In addition to his path-breaking theoretical work, Picard also made important contributions to applied mathematics, including the theories of telegraphy and elasticity.

Like his contemporary, Henri Poincaré, Picard was much concerned with the training of mathematics, physics, and engineering students.

In mathematics, in the study of differential equations, the Picard – Lindelöf theorem, Picard's existence theorem or Cauchy – Lipschitz theorem is an important theorem on existence and uniqueness of solutions to first-order equations with given initial conditions.

In complex analysis, a discipline within mathematics, the Picard theorem, named after Charles Émile Picard, is either of two distinct yet related theorems, both of which pertain to the range of an analytic function.

Guided by Maurolycus's methodology and Snellius's mathematics for doing so, Picard achieved this by measuring one degree of latitude along the Paris Meridian using triangulation along thirteen triangles stretching from Paris to the clocktower of Sourdon, near Amiens.

In mathematics, the Picard – Fuchs equation, named after Charles Émile Picard and Lazarus Fuchs, is a linear ordinary differential equation whose solutions describe the periods of elliptic curves.

In mathematics a combination is a way of selecting several things out of a larger group, where ( unlike permutations ) order does not matter.

The mathematics of crystal structures developed by Bravais, Federov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for the series International Tables of Crystallography, first published in 1935.

In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below.

Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory, and more.

A statistical analysis of the effect of dianetic therapy as measured by group tests of intelligence, mathematics and personality.

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.

In mathematics and abstract algebra, a group is the algebraic structure, where is a non-empty set and denotes a binary operation called the group operation.

He was the first to use the word " group " () as a technical term in mathematics to represent a group of permutations.

* E2 or E < sub > 2 </ sub > is an old name for the exceptional group G2 ( mathematics )

In mathematics, more specifically algebraic topology, the fundamental group ( defined by Henri Poincaré in his article Analysis Situs, published in 1895 ) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory ; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below.

In mathematics, specifically group theory, a quotient group ( or factor group ) is a group obtained by identifying together elements of a larger group using an equivalence relation.

# REDIRECT group ( mathematics )

He gathered a group of students around him to study mathematics, music, and philosophy, and together they discovered most of what high school students learn today in their geometry courses.

In mathematics, given two groups ( G, *) and ( H, ·), a group homomorphism from ( G, *) to ( H, ·) is a function h: G → H such that for all u and v in G it holds that

In mathematics, a ringed space is, intuitively speaking, a space together with a collection of commutative rings, the elements of which are " functions " on each open set of the space.

In mathematics, an invertible sheaf is a coherent sheaf S on a ringed space X, for which there is an inverse T with respect to tensor product of O < sub > X </ sub >- modules.

In mathematics, a sheaf spanned by global sections is a sheaf F on a locally ringed space X, with structure sheaf O < sub > X </ sub > that is of a rather simple type.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

In mathematics, more specifically in functional analysis, a Banach space ( pronounced ) is a complete normed vector space.

In mathematics, specifically in measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of X ; this is known as the σ-algebra of Borel sets.

In mathematics, a bilinear operator is a function combining elements of two vector spaces to yield an element of a third vector space that is linear in each of its arguments.

In mathematics terminology, the vector space of bras is the dual space to the vector space of kets, and corresponding bras and kets are related by the Riesz representation theorem.

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

In mathematics, compactification is the process or result of making a topological space compact.

In mathematics, any vector space, V, has a corresponding dual vector space ( or just dual space for short ) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors.

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.

High-dimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics ; these are abstract spaces, independent of the physical space we live in.

In mathematics, the dimension of an object is an intrinsic property independent of the space in which the object is embedded.

A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space.

In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions.

In modern mathematics, it is more common to define Euclidean space using Cartesian coordinates and the ideas of analytic geometry.