Collected Mathematical Papers

Reference

Shafarevich, Igor R.

Language Study & Reference

Springer

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.

Basic Notions of Algebra (Encyclopaedia of Mathematical Sciences)

Science & Math

Mathematics

Basic Notions of Algebra (Encyclopaedia of Mathematical Sciences, 11)

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.

Discourses on Algebra

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.

Basic Algebraic Geometry 1: Varieties in Projective Space

The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text and added new material. 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 the first volume and is suitable for beginning graduate students.

Basic Algebraic Geometry 2: Schemes and Complex Manifolds

Basic Notions of Algebra

Linear Algebra and Geometry

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book 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 book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Remizov, Alexey O.

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.

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.

See the best price to sell, buy, or rent books by Shafarevich, Igor R.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Shafarevich, Igor R.

See the best price to sell, buy, or rent books by Shafarevich, Igor R.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Collected Mathematical Papers

Basic Notions of Algebra (Encyclopaedia of Mathematical Sciences)

Basic Notions of Algebra (Encyclopaedia of Mathematical Sciences, 11)

Discourses on Algebra

Basic Algebraic Geometry 1: Varieties in Projective Space

Basic Algebraic Geometry 2: Schemes and Complex Manifolds

Basic Notions of Algebra

Linear Algebra and Geometry

Basic Algebraic Geometry 1: Varieties in Projective Space

Basic Algebraic Geometry 2: Schemes and Complex Manifolds