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 (, 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
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.
1027 TuStudent project presentations (may use poster rather than slides) in lecture slot..
28 W10-11am in Kemeny 209: Remaining student presentations.
June 1 SuProject write-ups due by end of day
30 F - June 3 Tu: Exam period (no final exam :) )

Books and notes