- Adjacency matrix
Graphs in matrix form.
- Collatz Conjecture
A seemingly simple problem that no one has been able to solve.
- Computability
There exist numbers that are not computable.
- Computational Theory
Computational Theory in Summer 2023/24
- Computational Theory (Autumn)
Computational Theory in Autumn 2023/24
- Conway's Game of Life
A simple game devised by Conway, based on ideas from von Neumann and Ulam.
- Eigenvalues
Investgiating matrices and transforms.
- Emerging Technologies (Autumn)
Emerging Technologies in Autumn 2023/24
- Entropy
Optimal disorder.
- Fundamentals of Data Analysis (Autumn)
Fundamentals of Data Analysis in Autumn 2023/24
- Git basics
Basic usage of a common source code management tool.
- Graph Isomorphism
When two graphs are the same.
- Griffiths Worked Examples
Some examples in quantum mechanics.
- Group ring
Generalizations of polynomials based on groups.
- Groups
Symmetries and algebra.
- Groups and Generators
Basic descriptions of groups.
- Information Entropy
Coined in 1948 by Shannon.
- Ireland
A map of Ireland in d3.js.
- Isomorphism Theorems for Groups
Providing a perspective on group structure.
- Johnson graph
Tricky graphs.
- Lambda Calculus
A framework for expressing mathematical concepts.
- Logic and Matrices
Using matrices to represent logic gates.
- Machine Learning and Statistics (Autumn)
Machine Learning and Statistics in Autumn 2023/24
- Modules and vector spaces
Fundamentals of algebra.
- Newtonian Mechanics
Classical mechanics.
- Normal subgroups
Fundamental to symmetry.
- Notebooks
A collection of Jupyter notebooks.
- Notebooks (Higher Ed 4.0)
Notebooks from a project.
- Permutation matrix
Permutations as matrices.
- Permutations
Shuffling and counting.
- Polynomial ring
Used in applications of abstract algebra, such as coding theory.
- Post Correspondence Problem
Emil Post’s undecidable problem.
- Primitive Recursive Functions
Fundamental to computable functions.
- Principles of Data Analytics
Principles of Data Analytics in Summer 2023/24
- Principles of Data Analytics (Autumn)
Principles of Data Analytics in Autumn 2023/24
- Quantum Entanglement
Qubits can interact with each other in unusual ways.
- Quantum Experiments
Quantum Experiments
- Quantum Gates
Used to manipulate qubits to perform calculations.
- Quantum Measurement
Converting qubits to classical bits.
- Qubits
Basic building blocks of quantum computation
- Reverse Polish Notation
Expressions without brackets.
- Right Angled Triangles
Javascript drawing of a right-angled triangle.
- Rings and fields
Algebraic structures.
- Rotation of a Plane
Rotations of the Cartesian plane.
- Ruler and Compass Construction
Construction of points in a plane using only an unmarked ruler and a compass
- Scales of Measurement
Ideas about types and data.
- Scheme basics
An original functional programming language.
- Simon's Problem
A simple problem to describe.
- Sin and Circles
An animation showing the relationship between sine waves and circles.
- Sin and Circles v2
A better animation showing the relationship between sine waves and circles.
- String Isomorphism
An important problem in computational complexity.
- Unitary Error Basis
Sets of orthonormal matrices.
- Vector Space
Fundamentals algebraic structure.
- Waves
Drawing a standing wave.