WorldCat Identities

Shafarevich, I. R. (Igorʹ Rostislavovich) 1923-2017

Overview
Works: 389 works in 1,434 publications in 9 languages and 16,545 library holdings
Genres: History  Textbooks 
Roles: Author, Editor, Honoree, Author of introduction, Dedicatee, Other, Contributor
Publication Timeline
.
Most widely held works by I. R Shafarevich
Basic algebraic geometry by I. R Shafarevich( Book )

120 editions published between 1972 and 2013 in 5 languages and held by 1,940 WorldCat member libraries worldwide

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, "For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must." The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field
Number theory by Z. I Borevich( Book )

78 editions published between 1964 and 1993 in 4 languages and held by 1,227 WorldCat member libraries worldwide

Geometries and groups by V. V Nikulin( Book )

29 editions published between 1983 and 1994 in English and held by 712 WorldCat member libraries worldwide

This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry."
Basic notions of algebra by I. R Shafarevich( )

33 editions published between 1990 and 2014 in English and held by 701 WorldCat member libraries worldwide

This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches
Algebra I : basic notions of algebra by A. I Kostrikin( Book )

13 editions published between 1988 and 2013 in English and held by 504 WorldCat member libraries worldwide

Linear algebra and geometry by I. R Shafarevich( )

19 editions published between 2012 and 2014 in English and held by 482 WorldCat member libraries worldwide

This title begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces
The socialist phenomenon by I. R Shafarevich( Book )

12 editions published between 1980 and 2013 in English and held by 464 WorldCat member libraries worldwide

Discourses on algebra by I. R Shafarevich( Book )

18 editions published between 2002 and 2009 in English and Japanese and held by 455 WorldCat member libraries worldwide

The classic geometry of Euclid has attracted many for its beauty, elegance, and logical cohesion. In this book, the leading Russian algebraist I.R. Shafarevich argues with examples that algebra is no less beautiful, elegant, and logically cohesive than geometry. It contains an exposition of some rudiments of algebra, number theory, set theory and probability presupposing very limited knowledge of mathematics. I.R. Shafarevich is known to be one of the leading mathematicians of the 20th century, as well as one of the best mathematical writers
Basic algebraic geometry by I. R Shafarevich( )

51 editions published between 1994 and 2017 in 4 languages and held by 447 WorldCat member libraries worldwide

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ̀̀For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ̀̀Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics
Arithmetic and geometry : papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday by I. R Shafarevich( Book )

21 editions published in 1983 in English and held by 391 WorldCat member libraries worldwide

Algebraic geometry I : algebraic curves, algebraic manifolds and schemes by V. I Danilov( Book )

19 editions published between 1994 and 2013 in English and held by 377 WorldCat member libraries worldwide

This book is a very readable introduction to algebraic geometry and will be immensely useful to mathematicians working in algebraic geometry and complex analysis and especially to graduate students in these fields
Algebra II : noncommutative rings, identities by A. I Kostrikin( Book )

8 editions published in 1991 in English and held by 369 WorldCat member libraries worldwide

The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra - Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le
Algebraic geometry IV : linear algebraic groups, invariant theory by A. N Parshin( Book )

16 editions published between 1994 and 2010 in English and held by 338 WorldCat member libraries worldwide

This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a well-known expert in the first mentioned field. He presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of part two, E.B. Vinberg and V.L. Popov, are among the most active researchers in invariant theory. The last 20 years have been a period of vigorous development in this field due to the influence of modern methods from algebraic geometry. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics
Algebraic geometry V : fano varieties by Vasilij Alekseevič Iskovskih( Book )

29 editions published between 1988 and 2010 in English and Russian and held by 319 WorldCat member libraries worldwide

Algebraic geometry II : cohomology of algebraic varieties, algebraic surfaces by V. I Danilov( Book )

23 editions published between 1994 and 2014 in English and held by 316 WorldCat member libraries worldwide

