 03:17 PM)

[These are all incorporated into the "revised, expanded" notes linked-to above.]

Below is from spring semester. Preliminary version of spring is bundled up into
[spring notes] [pdf] ... (updated Fri, 20 May '05, 08:53 AM)]

• [exam 09 solns] [pdf] ... (updated Sat, 07 May '05, 01:44 PM)
• [Exterior powers] [pdf] ... (updated Tue, 10 May '05, 08:58 AM)
• [hmwk 21] [pdf] due Wed 27 Apr [solns 21 (nearly ...)] [pdf] ... (updated Fri, 06 May '05, 04:09 PM)
• [hmwk 20] [pdf] due Wed 20 Apr [solns 20] [pdf] ... (updated Mon, 02 May '05, 04:28 PM)
• [Tensor products] [pdf] ... (updated Thu, 05 May '05, 10:53 AM)
• [hmwk 19] [pdf] due Wed 13 Apr [solns 19] [pdf] ... (updated Fri, 06 May '05, 10:30 AM)
• [exam 08 solns] [pdf] ... (updated Fri, 15 Apr '05, 02:26 PM)
• [Determinants I] [pdf] ... of matrices, precursor to exterior algebra ... (updated Fri, 06 May '05, 10:29 AM)
• [hmwk 18] [pdf] due Wed 30 Mar [solns 18] [pdf] ... (updated Sat, 02 Apr '05, 11:55 AM)
• [solns 15b] [pdf] rational functions invariant under permutations of variables ... (updated Tue, 15 Mar '05, 10:45 AM)
• [Dual spaces, bilinear forms ] [pdf] (draft) ... (updated Sun, 24 Apr '05, 12:58 PM)
• [hmwk 17] [pdf] due Wed 23 Mar [solns 17] [pdf] ... (updated Mon, 04 Apr '05, 10:45 AM)
• [Spectral theory] [pdf] (draft) ... (updated Fri, 01 Apr '05, 10:28 AM)
• [hmwk 16] [pdf] due Wed 02 Mar [solns 16] [pdf] ... (updated Sat, 12 Mar '05, 04:51 PM)
• [hmwk 15] due Wed 23 Feb [solns 15] [pdf] ... (updated Mon, 14 Mar '05, 02:02 PM)
• [Galois theory] [pdf] main theorems (draft) ... (updated Mon, 21 Mar '05, 11:17 AM)
  • [Solving cubic equations] [pdf] ... by radicals, using Lagrange resolvents ... (updated Fri, 04 Mar '05, 10:23 AM)
• [hmwk 14] due Wed 16 Feb ... [solns 14] [pdf](draft) ... (updated Sat, 12 Mar '05, 04:49 PM)
• [exam 06 solns] [pdf] ... (updated Sun, 20 Feb '05, 02:45 PM)
• [exam 05 solns] [pdf] ... (updated Sun, 20 Feb '05, 05:03 PM)
  • [Dirichlet's theorem] [pdf] on primes in arithmetic progressions ... (updated Sun, 20 Feb '05, 03:04 PM)
• [hmwk 13] due Wed 02 Feb ... [solns 13] [pdf] ... (updated Mon, 21 Mar '05, 11:30 AM)
• [hmwk 12] due Wed 26 Jan ... [solns 12] [pdf] ... (updated Sun, 20 Feb '05, 02:45 PM)

Below is from fall semester, in reverse chronological order.
Fall notes bundled up into
[fall notes] [pdf] ... (updated Fri, 08 Jul '05, 11:11 AM)

• [ more on cyclotomic things over Q ] ... (updated Tue, 07 Dec '04, 04:54 PM)
• [ hmwk 11 ] due Wed 08 Dec ... [ solns 11 ] ... (updated Mon, 13 Dec '04, 01:22 PM)
• [ roots of unity, cyclotomic fields, quadratic reciprocity ] ... (updated Sat, 12 Feb '05, 12:03 PM)
• [ exam 04 solns ] ... (updated Sun, 12 Dec '04, 05:45 PM)

• [ hmwk 10 ] due Wed 01 Dec ... [ solns 10 ] ... (updated Mon, 06 Dec '04, 10:15 AM)

• [ cyclotomic polynomials II ] ... (updated Wed, 24 Nov '04, 10:05 AM)
• [ hmwk 09 ] due Wed 17 Nov ... [ solns 09 ] ... (updated Sat, 20 Nov '04, 01:13 PM)

• [ Vandermonde determinants ] ... (updated Tue, 16 Nov '04, 10:30 AM)
• [ Eisenstein's criterion ] ... (updated Mon, 01 Nov '04, 01:56 PM)
• [ symmetric polynomials ] ... (updated Sat, 12 Feb '05, 12:03 PM)
• [ exam 03 solns ] ... (updated Fri, 12 Nov '04, 06:38 PM)

