Igor 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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320

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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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262

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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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272

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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

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326

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Springer Science & Business Media

Published Date

ISBN 10

3642379567

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9783642379567

A Ransomed Dissident

A Life in Art Under the Soviets

By: Igor Golomstock

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A Ransomed Dissident

A Life in Art Under the Soviets

By: Igor Golomstock

In 1939, a ten-year-old Igor Golomstock accompanied his mother, a medical doctor, to the vast network of labour camps in the Russian Far East. While she tended patients, he was minded by assorted 'trusty' prisoners – hardened criminals – and returned to Moscow an almost feral adolescent, fluent in obscene prison jargon but intellectually ignorant. Despite this dubious start he became a leading art historian and co-author (with his close friend Andrey Sinyavsky) of the first, deeply controversial, monograph on Picasso published in the Soviet Union. His writings on his 43 years in the Soviet Union offer a rare insight into life as a quietly subversive art historian and the post-Stalin dissident community. In vivid prose Golomstock shows the difficulties of publishing, curating and talking about Western art in Soviet Russia and, with self-deprecating humour, the absurd tragicomedy of life for the Moscow intelligentsia during Khruschev's thaw and Brezhnev's stagnation. He also offers a unique personal perspective on the 1966 trial of Sinyavsky and Yuri Daniel, widely considered the end of Khruschev's liberalism and the spark that ignited the Soviet dissident movement. In 1972 he was given 'permission' to leave the Soviet Union, but only after paying a 'ransom' of more than 25 years' salary, nominally intended to reimburse the state for his education. A remarkable collection of artists, scholars and intellectuals in Russia and the West, including Roland Penrose, came together to help him pay this astronomical sum. His memoirs of life once in the UK offer an insider's view of the BBC Russian Service and a penetrating analysis of the notorious feud between Sinyavsky and Aleksandr Solzhenitsyn. Nominated for the Russian Booker Prize on its publication in Russian in 2014, The Ransomed Dissident opens a window onto the life of a remarkable man: a dissident of uncompromising moral integrity and with an outstanding gift for friendship.

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291

Publisher

Bloomsbury Publishing

Published Date

ISBN 10

1786734494

ISBN 13

9781786734495

Finite Fields: Theory and Computation

The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography

By: Igor Shparlinski

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Finite Fields: Theory and Computation

The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography

By: Igor Shparlinski

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.

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532

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Springer Science & Business Media

Published Date

ISBN 10

940159239X

ISBN 13

9789401592390

Noncommutative Geometry

A Functorial Approach

By: Igor V. Nikolaev

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Noncommutative Geometry

A Functorial Approach

By: Igor V. Nikolaev

Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.

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Page Count

400

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110788705

ISBN 13

9783110788709

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

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326

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Springer Science & Business Media

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ISBN 10

3642379567

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9783642379567

Classical Algebraic Geometry

A Modern View

By: Igor V. Dolgachev

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Classical Algebraic Geometry

A Modern View

By: Igor V. Dolgachev

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

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Page Count

653

Publisher

Cambridge University Press

Published Date

ISBN 10

1139560786

ISBN 13

9781139560788

Algebraic Groups and Number Theory

By: Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk

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Algebraic Groups and Number Theory

By: Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk

The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

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379

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Cambridge University Press

Published Date

ISBN 10

052111361X

ISBN 13

9780521113618

Linear Groups

The Accent on Infinite Dimensionality

By: Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya. Subbotin

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Linear Groups

The Accent on Infinite Dimensionality

By: Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya. Subbotin

Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory. The hope is that this book can be part of a similar transition in the field of linear groups. Features This is the first book dedicated to infinite-dimensional linear groups This is written for experts and graduate students specializing in algebra and parallel disciplines This book discusses a very new theory and accumulates many important and useful results

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329

Publisher

CRC Press

Published Date

ISBN 10

135100803X

ISBN 13

9781351008037

Algebraic Groups and Number Theory: Volume 1

By: Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk

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Algebraic Groups and Number Theory: Volume 1

By: Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk

The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

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380

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Cambridge University Press

Published Date

ISBN 10

1009380656

ISBN 13

9781009380652

Infinite Groups

A Roadmap to Selected Classical Areas

By: Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya. Subbotin

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Infinite Groups

A Roadmap to Selected Classical Areas

By: Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya. Subbotin

In recent times, group theory has found wider applications in various fields of algebra and mathematics in general. But in order to apply this or that result, you need to know about it, and such results are often diffuse and difficult to locate, necessitating that readers construct an extended search through multiple monographs, articles, and papers. Such readers must wade through the morass of concepts and auxiliary statements that are needed to understand the desired results, while it is initially unclear which of them are really needed and which ones can be dispensed with. A further difficulty that one may encounter might be concerned with the form or language in which a given result is presented. For example, if someone knows the basics of group theory, but does not know the theory of representations, and a group theoretical result is formulated in the language of representation theory, then that person is faced with the problem of translating this result into the language with which they are familiar, etc. Infinite Groups: A Roadmap to Some Classical Areas seeks to overcome this challenge. The book covers a broad swath of the theory of infinite groups, without giving proofs, but with all the concepts and auxiliary results necessary for understanding such results. In other words, this book is an extended directory, or a guide, to some of the more established areas of infinite groups. Features An excellent resource for a subject formerly lacking an accessible and in-depth reference Suitable for graduate students, PhD students, and researchers working in group theory Introduces the reader to the most important methods, ideas, approaches, and constructions in infinite group theory.

