Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of foundations, algebra, geometry, applied and analysis respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Foundational Mathematics
Foundational mathematics is the study of the most basic concepts and logical structure of mathematics. It generally includes topics from theories of logic, set theory, computation, and model theory.
TODO these sub branches need note pages and links to them.
Algebra
Algebra is one of the older and more broad parts of mathematics. It is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics.
This includes topics of:
- Number Theory
- Combinatorics
- Algebraic Geometry
- Linear Algebra
TODO these sub branches need note pages and links to them.
Geometry
Geometry is the study of shapes, sizes, relative positions of figures, and the properties of space and spatial relationships (topology).
- Euclidean Geometry
- Non-Euclidean Geometry
- Discrete Geometry
- Graph Theory
- General Topology
TODO these sub branches need note pages and links to them.
Applied Mathematics
Applied mathematics is the study of mathematical methods that are typically used in science, engineering, business, and industry. It moves mathematical theory from pure mathematics to the real world application of mathematics.
It includes topics of:
- Mathematical Physics
- Computer Science
- Probability and Statistics
- Game Theory
- Systems & Control Theory
Analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
It includes topics of:
- Real Analysis and Measure Theory
- Complex Analysis
- Tensor & Vector Analysis
- Calculus
- Functional Analysis