# 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 |

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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.

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
```
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