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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 ...

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

Multi-index notation is used to shorten expressions that contain many indices. Let x in R^n and write x=(x_1,...,x_n). A multi-index alpha is an n-tuple of integers alpha_j ...

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

The number sign # sometimes used in mathematics to indicate the number of a quantity satisfying some condition, e.g., #{n:n>1}. The symbol is also used to denote a primorial.

A class of game in which players move alternately and each player is completely informed of previous moves. Finite, zero-sum, two-player games with perfect information ...

One petabyte is 10^(15) bytes. Unfortunately, the term is sometimes also used to mean 2^(50)=1024^5 bytes. However, the latter usage is deprecated, and the term pebibyte is ...

To compute an integral of the form int(dx)/(a+bx+cx^2), (1) complete the square in the denominator to obtain int(dx)/(a+bx+cx^2)=1/cint(dx)/((x+b/(2c))^2+(a/c-(b^2)/(4c^2))). ...

A point where a curve intersects itself along four arcs. The above plot shows the quadruple point at the origin of the quadrifolium (x^2+y^2)^3-4x^2y^2=0.

A function is termed regular iff it is analytic and single-valued throughout a region R.