The numbers before the titles of the lectures in the course outline below refer to sections in Numerical Polynomial Algebra.

L-1 Mon 23 Aug 1.1,2,5 introduction to numerical polynomial algebra
L-2 Wed 25 Aug 1.3,4 ideals and varieties
L-3 Fri 27 Aug 2.1,2 ideal bases and quotient rings
L-4 Mon 30 Aug 2.3 dual spaces and ideals
L-4 Wed  1 Sep 2.4 the central theorem
L-5 Fri  3 Sep 2.5 normal sets and border bases
  Mon  6 Sep   Labor Day holiday - no classes
L-7 Wed  8 Sep 3.1,2 empirical polynomials and condition
L-8 Fri 10 Sep 3.3,4 backward error and refinement
L-9 Mon 13 Sep 4.1,2 numerically stable algorithms
L-10 Wed 15 Sep 4.3,4 floating-point and interval arithmetic
L-11 Fri 17 Sep 5.1 intrinsic polynomials
L-12 Mon 20 Sep 5.2 zeros of empirical univariate polynomials
L-13 Wed 22 Sep 5.3 polynomial division
L-14 Fri 24 Sep 5.4 polynomial interpolation
L-15 Mon 27 Sep 6.1 algebraic predicates
L-16 Wed 29 Sep 6.2 divisors of empirical polynomial
L-17 Fri  1 Oct 6.3 multiple zeros and zero clusters
L-18 Mon  4 Oct 6.4 greatest common divisors
L-19 Wed  6 Oct   review of chapters 1 to 6
L-20 Fri  8 Oct   midterm exam on chapters 1 to 6
L-21 Mon 11 Oct 7.1,2 one empirical multivariate polynomial
L-22 Wed 13 Oct 7.3 singular points on algebraic manifolds
L-23 Fri 15 Oct 7.4 numerical absolute factorization
L-24 Mon 18 Oct 8.1 quotient rings and border bases
L-25 Wed 20 Oct 8.2 normal set representations
L-26 Fri 22 Oct 8.3 homotopies and polyhedral methods
L-27 Mon 25 Oct 8.4 numerical stability of Groebner bases
L-28 Wed 27 Oct 8.5 multiple zeros of intrinsic polynomial systems
L-29 Fri 29 Oct 9.1 regular systems of empirical polynomials
L-30 Mon  1 Nov 9.2 approximate representation of polynomial ideals
L-31 Wed  3 Nov 9.3 multiple zeros and zero clusters
L-32 Fri  5 Nov 9.4 singular systems of empirical polynomials
L-33 Mon  8 Nov 9.5,6 deficient systems; multivariate interpolation
L-34 Wed 10 Nov 10.1 algorithmic computation of Groebner bases
L-35 Fri 12 Nov 10.2 algorithms for normal set representations
L-36 Mon 15 Nov 10.3 numerical aspects of basis computation
L-37 Wed 17 Nov 11.1 extension of the central theorem
L-38 Fri 19 Nov 11.2 singular matrix eigenproblems
L-39 Mon 22 Nov 11.3 zero sets from finite multiplication matrices
L-40 Wed 24 Nov 11.4 a quasi zero dimensional approach
  Fri 26 Nov   no class because of Thanksgiving
L-41 Mon 29 Nov   review of chapters 1 to 6
L-42 Wed  1 Dec   review of chapters 7, 8, and 9
L-43 Fri  3 Dec   review of Chapters 10 and 11
Monday 6 December 2004, 1:00-3:00: Final Exam, room to be announced.