### Abstraction

One of the most important approaches is abstraction. In mathematics we may look at specific structures and then 'abstract' away the details to get to more general results.

For example, if we discover a structure, we try to discover the laws which govern it (usually in the form of equations - identities or axioms). We can then consider these laws on their own and work out the most general structures which satisfy them.

### Structures

This section contains maths topics which involve abstract concepts and discrete (non continuous) mathematics.

- Sets
- Logic
- Boolean Algebra
- Graph Theory
- Category Theory
- Combinatorics

### Terminology

- Field - Commutative division ring (different meaning of the word 'field' than fields on a manifold)
- Integral Domain - Commutative Ring with unity and no zero divisors
- Vector Space - Vectors over a field, Addition with scalar multiplication (vector & field (scalars))
- a(v+u) = a v + a u
- (a + b) v = a v + b v
- a (b v) = (a b) v
- 1 v = v

- Zero Divisor - A non-zero element 'a' of a commutative ring 'R' such that there is a non-zero element bR with ab=0