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About the course

Course outline

Getting started

Getting set up
Programming best practices
Floating point arithmetic

Manipulating functions

Derivatives
Interpolation
Integration
Solutions to exercises

Random numbers

Random numbers
Linear Congruential Generators
Probability distributions
Monte Carlo integration
Metropolis-Hastings algorithm
Solutions to exercises

Solving systems of equations

Matrices in numpy
Linear least squares
Polynomial fitting
Non-linear least squares
Solutions to exercises
- Orthogonal polynomials
- Lorentzian fit

Machine Learning

Machine Learning
ChatGPT ‘Real-Life Example’
Example : Higgs Boson

Differential equations

Initial value problems
Boundary value problems
Symplectic integrators
Poisson’s equation
Sparse matrices
Boundary conditions and numerical stability
Diffusion in multi-dimensions
Solutions to exercises

Spectral methods

Discrete Fourier transform
Advection-diffusion
Amplitude and phase errors
Burgers’ equation
Signal processing
Solutions to exercises

Performance

Timing, profiling and compiling

Summary

Summary

Homework

Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Exam questions and solutions
Project Instructions
Homework solutions

Repository
Open issue

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Solutions to exercises

Solutions to exercises#

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Metropolis-Hastings algorithm

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Probability distributions Exercise 1

By Andrew Cumming

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