  Concise introduction to a relatively new subject of non-linear algebra:
literal extension of text-book linear algebra to the case of non-linear
equations and maps. This powerful science is based on the notions of
discriminant (hyperdeterminant) and resultant, which today can be effectively
studied both analytically and by modern computer facilities. The paper is
mostly focused on resultants of non-linear maps. First steps are described in
direction of Mandelbrot-set theory, which is direct extension of the eigenvalue
problem from linear algebra, and is related by renormalization group ideas to
the theory of phase transitions and dualities.
