Introduction to Approximate Groups

Introduction to Approximate Groups PDF

Author: Matthew C. H. Tointon

Publisher: Cambridge University Press

Published: 2019-11-14

Total Pages:

ISBN-13: 1108571603

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Approximate groups have shot to prominence in recent years, driven both by rapid progress in the field itself and by a varied and expanding range of applications. This text collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction. The author presents a number of recent developments in the field, including an exposition of his recent result classifying nilpotent approximate groups. The book also features a considerable amount of previously unpublished material, as well as numerous exercises and motivating examples. It closes with a substantial chapter on applications, including an exposition of Breuillard, Green and Tao's celebrated approximate-group proof of Gromov's theorem on groups of polynomial growth. Written by an author who is at the forefront of both researching and teaching this topic, this text will be useful to advanced students and to researchers working in approximate groups and related areas.

Introduction to Approximate Groups

Introduction to Approximate Groups PDF

Author: Matthew C. H. Tointon

Publisher: Cambridge University Press

Published: 2019-11-14

Total Pages: 220

ISBN-13: 1108470734

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Provides a comprehensive exploration of the main concepts and techniques from the young, exciting field of approximate groups.

Non-Associative Algebra and Its Applications

Non-Associative Algebra and Its Applications PDF

Author: Lev Sabinin

Publisher: CRC Press

Published: 2006-01-13

Total Pages: 558

ISBN-13: 9780824726690

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With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.

An Introduction to the Theory of Groups

An Introduction to the Theory of Groups PDF

Author: Paul Alexandroff

Publisher: Courier Corporation

Published: 2013-07-24

Total Pages: 128

ISBN-13: 0486275973

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This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates. Includes a wealth of simple examples, primarily geometrical, and end-of-chapter exercises. 1959 edition.

Applying the Classification of Finite Simple Groups: A User’s Guide

Applying the Classification of Finite Simple Groups: A User’s Guide PDF

Author: Stephen D. Smith

Publisher: American Mathematical Soc.

Published: 2018-04-30

Total Pages: 231

ISBN-13: 1470442914

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Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.

Introduction to Group Theory

Introduction to Group Theory PDF

Author: Oleg Vladimirovič Bogopolʹskij

Publisher: European Mathematical Society

Published: 2008

Total Pages: 196

ISBN-13: 9783037190418

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This book quickly introduces beginners to general group theory and then focuses on three main themes : finite group theory, including sporadic groups combinatorial and geometric group theory, including the Bass-Serre theory of groups acting on trees the theory of train tracks by Bestvina and Handel for automorphisms of free groups With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples. Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.

Inverse Problems and Data Assimilation

Inverse Problems and Data Assimilation PDF

Author: Daniel Sanz-Alonso

Publisher: Cambridge University Press

Published: 2023-08-10

Total Pages: 227

ISBN-13: 1009414321

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A clear and concise mathematical introduction to the subjects of inverse problems and data assimilation, and their inter-relations.

Künneth Geometry

Künneth Geometry PDF

Author: M. J. D. Hamilton

Publisher: Cambridge University Press

Published: 2023-12-21

Total Pages: 200

ISBN-13: 1108905617

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This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.

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