Higner Algebra

A. Kurosh

За особеностите на екземпляра

Състояние:: Много добро
Забележка:: Леки забележки по корицата. Книжното тяло без забележки.
Език:: Английски
Наличност:: 1 бр.

За изданието

Издателство:: Mir Publishers
Град на издаване:: Moscow
Година:: 1980 г.
Език:: Английски
Страници:: 428
Корици:: Твърди
Категория:: Математика

The education of the mathematics major begins with the study of three basic disciplines: mathematical analysis, analytic geometry and higher algebra. These disciplines have a number of points of contact, some of which overlap; together they constitute the foundation upon which rests the whole edifice of modern mathematical science. Higher algebra - the subject of this text - is a far-reaching and natural generalization of the basic school course of elementary algebra. Central to elementary algebra is without doubt the problem of solving equations. The study of equations begins with the very simple case of one equation of the first degree in one unknown. From there on, the development proceeds in two directions: to systems of two and three equations of the first degree in two and, respectively, three unknowns, and to a single quadratic equation in one unknown and also to a few special types of higher-degree equations which readily reduce to quadratic equations (quartic equations, for example). Both trends are further developed in the course of higher algebra, thus determining its two large areas of study. One - the foundations of linear algebra - starts with the study of arbitrary systems of equations of the first degree (linear equations). When the number of equations equals the number of unknowns, solutions of such systems are obtained by means of the theory of determinants. The second half of the course of higher algebra, called the algebra of polynomials, is devoted to the study of a single equation in one unknown but of arbitrary degree. Since there is a formula for solving quadratic equations, it was natural to seek similar formulas for higher-degree equations. That is precisely how this division of algebra developed historically. Formulas for solving equations of third and fourth degree were found in the sixteenth century. The search was then on for formulas capable of expressing the roots of equations of fifth and higher degree in terms -of the coefficients of the equations by means of radicals, even radicals within radicals. It was futile, though it continued up to the beginning of the nineteenth century, when it was proved that no such formulas exist and that for all degrees beyond the fourth there even exist specific examples of equations with integral coefficients whose roots cannot be written down by means of radicals. This book was translated from the Russian by George Yankovsky. The book was published by first Mir Publishers in 1972, with reprints in 1975, 1980 and 1984. The book below is from the 1984 reprint.

Ключови думи: Higner Algebra, A. Kurosh