• Optional interlude: some not-so-finite algebra:
  • [ ordinals and well-ordered sets ] ... (updated Tue, 02 Nov '04, 06:06 PM)
  • [ example of transfinite induction: Lagrange replacement ] ... (updated Tue, 02 Nov '04, 05:15 PM)
• [hmwk 08 ] due Wed 03 Nov ... [solns 08 ] ... (updated Thu, 04 Nov '04, 12:27 PM)
• [ unique factorization in polynomials rings over UFDs: Gauss' lemma ] ... (updated Tue, 08 Feb '05, 09:54 AM)
• [hmwk 07 ] due Wed 27 Oct ... [solns 07 ] ... (updated Wed, 27 Oct '04, 11:54 AM)

• [ free modules, PIDs, finitely-generated modules over PIDs ] ... (updated Wed, 24 Nov '04, 11:24 AM)
• [ exam 02 solns ] ... (updated Fri, 22 Oct '04, 03:05 PM)

• [hmwk 06 ] due Wed 20 Oct ... [solns 06 ] ... (updated Mon, 25 Oct '04, 01:18 PM)
• [ structure theorem for f.g. modules over PIDs, Jordan form, etc. ] ... (updated Tue, 19 Oct '04, 04:29 PM)
• [ finite fields ] ... (updated Thu, 14 Oct '04, 11:28 AM)
• [hmwk 05 ] due Wed 13 Oct ... [solns 05 ] ... (updated Sun, 17 Oct '04, 01:48 PM)

• [ cyclotomic polynomials I ] ... (updated Sun, 24 Apr '05, 02:39 PM)
• [hmwk 04 ] due Wed 06 Oct ... [solns 04 ] ... (updated Thu, 07 Oct '04, 09:10 AM)

• [ some irreducible polynomials over finite fields ] ... (updated Sun, 03 Oct '04, 02:42 PM)
• [ field extensions basics ] ... (updated Tue, 12 Oct '04, 05:11 PM)
• [ linear algebra I: bases, dimension, kernels, images ] ... (updated Sat, 25 Sep '04, 01:38 PM)
• [ exam 01 solns ] ... (updated Thu, 30 Sep '04, 09:24 AM)

• [hmwk 03 ] due Wed 29 Sept ... [solns 03 ] ... (updated Thu, 30 Sep '04, 12:50 PM)

• [ commutative rings, polynomials, maximal ideals, prime ideals, sum-of-two-squares ] ... (updated Thu, 30 Sep '04, 12:35 PM)
• [ introduction for rings, fields, vector spaces, modules ] ... (updated Sat, 25 Sep '04, 01:25 PM)
• [hmwk 02 ] due Wed 22 Sept ... [solns 02 ] ... (updated Wed, 22 Sep '04, 11:27 AM)

• [ groups I] ... (updated Sat, 12 Feb '05, 12:04 PM)
• [hmwk 01 ] due Wed 15 Sept ... [solns 01 ] ... (updated Fri, 24 Sep '04, 03:08 PM)

• [ the integers ] ... (updated Mon, 27 Sep '04, 10:54 AM)

• In 2004-05, MWF 9:05-9:55, Vincent 206
• It is assumed that this is NOT your first course in abstract algebra, even though our review will start from first principles. Is is assumed that you have experience with linear algebra, with set theory as a descriptive language, and with the semantics and syntax of proof.
• Office hours MWF after class, or email anytime. Forming questions in email is a useful exercise.
• Grading:
  • weekly homework, worth 40% of the total, due each Wednesday at the beginning of class
  • 4 exams: Wed Feb 09, Wed Mar 09, Wed Apr 06, Wed May 04, each worth 10% of the total
  • final, Fri, May 13, 1:30-3:30, worth 20% of the grade.
  • grades will not be `curved'. This means that if everyone does well, everyone gets a good grade:

    A	=	93.00-100.0	A-	=	90.00-92.99
    B+	=	86.67-89.99	B	=	83.34-86.66	B-	=	80.00-83.33
    C+	=	76.67-79.99	C	=	73.34-76.66	C-	=	70.00-73.33
    D+	=	65.00-69.99	D	=	60.00-64.99		etc

  • When grading in the S/N system, an 'S' is equivalent to a 'C' or better.
  • We will follow IT/CLA policies on incompletes, scholastic misconduct, etc.
• To be graded, all writing must be coherent and succinct, legible, grammatically correct, and spelled correctly.
• Text will be my notes. You should also have at least one, preferably two or three, further references. Lang's Algebra is standard, but not meant for the novice.