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Representation of real numbers, and addition and subtraction on them
Multiplication and division of real numbers
Arithmetic on real numbers
Calculating square roots of real numbers
Calculating \(\pi\) and \(e\)
Numerical integration
Trigonometric functions
Root-finding algorithms
Constructing the Mandelbrot set
Identifying roots of linear equations
Identifying roots of non-linear equations
Discrete linear algebra
Linear algebra
Calculating convex hulls
Numerical methods for Ordinary Differential Equations (ODEs), including Euler's method
Numerical methods for Partial Differentiable Equations (PDEs)
Solving elliptic curves
Optimising smooth functions with gradient descent
Extensions to gradient descent
Unconstrained optimisation of discrete functions
Unconstrained optimisation of non-differentiable real functions
Constrained optimisation: Linear, quadtratic and convex programming
We initialise at some point in the parameter space.
We identifify nearby alternative points in parameter space, and move to the one with the most improvement.
Movement only occurs in one parameter at a time.