Alexandre Borovik's Books

Mathematics under the Microscope

Notes on Cognitive Aspects of Mathematical Practice

By: Alexandre Borovik

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Mathematics under the Microscope

Notes on Cognitive Aspects of Mathematical Practice

By: Alexandre Borovik

Discusses, from a working mathematician's point of view, the mystery of mathematical intuition: Why are certain mathematical concepts more intuitive than others? And to what extent does the 'small scale' structure of mathematical concepts and algorithms reflect the workings of the human brain?

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Page Count

345

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821847619

ISBN 13

9780821847619

Computational and Experimental Group Theory

AMS-ASL Joint Special Session, Interactions Between Logic, Group Theory, and Computer Science, January 15-16, 2003, Baltimore, Maryland

By: Alexandre Borovik,Alexei G. Myasnikov

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Computational and Experimental Group Theory

AMS-ASL Joint Special Session, Interactions Between Logic, Group Theory, and Computer Science, January 15-16, 2003, Baltimore, Maryland

By: Alexandre Borovik,Alexei G. Myasnikov

The focus of algorithmic group theory shifted from the decidability/undecidability type of result to the complexity of algorithms. This title contains papers that reflect that paradigm shift. It presents articles that are based on the AMS/ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science.

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234

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821834835

ISBN 13

9780821834831

Groups, Languages, Algorithms

AMS-ASL Joint Special Session on Interactions Between Logic, Group Theory, and Computer Science, January 16-19, 2003, Baltimore, Maryland

By: Alexandre Borovik

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Groups, Languages, Algorithms

AMS-ASL Joint Special Session on Interactions Between Logic, Group Theory, and Computer Science, January 16-19, 2003, Baltimore, Maryland

By: Alexandre Borovik

Since the pioneering works of Novikov and Maltsev, group theory has been a testing ground for mathematical logic in its many manifestations, from the theory of algorithms to model theory. The interaction between logic and group theory led to many prominent results which enriched both disciplines. This volume reflects the major themes of the American Mathematical Society/Association for Symbolic Logic Joint Special Session (Baltimore, MD), Interactions between Logic, Group Theory and Computer Science. Included are papers devoted to the development of techniques used for the interaction of group theory and logic. It is suitable for graduate students and researchers interested in algorithmic and combinatorial group theory. A complement to this work is Volume 349 in the AMS series, Contemporary Mathematics, Computational and Experimental Group Theory, which arose from the same meeting and concentrates on the interaction of group theory and computer science.

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Page Count

360

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821836188

ISBN 13

9780821836187

Coxeter Matroids

By: Alexandre V. Borovik,Israel M. Gelfand,Neil White

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Coxeter Matroids

By: Alexandre V. Borovik,Israel M. Gelfand,Neil White

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.

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Page Count

282

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461220661

ISBN 13

9781461220664

Mirrors and Reflections

The Geometry of Finite Reflection Groups

By: Alexandre V. Borovik,Anna Borovik

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Mirrors and Reflections

The Geometry of Finite Reflection Groups

By: Alexandre V. Borovik,Anna Borovik

This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.

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Page Count

172

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387790667

ISBN 13

9780387790664

Mathematics under the Microscope

Notes on Cognitive Aspects of Mathematical Practice

By: Alexandre Borovik

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Mathematics under the Microscope

Notes on Cognitive Aspects of Mathematical Practice

By: Alexandre Borovik

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Solve jigsaw puzzle

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Page Count

345

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821847619

ISBN 13

9780821847619

Groups, Languages, Algorithms

AMS-ASL Joint Special Session on Interactions Between Logic, Group Theory, and Computer Science, January 16-19, 2003, Baltimore, Maryland

By: Alexandre Borovik

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Groups, Languages, Algorithms

AMS-ASL Joint Special Session on Interactions Between Logic, Group Theory, and Computer Science, January 16-19, 2003, Baltimore, Maryland

By: Alexandre Borovik

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Solve jigsaw puzzle

Age

Page Count

360

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821836188

ISBN 13

9780821836187

Mirrors and Reflections

The Geometry of Finite Reflection Groups

By: Alexandre V. Borovik,Anna Borovik

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Mirrors and Reflections

The Geometry of Finite Reflection Groups

By: Alexandre V. Borovik,Anna Borovik

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Solve jigsaw puzzle

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Page Count

172

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387790667

ISBN 13

9780387790664

Coxeter Matroids

By: Alexandre V. Borovik,Israel M. Gelfand,Neil White

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Coxeter Matroids

By: Alexandre V. Borovik,Israel M. Gelfand,Neil White

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Page Count

282

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461220661

ISBN 13

9781461220664

Simple Groups of Finite Morley Rank

By: Tuna Altınel,Alexandre Borovik,Gregory L. Cherlin

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Simple Groups of Finite Morley Rank

By: Tuna Altınel,Alexandre Borovik,Gregory L. Cherlin

The book gives a detailed presentation of the classification of the simple groups of finite Morley rank which contain a nontrivial unipotent 2-subgroup. They are linear algebraic groups over algebraically closed fields of characteristic 2. Although the story told in the book is inspired by the classification of the finite simple groups, it goes well beyond this source of inspiration. Not only do the techniques adapted from finite group theory cover, in a peculiar way, various portions of the three generations of approaches to finite simple groups but model theoretic methods also play an unexpected role. The book contains a complete account of all this material, part of which has not been published. In addition, almost every general result about groups of finite Morley rank is exposed in detail and the book ends with a chapter where the authors provide a list of open problems in the relevant fields of mathematics. As a result, the book provides food for thought to finite group theorists, model theorists, and algebraic geometers who are interested in group theoretic problems.

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Page Count

556

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843052

ISBN 13

9780821843055

Computational and Experimental Group Theory

AMS-ASL Joint Special Session, Interactions Between Logic, Group Theory, and Computer Science, January 15-16, 2003, Baltimore, Maryland

By: Alexandre Borovik,Alexei G. Myasnikov

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Computational and Experimental Group Theory

AMS-ASL Joint Special Session, Interactions Between Logic, Group Theory, and Computer Science, January 15-16, 2003, Baltimore, Maryland

By: Alexandre Borovik,Alexei G. Myasnikov

Average ratings

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Write a review

Solve jigsaw puzzle

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Page Count

234

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821834835

ISBN 13

9780821834831

Book's by Alexandre Borovik

Mathematics under the Microscope

Mathematics under the Microscope

Computational and Experimental Group Theory

Computational and Experimental Group Theory

Groups, Languages, Algorithms

Groups, Languages, Algorithms

Coxeter Matroids

Coxeter Matroids

Mirrors and Reflections

Mirrors and Reflections

Mathematics under the Microscope

Mathematics under the Microscope

Groups, Languages, Algorithms

Groups, Languages, Algorithms

Mirrors and Reflections

Mirrors and Reflections

Coxeter Matroids

Coxeter Matroids

Simple Groups of Finite Morley Rank

Simple Groups of Finite Morley Rank

Computational and Experimental Group Theory

Computational and Experimental Group Theory

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