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Math Wiki:Major areas

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The entries below that are marked with an asterisk (*) are currently not being shown on the Main Page because the corresponding articles don't exist yet. If you notice that one of these entries actually has an existing article (a "bluelink" instead of a "redlink"), please edit the list to "unhide" the entry on the Main Page.

This is a rough classification based on what professional mathematicians actually research and teach at the university level, along with some major elementary topics. Topics covered in primary and secondary school mathematics are listed at Math Wiki:Topics by level.

Foundations of mathematics
Logic and * mathematical logic
Set theory
Category theory
* Philosophy of mathematics
Arithmetic
Number systems
Number theory
Algebra
Elementary algebra
Abstract algebra
* Group theory
Linear algebra
* Matrix theory
* Universal algebra
Analysis
Ordinary differential equations
Partial differential equations
* Integral equations
Real analysis
Complex analysis
* Functional analysis
* Variational methods
* Nonstandard analysis
* Measure theory
* Vector and tensor analysis
Graph theory
Geometry
Euclidean geometry
Analytic geometry
Non-Euclidean geometry
* Modern geometry
* Algebraic geometry
Differential geometry
Topology
Applied mathematics
Discrete mathematics
Combinatorics
Probability
Statistics
* Actuarial mathematics
* Decision theory
* Game theory
* Mathematical modeling
Optimization or * Mathematical programming
Numerical analysis or * Numerical methods
* Scientific computing
* Theory of computation
Related disciplines
Recreational mathematics (including games and puzzles)
History of mathematics
* Mathematics education
* Information theory
* Systems theory
* Operations research
Mathematical physics

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