HIGHER ALGEBRA

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.