Mathematics

01

Beautiful Numbers

Prime numbers, Fibonacci, the Golden Ratio, π, e, the Riemann zeta function and the mysteries hidden within numbers.

Prime Numbers
Fibonacci and the Golden Ratio
Euler's Identity
Pi
The Number e

02

Probability, Statistics & Volatility

Probability, distributions, standard deviation, Z-scores, sampling, the Central Limit Theorem, Monte Carlo simulation and financial volatility.

Probability
The Normal Distribution
Standard Deviation / Volatility
The Central Limit Theorem
Random Sampling

03

Simulation and Probability Distributions

Mathematics used to model, calculate and solve practical problems - from compound growth and optimisation to real-world systems.

Monte Carlo Simulation
Financial Return Distributions
Normal Distributions to Student-t Distributions to Skew-t Distributions
Regime Switching and GARCH

04

Mathematics of Risk

Correlation, default probability, joint default, portfolio risk, credit risk and the mathematics behind measuring uncertainty.

Mathematics and Risk
Correlated bivariate normal distribution
Joint Default Probability Calculator
Black-Scholes and Merton

05

Complex Numbers & Chaos

Complex numbers, iteration, fractals, the Mandelbrot Set and the surprising mathematics of chaotic systems.

Mandelbrot Set
Complex Numbers
Julia Sets
Chaos
Fractals
Riemann Integrals
The Riemann Hypothesis

06

Mathematics of the Solar System

Gravity, orbital mechanics, Kepler's laws, planetary motion and the mathematics governing our journey through the Solar System.

Orbital Mechanics
The mathematics of the Solar System
The mathematics of the Solar System
Stellar Evolution
Black Holes
Cosmology
The Mathematics of Light
Exoplanets & Probability
Asteroids and Impact Probability
The Mathematics of Time