"The purpose of computing is insight, not numbers."

                           - Richard Hamming



> Class and extra material:

 

 

 

 

 

Lecture Topic Class notes Links & extra
1 Course Intro, programming languages, C basics Lec 1 Snake in 5 minutes, Dinosaurs in 3 minutes
2 Variable representation, precision, accuracy, stability, variable scope 1 Lec 2 Golden ratio, Roundoff disasters
3 Variable scope 2, referencing, arrays, recursion, dynamical programming, interpolation and extrapolation motivation Lec 3 C (de) referencing, scope
4 Polynomial and rational interpolation, searching an ordered table, reading NR codes Lec 4 Interpolation in Matlab
5 Interpolation: spline, and multiple dimensions; Integration: Newton-Cotes formulae Lec 5 Integration in Matlab
6 Newton Cotes algorithms, Richardson extrapolation, Romberg open+closed methods, improper integrals, using Gaussian quadrature Lec 6 P vs. NP
7 Orthogonal polynomials, Gaussian quadrature, integration in multiple dimensions, Monte Carlo 1 Lec 7 Monte Carlo examples
8 Monte Carlo 2: generalizations, examples, variance reduction, importance and stratified sampling Lec 8 Mandelbrot zoom: short, long
Randomness
9 Diffusion problems with MC, working with data, moments of a distribution, Student t-test Lec 9 Student t-test
10 MCMC, pitfalls in statistics, chi-squared test, KS-test, maximal likelihood Lec 10 Simpson's paradox
11 Chi-squared minimization, root finding: bracketing, bisection, secant, false position, Brent, Newton-Raphson Lec 11 2D bracket
12 Root finding in multiple dimensions: Newton-Raphson, Broyden; Optimization: bracketing, golden-section, Brent, steepest descent Lec 12 Newton optimization
13 Optimization: conjugate vectors, quasi-Newton, simulated annealing. ODEs: Euler, Runge-Kutta, explicit vs. implicit methods, stiff equations, adaptive step, Bulirsch-Stoer Lec 13 ODEs in gaming
14 Review Review

 

 

 

 

 

Software access

 

 

 

Exams