Shreeram Shankar Abhyankar Livres

From young children to old persons, even in their nineties, anyone can play Bridge. Playing Bridge is the only exercise you will need to improve and retain your memory life long. Far from being a form of gambling, Bridge is actually an effortless way to meditation, and keeping the mind and body fresh and active. Perhaps because of this, Bridge players never get old. This book, written to help beginners learn the game, can be a text-book for learning Bridge in a joyful way. It explains the bidding system as 'Engineering' - engineered to help even young children to learn it easily. With many fully illustrated deals, it helps you come to grips with the game and sharpen your skills in order to get the best out of playing Bridge.

The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called asolid. Most points of a variety are simple points. Singularities are special points, or points of multiplicity greater than one. Points of multiplicity two are double points, points of multiplicity three are tripie points, and so on. A nodal point of a curve is a double point where the curve crosses itself, such as the alpha curve. A cusp is a double point where the curve has a beak. The vertex of a cone provides an example of a surface singularity. A reversible change of variables gives abirational transformation of a variety. Singularities of a variety may be resolved by birational transformations.