**Abelian group**- See
**group**. **Abelian variety****Algebra****Algebraic function****Algebraic geometry****Algebraic integer****Algebraic number theory****Algebraic variety****Algebraically closed field****Analytic function****Analytic number theory****Analysis****Automorphic function****Banach space****Boolean algebra****Cartesian product****Category****Cauchy sequence****Chaos****Class field theory****Closed set****Cohomology****Compact****Complete topological space****Complex analysis****Complex numbers****Composition law**- A
**function**that takes a pair of elements of some set to some other element of the set. If the pair (a,b) corresponds to c under this function, the law may be written as a ∘ b = c. **Connection****Continuous function****Convergence****Cusp form****Derivative****Diagram****Differentiable function****Differentiable manifold****Differential equation****Differential form****Diophantine equation****Direct product****Direct sum****Dirichlet series****Dynamical system****Elliptic curve****Extension field****Fiber bundle****Field****Fractal****Function**- A correspondence between elements of two sets A and B (that may be the same). The correspondence can be defined by a set of ordered pairs of the form (a,b) with a ∈ A and b ∈ B such that there is exactly one a ∈ A that is the first element of any pair. The set A is called the "domain" of the function, while the "range" of the function consists of all b ∈ B that occur as the second element of a pair. A function is usually denoted symbolically with a name such as "f" and written in the form f(a) = b if (a,b) is a pair of corresponding elements. A function is "injective" or "1-to-1" if there is no b ∈ B that occurs more than once as the second element of a pair. (I. e., f(a) = f(a′) implies a = a′.) A function is "surjective" or "onto" if the range of the function is all of B. (I. e. for all b ∈ B, b = f(a) for some a ∈ A.)
**Functional analysis****Galois group****Group**- A mathematical system G consiting of a set of elements and a
**composition law**satisfying three axioms:- identity element: there is an e ∈ G such that for all g ∈ G, e ∘ g = g ∘ e = g
- inverses: for all g ∈ G there is an inverse g′ ∈ G such that g ∘ g&prime = g′ ∘ g = e
- associativity: for all a, b, c ∈ G, a ∘ (b ∘ c) = (a ∘ b) ∘ c

- commutativity: for all a, b ∈ G, a ∘ b = b ∘ a

**Group representation****Harmonic analysis****Hilbert space****Holomorphic function****Homology****Homeomorphism****Homomorphism****Homotopy****Hopf algebra****Inner product****Integral equations****Isomorphism****Knot****L-function****Lattice****Lie algebra****Lie group****Linear algebra****Manifold****Mapping**- Synonym of
**function**. **Matrix****Meromorphic function****Metric space****Modular form****Modular function****Modular group****Morphism****Neighborhood****Normed linear space****Open set****P-adic numbers****Projective plane****Partial differential equation****Pole****Quantum group****Riemann sphere****Riemann surface****Ring****Ring of integers****Series****Sheaf****Tangent bundle****Taylor series****Tensor****Topology****Variety****Vector****Vector bundle****Vector space**

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