Mathematical Foundations
The mathematics that powers modern computing — linear algebra, probability and statistics, calculus, and set theory, the tools behind graphics, machine learning, and analysis.
Where the Foundations category covers discrete structures and the theory of computation, Mathematical Foundations covers the continuous and statistical mathematics that modern computing leans on: the linear algebra behind graphics and neural networks, the probability and statistics behind machine learning and analytics, the calculus behind optimisation, and the set theory that underlies it all.
This category maps to the CS2023 MSF (Mathematical and Statistical Foundations) knowledge area.
Core
The essentials. Start here.-
Set Theory
The mathematics of collections — sets, membership, and the operations on them. The shared vocabulary beneath logic, databases, type systems, and the rest of mathematics.
core beginner field -
Calculus Basics
The mathematics of change and accumulation — derivatives measure rates, integrals add them up. In computing it powers optimisation and the training of machine-learning models.
core intermediate field -
Linear Algebra
The mathematics of vectors and matrices — the language for representing and transforming data in bulk, and the engine under graphics and machine learning.
core intermediate field -
Probability and Statistics
The mathematics of uncertainty and evidence — probability models what might happen, statistics infers what is true from data. Together they underpin machine learning and analytics.
core intermediate field
Important
What you'll meet next.-
Bayesian Inference
Updating a belief about the world when new evidence arrives — Bayes' rule turned into a systematic method for learning from data while accounting for prior knowledge.
intermediate concept -
Information Theory
The mathematics of measuring, compressing, and transmitting information — entropy quantifies surprise, and channel capacity bounds how much data any link can carry.
intermediate field -
Linear Programming
Optimising a linear objective function subject to linear constraints — the foundational model for scheduling, resource allocation, and network flow, solved efficiently by the simplex method.
intermediate field -
Numerical Methods
Algorithms for computing approximate answers to mathematical problems a computer cannot solve exactly — root-finding, integration, solving differential equations, and fitting data.
intermediate field
Supplemental
Niche, historical, or specialized.-
Game Theory
The mathematical study of strategic interaction — how rational agents make decisions when the outcome for each depends on the choices of others — foundational to economics, auction design, network protocols, and AI multi-agent systems.
supplemental intermediate concept -
Markov Chains
A stochastic process where the next state depends only on the current state — not on history — used to model random walks, PageRank, queuing systems, language models, and Monte Carlo sampling.
supplemental intermediate concept -
Fourier Transform
A mathematical transform that decomposes a signal into its constituent frequencies — converting between time/space domain and frequency domain — the foundation of signal processing, audio compression, image compression, and convolution.
supplemental advanced concept -
Optimization Theory
The mathematical study of choosing the best solution from a set of feasible alternatives — minimising or maximising an objective function subject to constraints — underpinning machine learning, operations research, and engineering design.
supplemental advanced concept