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In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->... the module Z^i of i-cocycles Z^i is the kernel of d^i, which is a submodule of C^i.

Code 177 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

Code 2040 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

Code 912 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

A codeword is an element of an error-correcting code C. If C has length n, then a codeword in C has the form (c_1,c_2,...,c_n), where each c_i is a letter in the alphabet of ...

A set within which the values of a function lie (as opposed to the range, which is the set of values that the function actually takes).

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

A bilinear functional phi on a normed space E is called coercive (or sometimes elliptic) if there exists a positive constant K such that phi(x,x)>=K||x||^2 for all x in E.

If S is an infinite set, then the collection F_S={A subset= S:S-A is finite} is a filter called the cofinite (or Fréchet) filter on S.