Problems in Higher Algebra

D. K. Faddeev, I. S. Sominskii, quot;Problems in Higher Algebraquot;
W.H. Freeman and Company | 1965 | ISBN: 0716704269 | 498 pages | File type: PDF | 26 mb
Summary: Classic
Rating: 5

Translated by J. L. Brenner.
For those of you who haven't read about it, here you go:
Selections from this fine collection of problems have been quoted ever sicne its first appearance in 1954. It is time to make it more widely available to the wester world.

Comprising approximately 1000 problems in higher algebra, with hints and solutions, this book is recommended as an adjunct text , as a problme book, and for self study. The follwing is a sampling of variety of problmes in this collection:

1. Calculation of determinants. Inductive methods. Parititionng. Cases in which the entries are larger numbers.

2. Systems of linear equations.explanation of the point of view that the set of solutions orms a vector spaces.

3. Matrices. Inequlaities 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.
This book is one of the more important ones to review in preparation for olympiad style mathematics competitions, particularly the sections on complex numbers, systems of linear equations, polynomials, and symmetric functions. The chapters on polynomials and symmetric functions are quite unique and there are no equivalent sets of problems or treatments in other problem books on algebra.

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