Lecture |
Topic |
Read |
Blank notes
| Class notes |
Links & extra |
1
|
Course Intro, programming languages, C basics, random walk
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tutorials |
draft1
| Lec1
|
Snake in 5 minutes; Dinosaurs in 3 minutes
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2
|
Variable representation, precision, accuracy, loss of precision, recursion and differential equations
|
NR1
|
draft2 | Lec2 Snake
|
Roundoff disasters One-liners 2010
|
3 |
Stability, scope of variables, arrays, passing variables by value/reference
|
NR1
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draft3
| Lec3
|
C (de) referencing scope
|
4 |
Dynamical programming, continued fractions, interpolation and extrapolation: intro and Neville method, searching an ordered table, reading NR codes
|
NR3
|
draft4 | Lec4
|
Golden ratio Interpolation in Python
|
5 |
Interpolation: rational, spline, and multiple dimensions; Integration: Newton-Cotes formulae
|
NR3
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draft5
| Lec5
|
Integration in Python
|
6 |
Newton-Cotes algorithms, Richardson extrapolation, Romberg open+closed methods, improper integrals 1
|
NR4
|
draft6
| Lec6
|
P vs. NP
|
7 |
Improper integrals 2, orthogonal polynomials, Gaussian quadrature, integration in multiple dimensions
|
NR4
|
draft7
| Lec7
|
Monte Carlo examples
|
8 |
Statistics recap, Monte Carlo, MC examples, variance reduction, fractals, sampling from a distribution
|
NR
7.6-7.8
|
draft8
| Lec8
|
Mandelbrot zoom Logistic map
|
9 |
quasi-MC, importance+stratified sampling, diffusion with interactions, working with data, moments of a distribution 1
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7.6-7.8 NR 14
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draft9
| Lec9
|
Randomness
|
10 |
Pitfalls in statistics, moments of a distribution 2, estimating the significance of sample statistics
|
NR14
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11 |
Student t-test, MC in statistics, MC simulation as an integral, chi-squared test, KS-test
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NR14
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12 |
Maximal likelihood, Chi-squared minimization, root finding: bracketing, bisection, secant, false position, Brent, Newton-Raphson
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NR15
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13 |
Root finding in multiple dimensions: Newton-Raphson, Broyden; optimization: bracketing; ODEs: Euler, Runge-Kutta, explicit vs. implicit methods, stiff equations, adaptive step, Bulirsch-Stoer, shooting
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NR16
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