 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  # Glossary

## Cayley's Theorem

This result says that the symmetries of geometric objects can be expressed as groups of permutations.

## Continuous Symmetry

An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.

## Galois Theory

This area of mathematics relates symmetry to whether or not an equation has a "simple" solution.

## Group

A group is just a collection of objects (i.e., elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation, each element must have an inverse, the set must have an identity element, the set must be closed, and the set must be associative under the operation.

## Invarient

The state of appearing unchanged.

## Noether's Theorem

This result relates conserved physical quantities, like conservation of energy, to continuous symmetries of spacetime.

## Polynomial

A polynomial is an algebraic "sentence" containing an unknown quantity.