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A version of nim-like games in which the player taking the last piece is the loser. For most impartial games, this form is much harder to analyze, but it requires only a ...

A partial derivative of second or greater order with respect to two or more different variables, for example f_(xy)=(partial^2f)/(partialxpartialy). If the mixed partial ...

A number b_(2n) having generating function sum_(n=0)^(infty)b_(2n)x^(2n) = 1/2ln((e^(x/2)-e^(-x/2))/(1/2x)) (1) = 1/2ln2+1/(48)x^2-1/(5760)x^4+1/(362880)x^6-.... (2) For n=1, ...

Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

Given a complete graph K_n which is two-colored, the number of forced monochromatic triangles is at least {1/3u(u-1)(u-2) for n=2u; 2/3u(u-1)(4u+1) for n=4u+1; ...

Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...

In above figure, which constitutes a modified version of the painting Tirets by Francois Morellet, small circles seem to appear and disappear as the eye is moved over them.

The number k in the expression s(n)=kn for a multiperfect number is called its class.

A function for which several distinct functional values correspond (as a result of different continuations) to one and the same point (Knopp 1996, p. 94).