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Название: Problems in higher algebra
Автор: Faddeev D.K.
Comprising approximately 1,000 problems in higher algebra, with hints and solutions, this book is recommended as an adjunct text, as a problem book, and for self study. The following is a sample of the variety of problems in this collection: 1-Calculation of determinants. Inductive methods. Partitioning. Cases in which the entries are large numbers. 2- Systems of linear equations. Explanation of the point of view that the set of solutions forms a vector space. Use of modern terminology. 3l- Matrices. Inequalities that involve rectangular matrices. 4- polynomials and rational functions. Classical theorems on bounds for the roots with complete proofs. 5- Symmetric functions. Application to polynomial equations. 6- Linear algebra. Elementary and moderately advanced theorems. Euclidean norms. Jordan canonical forms. Conditions that the proper values of a matrix lie in the left half plane. A feature of the book is that every problem, or at the most every group of two or three problems, is independent and sections of the book can be sampled or omitted at the user's discretion. Selections form this fine collection of problems have been quoted ever since its first appearance in 1954. It is time to make it more widely available to the western world. The section on linear equations will be interesting because of its systematic coverage, and because it uses the vector-space of the n-tuples of coefficients to expound the principal results. Calculation of determinants has been lifted from the sterile to the fruitful by means of imaginative problems, many of them solved by use of mathematical induction. At the same time, there are plenty of simple problems, but written by a master who can make the material interesting.