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2 Topics in mathematics
An alphabetical and subclassified list of mathematical topics is available. The following list of subfields and topics reflects one organizational view of mathematics.
2.1 Quantity
In general, these topics and ideas present explicit measurements of sizes of numbers or sets, or ways to find such measurements.
- Number – Natural number – Pi – Integers – Rational numbers – Real numbers – Complex numbers – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbers – Integer sequences – Mathematical constants – Number names – Infinity – Base
2.2 Change
These topics give ways to measure change in mathematical functions, and changes between numbers.
- Arithmetic – Calculus – Vector calculus – Analysis – Differential equations – Dynamical systems and chaos theory – List of functions
2.3 Structure
These branches of mathematics measure size and symmetry of numbers, and various constructs.
- Abstract algebra – Number theory – Algebraic geometry – Group theory – Monoids – Analysis – Topology – Linear algebra – Graph theory – Universal algebra – Category theory – Order theory
2.4 Space
These topics tend to quantify a more visual approach to mathematics than others.
- Topology – Geometry – Trigonometry – Algebraic geometry – Differential geometry – Differential topology – Algebraic topology – Linear algebra – Fractal geometry
2.5 Discrete mathematics
Topics in discrete mathematics deal with branches of mathematics with objects that can only take on specific, separated values.
- Combinatorics – Naive set theory – Probability – Theory of computation – Finite mathematics – Cryptography – Graph theory – Game theory
