Math 56, SPRING 2013: Schedule, topics and worksheets

Readings refer to books listed below

week   date    readingdaily topics, demos & codesworksheets
1Mar 26 Tu[R] 1.4, [BG] 2.1Introduction. Algebraic and exponential convergence (converge.m). Big-O and little-o. Taylor series.
27 W X-hrResources 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
2Apr 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. 8HW1 due. Rules of floating point operations. Catastrophic cancellation (catastrophic.m). Condition number. Derivatives by finite differences. condnum
39 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-hrHTML, [BG] 3.7 Basic HTML. Breaking then fixing our bisection codes! (bring laptops)
11 Th [TB] Ch.15,12, [GC] 7.4.2, [BG] 4.3-4.3.2HW2 due; Quiz 1 (study topics). Accuracy of stable algorithms. Stability of linear systems, condition number of a matrix (linsys).
414 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-hrpractise 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
521 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.
630 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
77 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-hrQuiz 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
814 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 (, its plot). Numerical integration: periodic trapezoid rule, error analysis.
921 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
1028 TuStudent project presentations (may use poster rather than slides) in lecture slot.. Also strongly encouraged that day: 4-6pm undergraduate poster session.
31 FrProject write-ups due (noon)
31 F - June 4 Tu: Exam period (no final exam :) )

Books and notes