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Higher Algebra - Kurosh
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Higher Algebra by A. Kurosh. 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. 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. All credits to the original uploader. DJVU | OCR | 15.8 MB | Pages: 432 | ====================================== =++++++++++++++++++++++++++++++++++++= =+ += =+ Released on TPB by mirtitles.org += =+ += =++++++++++++++++++++++++++++++++++++= ====================================== Table of Contents Introduction 7 Chapter 1. Systems of linear equations. Determinants 15 Chapter 2. Systems of linear equations ( general theory) 59 Chapter 3. The algebra of matrices 87 Chapter 4. Complex numbers 110 Chapter 5. Polynomials and their roots 126 Chapter 6. Quadratic forms 161 Chapter 7 Linear spaces 178 Chapter 8 Euclidean spaces204 Chapter 9. Evaluating roots of polynomials 225 Chapter 10. Fields and polynomials 257 Chapter 11. Polynomials in several unknowns 303 Chapter 12. Polynomials with rational coefficients 341 Chapter 13. Normal form of a matrix 355 Chapter 14. Groups. 382 Bibliography 414 Index 416-------------------------------------Torrent downloaded from http://thepiratebay.se
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