# Faddeev, Sominsky - Problems in Higher Algebra

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```Problems in Higher Algebra

This book of problems in higher algebra grew out of a course
of instruction at the Leningrad State University and the Herzen
Pedagogical Institute. It is designed for students of universities
and teachers colleges as a problem book in higher algebra.

The problems included here are of two radically different types. On
the one hand, there are a large number of numerical examples aimed at
developing computational skills and illustrating the basic
propositions of the theory. The authors believe that the number of
problems is sufficient to cover work in class, at home and for tests.

On the other hand, there are a rather large number of problems
of medium difficulty and many which will demand all the ini-
tiative and ingenuity of the student. Many of the problems of
this category are accompanied by hints and suggestions to be
found in Part II. These problems are starred.

Answers are given to all problems, some of the problems are
supplied with detailed solutions.

This book was translated from the Russian by George Yankovsky. The

All credits to the original uploader.

PDF | 3.4 MB | Pages: 318 | Bookmarked | OCR | Cover

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Contents
Part I
PROBLEMS

CHAPTER I. COMPLEX NUMBERS 11

CHAPTER 2. EVALUATION OF DETERMINANTS 25

CHAPTER 3. SYSTEMS OF LINEAR EQUATIONS 61

CHAPTER 4. MATRICES 76

CHAPTER 5. POLYNOMIALS AND RATIONAL FUNCTIONS OF ONE VARIABLE 88

CHAPTER 6. SYMMETRIC FUNCTIONS 116

CHAPTER 7. LINEAR ALGEBRA 133

PART II

HINTS TO SOLUTIONS

CHAPTER 1. COMPLEX NUMBERS 151
CHAPTER 2. EVALUATION OF DETERMINANTS 153
CHAPTER 4. MATRICES 159
CHAPTER 5. POLYNOMIALS AND RATIONAL FUNCTIONS OF ONE VARIABLE 160
CHAPTER 6. SYMMETRIC FUNCTIONS 164
CHAPTER 7. LINEAR ALGEBRA 166

PART III

CHAPTER 1. COMPLEX NUMBERS 168
CHAPTER 2. EVALUATION OF DETERMINANTS 186
CHAPTER 3. SYSTEMS OF LINEAR EQUATIONS 196
CHAPTER 4. MATRICES 203
CHAPTER 5. POLYNOMIALS AND RATIONAL FUNCTIONS OF ONE VARIABLE 221
CHAPTER 6. SYMMETRIC FUNCTIONS 261
CHAPTER 7. LINEAR ALGEBRA 286
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