Applied Mathematics

Convex optimisation solves problems where local optima are global. You will learn convex sets and functions, duality, algorithms and how to model engineering and machine-learning problems as convex programs.

This topic covers the mathematical foundations of secure communication, including number theory, abstract algebra, and probability. Learners will understand how algorithms like RSA and elliptic curve cryptography secure data transmission and digital signatures.

Financial mathematics applies mathematical modeling and quantitative methods to financial markets. Learners will understand how to price derivative securities, manage portfolio risk, and model asset price movements using stochastic calculus and interest rate theory.

FEA and CFD simulate stresses, heat and fluid flow numerically. You will learn the underlying methods, meshing, boundary conditions, validation and how to use tools such as ANSYS, Abaqus or OpenFOAM responsibly.

Information theory quantifies information, compression and communication. You will learn entropy, mutual information, channel capacity and coding, and why these ideas underpin statistics and machine learning.

Mathematical modeling is the process of translating real-world phenomena into mathematical equations to analyze and predict behaviors. Learners will understand how to formulate, solve, and validate models across physics, biology, and social sciences.

Machine learning rests on linear algebra, calculus, probability and optimisation. You will learn exactly the mathematics needed to read ML papers and textbooks, with the resources that teach it in that order.

Numerical methods are algorithms used to obtain approximate numerical solutions to mathematical problems that lack analytical solutions. Learners will understand how to solve differential equations, find roots, and perform numerical integration using computers.

Optimization is the study of finding the best solution to a problem given a set of constraints. Learners will understand how to formulate and solve linear, non-linear, and integer programming problems using various mathematical algorithms.

Quantitative finance applies mathematics to pricing and risk. You will learn stochastic calculus, derivatives pricing, portfolio theory and the programming and interview preparation used in quant roles.

Stochastic calculus handles calculus for random processes. You will learn Brownian motion, Itô's lemma, stochastic differential equations and the applications to option pricing and filtering.