Igor Rostislavovich Shafarevich's Books

Basic Algebraic Geometry 1

By: Igor R. Shafarevich

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This book is a revised and expanded new edition of the first four chapters of Shafarevich’s well-known introductory book on algebraic geometry. Besides correcting misprints and inaccuracies, the author has added plenty of new material, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and elliptic curves, the Bertini theorems, and normal surface singularities.

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Page Count

320

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642579086

ISBN 13

9783642579080

Geometries and Groups

By: Viacheslav V. Nikulin,Igor R. Shafarevich

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Geometries and Groups

By: Viacheslav V. Nikulin,Igor R. Shafarevich

This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a general theory of such geometries, based on their relation with discrete groups of motions of the Euclidean plane or 3-space; we also consider the relation between discrete groups of motions and crystallography. The description of locally Euclidean geometries of one type shows that these geometries are themselves naturally represented as the points of a new geometry. The systematic study of this new geometry leads us to 2-dimensional Lobachevsky geometry (also called non-Euclidean or hyperbolic geometry) which, following the logic of our study, is constructed starting from the properties of its group of motions. Thus in this book we would like to introduce the reader to a theory of geometries which are different from the usual Euclidean geometry of the plane and 3-space, in terms of examples which are accessible to a concrete and intuitive study. The basic method of study is the use of groups of motions, both discrete groups and the groups of motions of geometries. The book does not presuppose on the part of the reader any preliminary knowledge outside the limits of a school geometry course.

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Page Count

262

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642615708

ISBN 13

9783642615702

Basic Notions of Algebra

By: Igor R. Shafarevich

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Basic Notions of Algebra

By: Igor R. Shafarevich

Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.

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Page Count

272

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540251774

ISBN 13

9783540251774

Basic Algebraic Geometry 1

Varieties in Projective Space

By: Igor R. Shafarevich

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Basic Algebraic Geometry 1

Varieties in Projective Space

By: Igor R. Shafarevich

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 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.

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Page Count

326

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642379567

ISBN 13

9783642379567

Basic Algebraic Geometry 2

By: Igor Rostislavovich Shafarevich

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Basic Algebraic Geometry 2

By: Igor Rostislavovich Shafarevich

The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics.

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Page Count

292

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540575545

ISBN 13

9783540575542

Discourses on Algebra

By: Igor R. Shafarevich

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Discourses on Algebra

By: Igor R. Shafarevich

Using various examples this monograph shows that algebra is one of the most beautiful forms of mathematics. In doing so, it explains the basics of algebra, number theory, set theory and probability. The text presupposes very limited knowledge of mathematics, making it an ideal read for anybody new to the subject. The author, I.R. Shafarevich, is well-known across the world as one of the most outstanding mathematicians of this century as well as one of the most respected mathematical writers.

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Page Count

288

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642563252

ISBN 13

9783642563256

Book's by Igor Rostislavovich Shafarevich

Basic Algebraic Geometry 1

Basic Algebraic Geometry 1

Geometries and Groups

Geometries and Groups

Basic Notions of Algebra

Basic Notions of Algebra

Basic Algebraic Geometry 1

Basic Algebraic Geometry 1

Basic Algebraic Geometry 2

Basic Algebraic Geometry 2

Discourses on Algebra

Discourses on Algebra

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