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This is a list of mathematical objects, organized by branch.
Algebra
Elementary algebra
Linear algebra
Abstract algebra
Calculus and Mathematical Analysis
- Continuous functions, Differentiable functions, Analytic functions
- Pathological functions
- Weierstrass function - Commonly used as an example of a continuous, nowhere-differentiable function
- Dirichlet function - Commonly used as an example of a nowhere continuous function
- Bump function - Commonly used as an example of a Non-analytic smooth function
- Derivative, Gradient
- Integral
- Jacobian matrix
Nonstandard analysis
Differential equations
Category theory
Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects
Combinatorics
Computer science and Theoretical computer science
Geometry
Euclidian geometry
- Points, Lines, Line segments,
- Polytopes, Regular polytopes
- Conic sections
- Spheres, Ellipsoids, Paraboloids, Hyperboloids,
- Cylinders, Cones
Fractal geometry
Graph theory
Mathematical logic
Number theory
Set theory
Topology
- Closed sets
- Filters
- Neighborhoods
- Nets
- Open sets
- Topological spaces
- Uniformities
- Manifolds
- Möbius strip, Klein bottle
Algebraic topology
Differential topology
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