"This EMS volume consists of two parts. The first part is devoted to cohomology of algebraic varieties. The second part deals with algebraic surfaces. The authors, who are well-known experts in the field, have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics."--BOOK JACKET. "This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetical algebraic geometry, complex analysis and related fields."--Jacket
Number theory IV : transcendental numbers by I. R Shafarevich( Book )

20 editions published between 1998 and 2011 in English and held by 311 WorldCat member libraries worldwide

This book is a survey of the most important directions of research in transcendental number theory. The central topics in this theory include proofs of irrationality and transcendence of various numbers, especially those that arise as the values of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle, which Lindemann showed to be impossible in 1882, when he proved that $Öpi$ is a transcendental number. Euler's conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert's famous list of open problems; this conjecture was proved by Gel'fond and Schneider in 1934. A more recent result was ApÖ'ery's surprising proof of the irrationality of $Özeta(3)$ in 1979. The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different branches of number theory, this monograph provides both an overview of the central ideas and techniques of transcendental number theory, and also a guide to the most important results
Algebraic geometry III : complex algebraic varieties, algebraic curves and their Jacobians by V. S Kulikov( Book )

16 editions published between 1994 and 1998 in English and held by 308 WorldCat member libraries worldwide

Dealing with the subject of complex algebraic geometry, this work offers a succinct summary of the areas it covers, while providing coverage of certain important fields. It presents an introduction to the work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties
Number theory II : algebraic number theory( Book )

11 editions published in 1992 in English and held by 297 WorldCat member libraries worldwide

Algebra VII : combinatorial group theory, applications to geometry by A. N Parshin( Book )

15 editions published between 1991 and 2013 in English and held by 286 WorldCat member libraries worldwide

From the reviews of the first printing of this book, published as volume 58 of the Encyclopaedia of Mathematical Sciences: " ... This book will be very useful as a reference and guide to researchers and graduate students in algebra and and topology." Acta Scientiarum Mathematicarum, Ungarn, 1994 " ... The book under review consists of two monographs on geometric aspects of group theory: Combinatorial group theory and fundamental groups" by D.J. Collins and H. Zieschang ... : "Some problems of group theory related to geometry" by R.I. Grigorchuk and P.F. Kurchanov. ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ... In summary, a very interesting book! Bulletin of the London Mathematical Society, 1996 " ... In both essays the authors give clear and comprehensive definitions, examples and statements (but not proofs) of theorems, so that the book can be understood by a reader with a minimal background in group theory or geometry. Such a reader, needing to find out what is known in this area, will find this a full and accessible store of information." Contemporary Physics, 1994 " ... This survey (Part II) presents for the first time that problems in monograph form and by the way offers a unifying treatment of the various approaches to their solutions, as far as they are known, together with hints to open problems. A titbit for every interested reader!" Monatshefte für Mathematik, 1995
Number theory I : fundamental problems, ideas and theories by I︠U︡. I Manin( Book )

16 editions published between 1992 and 1995 in English and held by 286 WorldCat member libraries worldwide

 
moreShow More Titles
fewerShow Fewer Titles
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.59 (from 0.38 for The social ... to 0.83 for Konserwaty ...)

Geometries and groups
Covers
Number theoryGeometries and groupsBasic notions of algebraDiscourses on algebraBasic algebraic geometryAlgebraic geometry I : algebraic curves, algebraic manifolds and schemesAlgebraic geometry IV : linear algebraic groups, invariant theoryAlgebraic geometry V : fano varieties
Alternative Names
Chafarevich, I. R.

Chafarevich, Igor Rostislavovich

Chafarevitch, I. 1923-

Chafarevitch, I. R.

Chafarevitch, I. R. 1923-

Chafarevitch, I. R., 1923-2017

Chafarévitch, Igor

Chafarévitch, Igor 1923-

Chafarévitch, Igor 1923-2017

Chafarevitch Igor R.

Chafarevitch, Igor R. 1923-

Chafarevitch, Igor R. 1923-2017

Chafarevitch, Igor R. (Igor Rostislavovich), 1923-

Chafarevitch Igor Rostislavovitch

Chafarevitch Igor Rostislavovitch 1923-....

