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The convolution of two complex-valued functions on a group G is defined as (a*b)(g)=sum_(k in G)a(k)b(k^(-1)g) where the support (set which is not zero) of each function is ...

The contour C_epsilon illustrated above.

An impossible figure that locally (but only locally!) looks like a torus.

The indefinite summation operator Delta^(-1) for discrete variables, is the equivalent of integration for continuous variables. If DeltaY(x)=y(x), then Delta^(-1)y(x)=Y(x).

Given a commutative unit ring R and an extension ring S, an element s of S is called integral over R if it is one of the roots of a monic polynomial with coefficients in R.

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

An optical illusion, illustrated above, in which the eye perceives a white upright equilateral triangle where none is actually drawn.

A list of problems in low-dimensional topology maintained by Kirby (1995). The list currently runs about 380 pages.

The knot curve is a quartic curve with implicit Cartesian equation (x^2-1)^2=y^2(3+2y). (1) The x- and y-intercepts are (0,-1), (0,1/2), and (+/-1,0). It has horizontal ...

This is proven in Rademacher and Toeplitz (1957).