| week | date | reading | daily topics, demos & codes | worksheets |
|---|---|---|---|---|
| 1 | Mar 26 Tu | [R] 1.4, [BG] 2.1 | Introduction. Algebraic and exponential convergence (converge.m). Big-O and little-o. Taylor series. | |
| 27 W X-hr | Resources page | Matlab (intro56.m, and tom.m); LaTeX (test.tex which needs squiggle.eps, and gives test.pdf). | ||
| 28 Th | [R] 1.5, [BG] 2.8.3 | Convergence rate and the complex plane. Effective 2d plots. Super-exponential convergence. | converge | |
| 2 | Apr 2 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. Good coding (zeta.m and testzeta.m). Floating point, summing series. | newton |
| 4 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 | 9 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 |
| 10 W X-hr | HTML, [BG] 3.7 | Basic HTML. Breaking then fixing our bisection codes! (bring laptops) | ||
| 11 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. Stability of linear systems, condition number of a matrix (linsys). | ||
| 4 | 14 Tu | [BG] 7.2, [R] 7.7 | Fourier series with complex exponentials. Deriving Discrete Fourier Transform via quadrature approximation. Trigonometric interpolation. | fourier |
| 15 W X-hr | practise problems for midterm 1. | |||
| 16 Th | [BG] 7.2.2 | HW3 due. DFT: Roots of unity & sum lemma, inversion formula, unitarity. | ||
| Midterm 1: Thurs April 16, 6-8pm, Kemeny 004. Topics | ||||
| 5 | 21 Tu | [BG] 7.2.2 | Aliasing formula, Nyquist sampling theorem. Getting to know DFT matrix. Audio signal analysis application, physical frequency units (audiofft.m) | dft |
| 22 W X-hr | (no X-hr) | |||
| 23 Th | [BG] 7.2.3, history | HW4 due. The Fast Fourier Transform (Cooley-Tukey algorithm). Applications of FFT: convolution and deconvolution. | ||
| 6 | 30 Tu | Gourdan 1, 2, [CP] 9.5, this | Super-algebraic convergence, review other convergence types. Large integer addition (bigintadd.m, testbigintadd.m), Acyclic convolution. Strassen's fast multiplication. Fast division via Newton iteration for reciprocal. | arbprec |
| May 1 W X-hr | (no X-hr) | |||
| 2 Th | Gourdan, Sandifer, BBB, App. 12-15, Salamin | HW5 due. Error bounds in trigonometric polynomial interpolation. Computing digits of pi: Taylor with Machin formulae (atanCplane), Brent-Salamin quadratic convergent iteration. High accuracy floating-point computation in Python/SAGE/mpmath. | machin | |
| 7 | 7 Tu | quest, BBP | Project 1-page description due. 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 | |||
| 9 Th | [S] Ch. 1, [H] 2.3-2.4, Brent | HW6 due. Computational number theory: basics and applications of factoring, modular arithmetic, GCD via Euclid, trial division, complexity thereof. | factorbasic | |
| 8 | 14 Tu | Brent, 2 sieves | Finding large factors: Fermat's method, Kraitchik's improvement, linear algebra mod 2. | kraitchik |
| Midterm 2: Tues May 14, 6-8pm, Kemeny 004 Topics | ||||
| 16 Th | [EMA] Ch. 6; [CP] Ch. 6.1 | Quadratic sieve, frequency of smooth numbers (smoothhist.py, its plot). Numerical integration: periodic trapezoid rule, error analysis. | ||
| 9 | 21 Tu | HW7 due. Product quadrature, Clenshaw-Curtis quadrature (democlencurt.m which needs clencurt.m) | clencurt | |
| 22 W X-hr | ||||
| 23 Th | Adaptive quadrature (adaptivequad.m). Statistical tests in experimental mathematics: testing bias and correlation in digit strings (sampling). | hyptest | ||
| 10 | 28 Tu | Student project presentations (may use poster rather than slides) in lecture slot.. Also strongly encouraged that day: 4-6pm undergraduate poster session. | ||
| 31 Fr | Project write-ups due (noon) | |||
| 31 F - June 4 Tu: Exam period (no final exam :) ) | ||||