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Calculus I

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

If a is an arbitrary integer relatively prime to n and g is a primitive root of n, then there exists among the numbers 0, 1, 2, ..., phi(n)-1, where phi(n) is the totient ...

A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

Like the entire harmonic series, the harmonic series sum_(k=1)^infty1/(p_k)=infty (1) taken over all primes p_k also diverges, as first shown by Euler in 1737 (Nagell 1951, ...

A polygonal number of the form n(3n-1)/2. The first few are 1, 5, 12, 22, 35, 51, 70, ... (OEIS A000326). The generating function for the pentagonal numbers is ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

A theorem of fundamental importance in spectroscopy and angular momentum theory which provides both (1) an explicit form for the dependence of all matrix elements of ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...