Open Questions: Glossary of Mathematics
- 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
A group is "commutative" or "abelian" if in addition one has
- 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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Copyright © 2002 by Charles Daney, All Rights Reserved