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The 2-1 equation A^n+B^n=C^n (1) is a special case of Fermat's last theorem and so has no solutions for n>=3. Lander et al. (1967) give a table showing the smallest n for ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

An abstract vector space of dimension n over a field k is the set of all formal expressions a_1v_1+a_2v_2+...+a_nv_n, (1) where {v_1,v_2,...,v_n} is a given set of n objects ...

In functional analysis, the Banach-Alaoglu theorem (also sometimes called Alaoglu's theorem) is a result which states that the norm unit ball of the continuous dual X^* of a ...

Let f(x,y)=u(x,y)+iv(x,y), (1) where z=x+iy, (2) so dz=dx+idy. (3) The total derivative of f with respect to z is then (df)/(dz) = ...

An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

Differential evolution is a stochastic parallel direct search evolution strategy optimization method that is fairly fast and reasonably robust. Differential evolution is ...