| 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 |