This textbook, written by a dedicated and successful pedagogue who developed the present undergraduate algebra course at Moscow State University, differs in several respects from other algebra textbooks available in English. The book reflects the Soviet approach to teaching mathematics with its emphasis on applications and problem-solving -- note that the mathematics department in Moscow is called the I~echanics-Mathematics" Faculty. 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. Thes~ problems are intended to be challenging but doable by the student; the harder ones have hints at the back of the book. 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 is 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.

Introduction to Algebra (Universitext)

Science & Math

Kostrikin, A.I.

Mathematics

Springer

In August 1989, more than 700 Soviet algebraists and more than 200 foreign mathematicians convened in Novosibirsk in the former Soviet Union for the International Conference on Algebra. Dedicated to the memory of A. I. Mal'cev, the great Russian algebraist and logician, the conference marked the first time since the International Congress of Mathematicians was held in Moscow in 1966 that Soviet algebraists could meet with a large number of their foreign colleagues. This volume contains the proceedings from this historic conference. Some of the Soviet contributions to this volume are not easily available from other sources. 
Some of the major figures in the field, including P. M. Cohn, P. Gabriel, N. Jacobson, E. R. Kolchin, and V. Platonov, contributbed to this volume. The papers span a broad range of areas including groups, Lie algebras, associative and nonassociative rings, fields and skew fields, differential algebra, universal algebra, categories, combinatorics, logic, algebraic geometry, geometry, topology, and mathematical physics.

Proceedings of the International Conference on Algebra Dedicated to the Memory of A.I. Malcev, Parts 1, 2, 3 (Contemporary Mathematics)

International Conference on Algebra

Ershov, Yu L.

Bokut, L. A.

Maltsev, A. I.

Ershov, Iurii Leonidovich

Amer Mathematical Society

In August 1989, more than 700 Soviet algebraists and more than 200 foreign mathematicians convened in Novosibirsk in the former Soviet Union for the International Conference on Algebra. Dedicated to the memory of A. I. Mal'cev, the great Russian algebraist and logician, the conference marked the first time since the International Congress of Mathematicians was held in Moscow in 1966 that Soviet algebraists could meet with a large number of their foreign colleagues. This volume contains the proceedings from this historic conference. Some of the Soviet contributors to this volume are not easily available from other sources. Some of the major figures in the field, including P. M. Cohn, P. Gabriel, N. Jacobson, E. R. Kolchin, and V. Platonov, contributed to this volume. The papers span a broad range of areas including groups, Lie algebras, associative and nonassociative rings, fields and skew fields, differential algebra, universal algebra, categories, combinatorics, logic, algebraic geometry, topology, and mathematical physics.

Proceedings of the International Conference on Algebra Dedicated to the Memory of A.I. Malcev (Contemporary Mathematics, 131) Parts 1,2,3. THREE VOLUME SET

Book by International Conference on Algebra, Bokut, L. A., Maltsev, A. I., Ershov, Iurii Leonidovich, Kostrikin, A. I.

Proceedings of the International Conference on Algebra Dedicated to the Memory of A.I. Malcev (Contemporary Mathematics, 131)

Proceedings of the International Conference on Algebra Dedicated to the Memory of A.I. Malcev (003) (Contemporary Mathematics, 131)

Perhaps it is not inappropriate for me to begin with the comment that this book has been an interesting challenge to the translator. It is most unusual, in a text of this type, in that the style is racy, with many literary allusions and witticisms: not the easiest to translate, but a source of inspiration to continue through material that could daunt by its combinatorial complexity. Moreover, there have been many changes to the text during the translating period, reflecting the ferment that the subject of the restricted Burnside problem is passing through at present. I concur with Professor Kostrikin's "Note in Proof', where he describes the book as fortunate. I would put it slightly differently: its appearance has surely been partly instrumental in inspiring much endeavour, including such things as the paper of A. I. Adian and A. A. Razborov producing the first published recursive upper bound for the order of the universal finite group B(d,p) of prime exponent (the English version contains a different treatment of this result, due to E. I. Zel'manov); M. R. Vaughan-Lee's new approach to the subject; and finally, the crowning achievement of Zel'manov in establishing RBP for all prime-power exponents, thereby (via the classification theorem for finite simple groups and Hall-Higman) settling it for all exponents. The book is encyclopaedic in its coverage of facts and problems on RBP, and will continue to have an important influence in the area.

Around Burnside (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)

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