Algebra
ianmcloughlin.github.io linkedin github- Adjacency matrix
Graphs in matrix form.
- Collatz Conjecture
A seemingly simple problem that no one has been able to solve.
- Conway's Game of Life
A simple game devised by Conway, based on ideas from von Neumann and Ulam.
- Eigenvalues
Investgiating matrices and transforms.
- Entropy
Optimal disorder.
- Graph Isomorphism
When two graphs are the same.
- Group ring
Generalizations of polynomials based on groups.
- Groups
Symmetries and algebra.
- Groups and Generators
Basic descriptions of groups.
- Isomorphism Theorems for Groups
Providing a perspective on group structure.
- Johnson graph
Tricky graphs.
- Logic and Matrices
Using matrices to represent logic gates.
- Modules and vector spaces
Fundamentals of algebra.
- Newtonian Mechanics
Classical mechanics.
- Normal subgroups
Fundamental to symmetry.
- Permutation matrix
Permutations as matrices.
- Permutations
Shuffling and counting.
- Polynomial ring
Used in applications of abstract algebra, such as coding theory.
- 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
- 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.
- Vector Space
Fundamentals algebraic structure.
- Waves
Drawing a standing wave.