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. Wikiwand - on Seamless Wikipedia browsing. On steroids.