# Math 56, SPRING 2014: Schedule, topics and worksheets

Readings refer to notes and books listed below

week   date    readingdaily topics, demos & codesworksheets
1Mar 25 Tu[R] 1.4, [BG] 2.1Syllabus, introduction. Algebraic and exponential convergence (converge.m). Big-O and little-o. asymp.
26 W X-hrResources 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.
2Apr 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. 8HW1 due. Rules of floating point operations. Catastrophic cancellation (catastrophic.m). Condition number. Derivatives by finite differences. condnum
38 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] 4.3-4.3.2HW2 due; Quiz 1 (study topics). Accuracy of stable algorithms. Condition number of matrix-vector multiplication, condition number of a matrix (linsys).
415 Tu [BG] 7.2, [R] 7.7 Stability of linear systems. Fourier series with complex exponentials. fourier
16 W X-hrDan'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.
521 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).
629 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-hrDan: 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
77 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-hrQuiz 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
813 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).
920 Tu HW7 due. Numerical integration: periodic trapezoid rule, error analysis. Clenshaw-Curtis quadrature theory. clencurt
21 W X-hrCoding and testing quadrature schemes