| week | date | reading | daily topics, demos & codes | worksheets |
|---|---|---|---|---|
| 1 | Mar 25 Tu | [R] 1.4, [BG] 2.1 | Syllabus, introduction. Algebraic and exponential convergence (converge.m). Big-O and little-o. | asymp. |
| 26 W X-hr | Resources page | Dan: Matlab (intro56.m, and tom.m); LaTeX (test.tex which needs squiggle.eps, and gives test.pdf). | ||
| 27 Th | [R] 1.5, [BG] 2.8.3 | Taylor series convergence rate and the complex plane. Effective 2d plots. Super-exponential convergence. | ||
| 2 | Apr 1 Tu | [R] 5.3, 2.1-2, 3.1, [H] 1.4-1.8, [TB] Ch.13, [M126] p.12, [BG] 2.2.2 | Newton and sqrt iteration, quadratic convergence. Floating point (1-page summary), summing series. | newton |
| 2 W X-hr | ||||
| 3 Th | [M126] p.10, [BG] 2.2.3, [R] Ch. 8 | HW1 due. Rules of floating point operations. Catastrophic cancellation (catastrophic.m). Condition number. Derivatives by finite differences. | condnum | |
| 3 | 8 Tu | [GC] Ch.6, [TB] Ch.14-15, [R] Ch.4, [BG] 2.3, 3.2, 3.5 | Balancing finite difference errors. Stability of algorithms, backwards stability. | backstab |
| 9 W X-hr | Coding finite differencing and testing its error performance. | |||
| 10 Th | [TB] Ch.15,12, [GC] 7.4.2, [BG] 4.3-4.3.2 | HW2 due; Quiz 1 (study topics). Accuracy of stable algorithms. Condition number of matrix-vector multiplication, condition number of a matrix (linsys). | ||
| 4 | 15 Tu | [BG] 7.2, [R] 7.7 | Stability of linear systems. Fourier series with complex exponentials. | fourier |
| 16 W X-hr | Dan's practise problems for midterm 1. (Also see topics wk 1-3 and practise problems). | |||
| 17 Th | [BG] 7.2.2 | HW3 due. Deriving Discrete Fourier Transform (DFT) via quadrature approximation. Trigonometric interpolation. Band-limited functions. Getting to know DFT matrix. Roots of unity. | dftsum | |
| Midterm 1: Thurs April 16, 6-8pm, Kemeny 004. | ||||
| 5 | 21 Tu | [BG] 7.2.2 | Sum lemma. Inversion formula, unitarity. Aliasing formula, Nyquist sampling theorem. | alias |
| 22 W X-hr | (none) | |||
| 23 Th | [BG] 7.2.3, history | HW4 due. Audio signal analysis application, physical frequency units (audiofft.m) The Fast Fourier Transform (Danielson-Lanczos lemma, Cooley-Tukey algorithm). | ||
| 6 | 29 Tu | Gourdan 1, 2, [CP] 9.5, this | Review smoothness and Fourier decay, super-algebraic convergence. Applications of FFT: Convolution and deconvolution, Acyclic convolution. Large integer addition (bigintadd.m, testbigintadd.m). Strassen's fast multiplication. | arbprec |
| May 1 W X-hr | Dan: filtering and convolution | |||
| 2 Th | Gourdan, Sandifer, BBB, App. 12-15, Salamin | HW5 due. Fast division via Newton iteration for reciprocal. [Ingredients of arbitrary precision arithmetic library.] Error bounds in trigonometric polynomial interpolation. Computing digits of pi: Taylor with Machin formulae (atanCplane). High accuracy floating-point computation in Python/SAGE/mpmath. | machin | |
| 7 | 7 Tu | quest, BBP | Project 1-page description due this week. Brent-Salamin quadratic convergent iteration. Regularization for deconvolution in presence of noise. Borwein-Bailey-Plouffe algorithm for binary digits of log 2, and pi. | matlabvspython |
| 8 W X-hr | Quiz 2, and bit of review for Midterm 2. | |||
| 9 Th | [S] Ch. 1, [H] 2.3-2.4, Brent | HW6 due. Computational number theory: basics and applications of factoring, modular arithmetic, trial division, complexity thereof. | factorbasic | |
| 8 | 13 Tu | Brent, 2 sieves | GCD via Euclid. Finding large factors: Fermat's method. | kraitchik |
| Midterm 2: Tues May 13, 6-8pm, Kemeny 120 Topics | ||||
| 15 Th | [EMA] Ch. 6; [CP] Ch. 6.1 | Kraitchik's method, linear algebra mod 2. Quadratic sieve, frequency of smooth numbers (smoothhist.py, its plot). | ||
| 9 | 20 Tu | HW7 due. Numerical integration: periodic trapezoid rule, error analysis. Clenshaw-Curtis quadrature theory. | clencurt | |
| 21 W X-hr | Coding and testing quadrature schemes | |||
| 22 Th | Clenshaw-Curtis in practice (democlencurt.m which needs clencurt.m). Adaptive quadrature (adaptivequad.m), oscillatory quadrature via complex contour integration (oscquad.m and gauss.m), higher dimensions. | |||
| 10 | 27 Tu | Student project presentations (may use poster rather than slides) in lecture slot.. | ||
| 28 W | 10-11am in Kemeny 209: Remaining student presentations. | |||
| June 1 Su | Project write-ups due by end of day | |||
| 30 F - June 3 Tu: Exam period (no final exam :) ) | ||||