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There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...

Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is ...

There are several functions called "Lommel functions." One type of Lommel function appear in the solution to the Lommel differential equation and are given by ...