By V.I. Arnold, Alexander Varchenko, S.M. Gusein-Zade

... there's not anything so enchanting, so grandiose, not anything that stuns or captivates the human soul really lots as a primary path in a technology. After the 1st 5 - 6 lectures one already holds the brightest hopes, already sees oneself as a seeker after fact. I too have wholeheartedly pursued technology passionately, as one might a loved girl. i used to be a slave, and sought no different sunlight in my existence. Day and evening I stuffed myself, bending my again, ruining myself over my books; I wept whilst I beheld others exploiting technology fot own achieve. yet i used to be no longer lengthy enthralled. in fact each technology has a starting, yet by no means an finish - they cross on for ever like periodic fractions. Zoology, for instance, has came across thirty-five thousand kinds of existence ... A. P. Chekhov. "On the line" during this booklet a commence is made to the "zoology" of the singularities of differentiable maps. This conception is a tender department of study which at present occupies a crucial position in arithmetic; it's the crossroads of paths major from very summary corners of arithmetic (such as algebraic and differential geometry and topology, Lie teams and algebras, advanced manifolds, commutative algebra and so on) to the main utilized parts (such as differential equations and dynamical platforms, optimum regulate, the idea of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).