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Page Count

411

Publisher

CRC Press

Published Date

ISBN 10

1000848310

ISBN 13

9781000848311

Complexity and Randomness in Group Theory

GAGTA BOOK 1

By: Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil

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Complexity and Randomness in Group Theory

GAGTA BOOK 1

By: Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil

This book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.

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Page Count

386

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110667029

ISBN 13

9783110667028

Algebraic Geometry

Korea-Japan Conference in Honor of Igor Dolgachev's 60th Birthday, July 5-9, 2004, Korea Institute for Advanced Study, Seoul, Korea

By: Igor V. Dolgachev,JongHae Keum,Shigeyuki Kondō

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Algebraic Geometry

Korea-Japan Conference in Honor of Igor Dolgachev's 60th Birthday, July 5-9, 2004, Korea Institute for Advanced Study, Seoul, Korea

By: Igor V. Dolgachev,JongHae Keum,Shigeyuki Kondō

This volume contains the proceedings of the Korea-Japan Conference on Algebraic Geometry in honor of Igor Dolgachev on his sixtieth birthday. The articles in this volume explore a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered by this volume are algebraic curve theory, algebraic surface theory, moduli space, automorphic forms, Mordell-Weil lattices, and automorphisms of hyperkahler manifolds. This book is an excellent and rich reference source for researchers.

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256

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821842013

ISBN 13

9780821842010

Computational and Algorithmic Problems in Finite Fields

By: Igor Shparlinski

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Computational and Algorithmic Problems in Finite Fields

By: Igor Shparlinski

This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.

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253

Publisher

Springer Science & Business Media

Published Date

ISBN 10

940111806X

ISBN 13

9789401118064

Groups With Prescribed Quotient Groups And Associated Module Theory

By: Leonid A Kurdachenko,Javier Otal,Igor Ya Subbotin

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Groups With Prescribed Quotient Groups And Associated Module Theory

By: Leonid A Kurdachenko,Javier Otal,Igor Ya Subbotin

The influence of different gomomorphic images on the structure of a group is one of the most important and natural problems of group theory. The problem of describing a group with all its gomomorphic images known, i.e. reconstructing the whole thing using its reflections, seems especially natural and promising. This theme has a history that is almost a half-century long. The authors of this book present well-established results as well as newer, contemporary achievements in this area from the common integral point of view. This view is based on the implementation of module theory for solving group problems. Evidently, this approach requires investigation of some specific types of modules: infinite simple modules and just infinite modules (note that every infinite noetherian module has either an infinite simple factor-module or a just infinite factor-module). This book will therefore be useful for group theorists as well as ring and module theorists. Also, the level, style, and presentation make the book easily accessible to graduate students.

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245

Publisher

World Scientific

Published Date

ISBN 10

9814489867

ISBN 13

9789814489867

Asymptotology

Ideas, Methods, and Applications

By: Igor V. Andrianov,Leonid I. Manevitch

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Asymptotology

Ideas, Methods, and Applications

By: Igor V. Andrianov,Leonid I. Manevitch

Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G.

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262

Publisher

Springer Science & Business Media

Published Date

ISBN 10

144199162X

ISBN 13

9781441991621

Vertex Operator Algebras and the Monster

By: Igor Frenkel,James Lepowsky,Arne Meurman

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Vertex Operator Algebras and the Monster

By: Igor Frenkel,James Lepowsky,Arne Meurman

This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine.

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563

Publisher

Academic Press

Published Date

ISBN 10

0080874541

ISBN 13

9780080874548

Artinian Modules over Group Rings

By: Leonid Kurdachenko,Javier Otal,Igor Ya Subbotin

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Artinian Modules over Group Rings

By: Leonid Kurdachenko,Javier Otal,Igor Ya Subbotin

This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.

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253

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Springer Science & Business Media

Published Date

ISBN 10

3764377658

ISBN 13

9783764377656

Recurrence Sequences

By: Graham Everest, Alf van der Poorten,Igor Shparlinski,Thomas Ward

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Recurrence Sequences

By: Graham Everest, Alf van der Poorten,Igor Shparlinski,Thomas Ward

Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.

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Page Count

338

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470423154

ISBN 13

9781470423155

Lectures on Invariant Theory

By: Igor Dolgachev

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Lectures on Invariant Theory

By: Igor Dolgachev

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

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244

Publisher

Cambridge University Press

Published Date

ISBN 10

0521525489

ISBN 13

9780521525480

Basic Algebraic Geometry 2

Schemes and Complex Manifolds

By: Igor R. Shafarevich

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Basic Algebraic Geometry 2

Schemes and Complex Manifolds

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 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.

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271

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642380107

ISBN 13

9783642380105

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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288

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Springer Science & Business Media

Published Date

ISBN 10

3642563252

ISBN 13

9783642563256

The Socialist Phenomenon: A Historical Survey of Socialist Policies and Ideals

By: Igor Shafarevich

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The Socialist Phenomenon: A Historical Survey of Socialist Policies and Ideals

By: Igor Shafarevich

The Socialist Phenomenon is a powerful survey of socialism and socialist thought from ancient times to the present day. Most assume that socialism and communism began with the writings of Karl Marx, but through his book Shafarevich lays out with amazing clarity that socialism is an evil that has been present in man’s thoughts and actions for thousands of years. In the age of “democratic socialism” and other modern iterations, The Socialist Phenomenon reminds us of the truth about socialism and the dangers that come when societies embrace socialist policies and ideals.

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Page Count

384

Publisher

Gideon House Books

Published Date

ISBN 10

1943133778

ISBN 13

9781943133772

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