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Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

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 ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

The 5.1.2 fifth-order Diophantine equation A^5=B^5+C^5 (1) is a special case of Fermat's last theorem with n=5, and so has no solution. improving on the results on Lander et ...

The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

The Fourier transform is a generalization of the complex Fourier series in the limit as L->infty. Replace the discrete A_n with the continuous F(k)dk while letting n/L->k. ...

A fullerene is a cubic polyhedral graph having all faces 5- or 6-cycles. Examples include the 20-vertex dodecahedral graph, 24-vertex generalized Petersen graph GP(12,2), ...

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...