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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

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