List of mathematical objects

This is a list of mathematical objects, organized by branch.

List of mathematical objects by branch

Algebra

Elementary algebra

• Algebraic operations
• Algebraic functions
• Algebraic expressions
• Polynomials

Linear algebra

• Scalars, Vectors
• Matrices, Tensors
• Kernel
• Linear span
• Bases
• Linear maps
• Parallelepiped

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

• Infinitesimals
• Fluxion

Differential equations

• Dirac delta function
• Heaviside step function
• Laplace transform

Category theory

• Categories
• Functors
• Morphisms
• objects
• Natural transformations

Combinatorics

• permutations, derangements, combinations

Computer science and Theoretical computer science

• Data structures
  • Arrays
  • Linked lists
  • Hash tables
  • Stacks and Queues
  • Heap
  • Graphs
  • Trees
• Objects
• Integers
• Floats
• Variables
• Languages

Geometry

Euclidian geometry

• Points, Lines, Line segments,
• Polytopes, Regular polytopes
  • Polygons - 2-dimensional polytope
    • Convex polygon
      • Triangles
      • Squares
      • Pentagons
      • Hexagons
  • Polyhedra 3-dimensional polytope
    • Platonic solids
      • Tetrahedron
      • Cube
      • Octahedron
      • Dodecahedron
      • Icosahedron
• Conic sections
  • Circles
  • Ellipses
  • Parabolas
  • Hyperbolas
• Spheres, Ellipsoids, Paraboloids, Hyperboloids,
• Cylinders, Cones

Fractal geometry

• Mandelbrot set
• Julia sets
• Sierpiński triangle
• Sierpiński carpet, Menger sponge
• Cantor set

Graph theory

• Graphs, Trees, Nodes, Edges

Mathematical logic

• Truth values
• Logical connectives
• Propositions and Predicates
• Formulas
• Terms
• Signatures
• Mathematical proofs
• Theorems

Number theory

• Numbers
  • Natural numbers
  • Integers
  • Rational numbers
• Arithmetic operations
  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Modulo operation
  • Exponents
• Fractions
• Successor function

Set theory

• Sets, Set partitions
• Functions, and Relations
• Membership relation
• Cardinal numbers
• Ordinal numbers

Topology

• Closed sets
• Filters
• Neighborhoods
• Nets
• Open sets
• Topological spaces
• Uniformities
• Manifolds
  • Atlases
  • Charts
• Möbius strip, Klein bottle

Algebraic topology

• Cohomology groups
• Cohomotopy groups^[1]
• Homology groups
• Homotopy groups
• Knots
  • Unknot
  • Trefoil knot
• Holes
• Toruses
• Alexander horned sphere

Differential topology

• Differentiable manifolds
• Hairy balls

References

1. Hu, Sze-Tsen (1971) [1959]. "Chapter VII. Cohomotopy Groups" (PDF). Homotopy theory (PDF). Academic Press. pp. 205–228. LCCN 59-11526. Retrieved August 28, 2024.