Chafarevitch, Igor Rostislavovitch 1923-2017

Igor Chafarevitch mathématicien russe

Igor' Rostislavovič Šafarevič matematico sovietico

Igor Rostislavovič Šafarevič ruský matematik

Igor Rostislawowitsch Schafarewitsch russischer Mathematiker

Igor Ŝafareviĉ Rusa matematikisto

Igor Șafarevici

Igor Safarevics orosz matematikus

Igor Šafarevitš

Igor Šafarevõtš

Igor Shafarevich matemático ruso

Igor Shafarevich Russian mathematician

Igor Shafarevich Soviet and Russian mathematician

Igor Sjafarevitsj Russisch wiskundige

Igor Sjafarevitsj russisk matematikar

Igor Sjafarevitsj russisk matematiker

Igor Szafariewicz

Igor Xafarevitx

Šafarevič, I.

Šafarevič, I. 1923-

Šafarevič, I. 1923-2017

Šafarevič, I. R.

Šafarevič, I. R. 1923-

Šafarevič, I.R. 1923-2017

Šafarevič, Igorʹ.

Šafarevič, Igor' 1923-

Šafarevič, Igor' 1923-2017

Šafarevič Igor' R.

Šafarevič, Igor R. 1923-

Šafarevič, Igor R., 1923-2017

Šafarevič Igor' Rostislavovič

Šafarevič, Igorʹ Rostislavovič 1923-

Šafarevič, Igorʹ Rostislavovič 1923-2017

Șafarevici, I. R. 1923-

Șafarevici, I. R., 1923-2017

Šafarevičius Igoris

Safarevié, Igor 1923-

Šafrevič Igor

Šafrevič Igor Rostislavovič

Schafarewitsch, I.R.

Schafarewitsch, I. R. 1923-

Schafarewitsch, I. R. 1923-2017

Schafarewitsch, Igor.

Schafarewitsch, Igor R.

Schafarewitsch Igor R. 1923-....

Schafarewitsch, Igor R. 1923-2017

Schafarewitsch, Igor Rostislavovitsch 1923-

Shafarevich, I.R.

Shafarevich, I.R. 1923-

Shafarevich, I. R. 1923-2017

Shafarevich, I. R. (Igor Rostislavovich)

Shafarevich, I. R. (Igorʹ Rostislavovich), 1923-

Shafarevich, Igor

Shafarevich, Igor 1923-

Shafarevich, Igor R.

Shafarevich Igor R. 1923-....

Shafarevich, Igor' R. 1923-2017

Shafarevich, Igor' Rostislavich

Shafarevich, Igorʹ Rostislavovich

Shafarevich, Igorʹ Rostislavovich 1923-

Shafarevich, Igorʹ Rostislavovich, 1923-2017

Sjafarevitsj, I.R. 1923-

Sjafarewitsj, I.R. 1923-

Szafarewicz, Igor R.

Szafariewicz, Igor.

Szafariewicz, Igor 1923-

Szafariewicz, Igor, 1923-2017

Xafarevitx, Igor R. 1923-

Ιγκόρ Σαφάρεβιτς

Игор Шафаревич

Шафаревич И.

Шафаревич И.Р.

Шафаревич, И. Р 1923-

Шафаревич, И. Р. (Игорь Ростиславович), 1923-2017

Шафаревич, Игор Ростилавович 1923-...

Шафаревич, Игор Ростилавович, 1923-2017

Шафаревич, Игор Ростиславович.

Шафаревич Игорь

Шафаревич, Игорь 1923-

Шафаревич, Игорь (Игорь Ростиславович), 1923-

Шафаревич, Игорь Ростиславович.

Шафаревич, Игорь Ростиславович 1923-...)

Шафаревич, Игорь Ростиславович 1923-2017

Шафаревич Ігор Ростиславович

Ігар Расціслававіч Шафарэвіч

ایقور شافرویچ

이고리 샤파레비치

シャハレビッチ

シャファレヴィッチ

シャファレヴィッチ, イゴール R

伊戈爾·沙發列維奇

Languages