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The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

The universal cover of a connected topological space X is a simply connected space Y with a map f:Y->X that is a covering map. If X is simply connected, i.e., has a trivial ...

Calculus I

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...

A complete oriented graph (Skiena 1990, p. 175), i.e., a graph in which every pair of nodes is connected by a single uniquely directed edge. The first and second 3-node ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

A Haar graph H(n) is a bipartite regular indexed by a positive integer and obtained by a simple binary encoding of cyclically adjacent vertices. Haar graphs may be connected ...