List of mathematical objects
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This is a list of mathematical objects, organized by branch.
List of mathematical objects by branch
Algebra
Elementary algebra
Linear algebra
Abstract algebra
- Groups
- Rings, Modules
- monoids
- Fields, Vector spaces
- Algebras
- Chain complexes
- Operations
- group-theoretic lattices, Order-theoretic lattices
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
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
- Truth values
- Logical connectives
- Propositions and Predicates
- Formulas
- Terms
- Signatures
- Mathematical proofs
- Theorems
Number theory
Set theory
Topology
- Closed sets
- Filters
- Neighborhoods
- Nets
- Open sets
- Topological spaces
- Uniformities
- Manifolds
- Möbius strip, Klein bottle
Algebraic topology
- Cohomology groups
- Cohomotopy groups[1]
- Homology groups
- Homotopy groups
- Knots
- Holes
- Toruses
- Alexander horned sphere
Differential topology
References
- ↑ Hu, Sze-Tsen (1971). "Chapter VII. Cohomotopy Groups" (PDF). Homotopy theory (PDF). Academic Press. pp. 205–228. LCCN 59-11526. Retrieved August 28, 2024. Unknown parameter
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