Mathematics. Dictionary

A fiber bundle for which the base space is a differentiable manifold and each fiber over a point of that manifold is the tangent space of that point.

An n-dimensional vector space that represents the set of all vectors tangent to given n-dimensional M at point x.

A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.

The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗.

One of ten equal parts of a whole.

Any value (variable or constant) or expression separated from another term by a space or an appropriate character, in an overall expression or table.

A polyhedron with four faces; the regular tetrahedron, the faces of which are equal equilateral triangles, is one of the Platonic solids.

A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called lemmas.

The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).

Subgroup of an abelian group whose generators have finite order.

any irrational number that is not an algebraic number

The replacement of the variables in an algebraic expression by their values in terms of another set of variables; a mapping of one space onto another or onto itself; a function that changes the position or direction of the axes of a coordinate system.

A matrix (of dimension n×m) that represents some linear transformation from ℝm→ℝn.

A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the ith row and jth column describes the probability of moving from state i to state j in one time step.

A relation between two mathematical figures such as a straight line where the coordinates of each point in one figure is a constant added to the coordinates of a corresponding point in the other figure.

The matrix derived from performing a transpose operation on a given matrix.

A line intersecting a pair of parallel lines.

A (convex) quadrilateral with two (non-adjacent) parallel sides.

A method of finding an approximate value for a definite integral, based on dividing the area under the graph of the function into a series of strips, each of which is approximately a trapezoid, and summing the area of all the trapezoids to approximate the area.

A polygon with three sides and three angles.

The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.

The branch of mathematics that deals with the relationships between the sides and angles of (in particular) right-angled triangles, as represented by the trigonometric functions, and with calculations based on said relationships.

The number 1,000,000,000,000; a thousand billions.

A sequence of three elements or 3-tuple.

The removal of the least significant digits from a decimal number.

A table showing all possible truth values for an expression, derived from the truth values of its components.

Either of a pair of prime numbers that differ by two.