Foundations Of Linear Algebra

Fundamentals of Functional Analysis to the English Translation This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces..

Problems and Exercises in Discrete Mathematics Part II follows the same structure as Part I, and gives helpful hints and solutions. The exercises are preceded by ample theoretical background material. Part I contains problems on such topics as Boolean algebra, k-valued logics, graphs and networks, elements of coding theory, automata theory, algorithms theory, combinatorics, Boolean minimization and logical design.

Here, general topology (Ch. Topology as a subject, in our opinion, plays a central role in university education.

However, it is the belief of the authors, this understanding can be deepened with a guided set of exercises leading from the so called "elementary" to the somewhat more "advanced" form.

Every chapter of this book begins with the succinct theoretical exposition of the minimum of knowledge required to solve the problems and exercises therein. Such equations, and the development of techniques for solving them, have always held a privileged place in the mathematical sciences.Differential and Integral Equations through Practical Problems and Exercises Many important phenomena are described and modeled by means of differential and integral equations. The eight chapters of this book contain a large number of problems and exercises, selected on the basis of long experience in teaching students, which together with the author's original problems cover the whole range of current methods employed in solving the integral, differential equations, and the partial differential equations of order one, without, however, renouncing the classical problems.

Part I contains problems on such topics as Boolean algebra, k-valued logics, graphs and networks, elements of coding theory, automata theory, algorithms theory, combinatorics, Boolean minimization and logical design.

For U. S.

It is designed for a comprehensive one-year course in linear algebra (112 lecture hours) for mathematics majors.Many of the students studying linear algebra either are familiar with the care and feeding of computers before they begin their studies or are simultaneously en­ rolled in an introductory computer science course.

For U. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material.

Beginning with Chap­ ter VII, there is an implicit assumption that the student has access to a personal computer and knows how to use it. Thus, for example, the introduction of finite fields is dictated by the needs of students studying algebraic coding theory as an immediate followup to their linear algebra studies. My intention is to provide not only a solid basis in the abstract theory of linear algebra, but also to provide examples of the application of this theory to other branches ofmathematics and computer science. It is designed for a comprehensive one-year course in linear algebra (112 lecture hours) for mathematics majors.