Introduction to Algebra has 7 ratings and 1 review. This textbook, written by a dedicated and successful pedagogue who developed the present undergraduat.. . Pris: kr. Häftad, Skickas inom vardagar. Köp Introduction to Algebra av A I Kostrikin på KOSTRIKIN, A. I., Introduction to algebra, translated by N. Koblitz (Universitext, Springer-Verlag,. Berlin-Heidelberg-New York, ), pp., £ This book .

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Solvability of equations in radicals. The states of a molecule. The heated plate problem. Systems of linear equations. Equivalence of linear systems.

Reducing to step form. Studying a system of linear equations. Some remarks and examples. Determinants of small order. The principle of mathematical induction.

## Introduction to Algebra

The fundamental theorem of arithmetic. The division algorithm in ZZ. The rank of a matrix. The space of solutions. Solving a homogeneous linear system. Solving a non-homogeneous system. The rank of a product of matrices.

### Alexei Kostrikin – Wikipedia

Equivalence classes of matrices. Basic properties of determinants. Further properties of determinants. Expanding the determinant along an arbitrary column. The properties of determinants relating to columns.

Determinants of special matrices. Building up a theory of determinants. Criterion for a matrix to be non-singular. Computing the rank of a matrix. Algebraic structures groups, rings, fields. Sets with algebraic operations. The symmetric group and the alternating group Exercises. Cosets of a subgroup. The definition and general properties of rings. The ring of residue classes. Ring homomorphisms and ideals.

The concept of quotient group and quotient ring.

The characteristic of a field. A remark on linear systems. Complex numbers and polynomials. The field of complex numbers. Geometrical interpretation of operations with complex numbers. Raising to powers and extracting roots. Polynomials in one variable.

Polynomials in several variables. Factoring in polynomial rings. Unique factorization in Euclidean rings. The field of fractions. Construction of the field of fractions of kosstrykin integral domain.

The field of rational functions. General properties of roots. Roots and linear factors. Differentiation in polynomial rings. The ring of symmetric polynomials. The fundamental theorem on symmetric polyno. Introduction to Algebra av A I Kostrikin.

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## Alexei Kostrikin

This textbook, written by a dedicated and successful pedagogue who developed the present undergraduate algebra course at Moscow State University, differs in several respects kostrykim other algebra textbooks available in English. In the first place, Kostrikin’s textbook motivates many of the algebraic concepts by practical examples, for instance, the heated plate problem used to introduce linear equations in Chapter 1. In the second place, there are a large number of exercises, so that the student can convert a vague passive understanding to active mastery of the new ideas.

This feature also makes the book ideally suited for learning algebra on one’s own outside of the framework of an organized course. In the third place, the author treats material which is usually not part of an elementary course but which kowtrykin fundamental in applications. Thus, Part II includes an introduction to the classical groups and to representation theory.

With many American colleges now trying to bring their undergraduate mathematics curriculum closer to applications, it seems worthwhile to translate Soviet textbooks which reflect their greater experience in this area of mathematical pedagogy.

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