The History of Combinatorial Group Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461394872
Total Pages : 240 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis The History of Combinatorial Group Theory by : B. Chandler

Download or read book The History of Combinatorial Group Theory written by B. Chandler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.

Combinatorial Group Theory

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Publisher : Courier Corporation
ISBN 13 : 0486438309
Total Pages : 466 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Combinatorial Group Theory by : Wilhelm Magnus

Download or read book Combinatorial Group Theory written by Wilhelm Magnus and published by Courier Corporation. This book was released on 2004-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.

Topics in Combinatorial Group Theory

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Publisher : Birkhäuser
ISBN 13 : 3034885873
Total Pages : 174 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Topics in Combinatorial Group Theory by : Gilbert Baumslag

Download or read book Topics in Combinatorial Group Theory written by Gilbert Baumslag and published by Birkhäuser. This book was released on 2012-12-06 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.

Combinatorial Group Theory

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Publisher : Springer
ISBN 13 : 3642618960
Total Pages : 354 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Combinatorial Group Theory by : Roger C. Lyndon

Download or read book Combinatorial Group Theory written by Roger C. Lyndon and published by Springer. This book was released on 2015-03-12 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews

Algorithms and Classification in Combinatorial Group Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461397308
Total Pages : 235 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Algorithms and Classification in Combinatorial Group Theory by : Gilbert Baumslag

Download or read book Algorithms and Classification in Combinatorial Group Theory written by Gilbert Baumslag and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.

Combinatorial Set Theory

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Publisher : Springer
ISBN 13 : 3319602314
Total Pages : 594 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer. This book was released on 2017-12-20 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Combinatorial Group Theory and Topology

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Publisher : Princeton University Press
ISBN 13 : 0691084106
Total Pages : 564 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Combinatorial Group Theory and Topology by : S. M. Gersten

Download or read book Combinatorial Group Theory and Topology written by S. M. Gersten and published by Princeton University Press. This book was released on 1987-05-21 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.

Combinatorial Group Testing and Its Applications

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Publisher : World Scientific
ISBN 13 : 9810241070
Total Pages : 337 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Combinatorial Group Testing and Its Applications by : Dingzhu Du

Download or read book Combinatorial Group Testing and Its Applications written by Dingzhu Du and published by World Scientific. This book was released on 2000 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group testing has been used in medical, chemical and electrical testing, coding, drug screening, pollution control, multiaccess channel management, and recently in data verification, clone library screening and AIDS testing. The mathematical model can be either combinatorial or probabilistic. This book summarizes all important results under the combinatorial model, and demonstrates their applications in real problems. Some other search problems, including the famous counterfeit-coins problem, are also studied in depth. There are two reasons for publishing a second edition of this book. The first is the usual need to update the text (after six years) and correct errors. The second -- and more important -- reason is to accommodate the recent sudden growth of interest in applying the idea of group testing to clone library screening. This development is much more than just a new application, since the new application brings with it new objectives which require a new twist of theory. It also embraces the growing importance of two topics: nonadaptive algorithms and error tolerance. Two new chapters, one on clone library screening and the other on error tolerance, have been added. Also included is a new chapter on counterfeit coins, the most famous search problem historically, which recently drew on an unexpected connection to some deep mathematical theory to yield new results. Finally, the chapters have been recognized into parts to provide focuses and perspectives.

The Unity of Combinatorics

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Publisher : American Mathematical Soc.
ISBN 13 : 1470465094
Total Pages : 353 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Unity of Combinatorics by : Ezra Brown

Download or read book The Unity of Combinatorics written by Ezra Brown and published by American Mathematical Soc.. This book was released on 2021-04-05 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

Combinatorial Group Theory and Topology. (AM-111), Volume 111

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Publisher : Princeton University Press
ISBN 13 : 1400882087
Total Pages : 560 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Combinatorial Group Theory and Topology. (AM-111), Volume 111 by : S. M. Gersten

Download or read book Combinatorial Group Theory and Topology. (AM-111), Volume 111 written by S. M. Gersten and published by Princeton University Press. This book was released on 2016-03-02 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.

Topics in Geometric Group Theory

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Publisher : University of Chicago Press
ISBN 13 : 9780226317199
Total Pages : 320 pages
Book Rating : 4.3/5 (171 download)

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Book Synopsis Topics in Geometric Group Theory by : Pierre de la Harpe

Download or read book Topics in Geometric Group Theory written by Pierre de la Harpe and published by University of Chicago Press. This book was released on 2000-10-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Combinatorial Group Theory

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Publisher : Cambridge University Press
ISBN 13 : 0521341337
Total Pages : 325 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Combinatorial Group Theory by : Daniel E. Cohen

Download or read book Combinatorial Group Theory written by Daniel E. Cohen and published by Cambridge University Press. This book was released on 1989-08-17 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author aims to show the value of using topological methods in combinatorial group theory.

Permutation Groups and Combinatorial Structures

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Publisher : Cambridge University Press
ISBN 13 : 0521222877
Total Pages : 153 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Permutation Groups and Combinatorial Structures by : Norman Biggs

Download or read book Permutation Groups and Combinatorial Structures written by Norman Biggs and published by Cambridge University Press. This book was released on 1979-08-16 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.

Combinatorial Group Theory, Discrete Groups, and Number Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821839853
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Combinatorial Group Theory, Discrete Groups, and Number Theory by : Discrete Groups Conference on Combinatorial Group Theory

Download or read book Combinatorial Group Theory, Discrete Groups, and Number Theory written by Discrete Groups Conference on Combinatorial Group Theory and published by American Mathematical Soc.. This book was released on 2006 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Read Write Inc. Fresh Start is a specially adapted literacy programme for all pupils in Years 5, 6 and 7 who are working below National Curriculum level 3. Like Read Write Inc. Phonics for pupils in the early years, the scheme starts by introducing pupils to all the letter sounds through use of the Speed Sounds cards and the green and red flashcards.Pupils progress through these sets of workbooks at their own pace, after they have completed the Introductory module. Modules 1-10 include both fiction and non-fiction texts and cover a range of cross-curricular topics. Practise in writing, spelling, editing and comprehension is provided at every level.

Combinatorial Group Theory and Applications to Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540637042
Total Pages : 252 pages
Book Rating : 4.6/5 (37 download)

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Book Synopsis Combinatorial Group Theory and Applications to Geometry by : D.J. Collins

Download or read book Combinatorial Group Theory and Applications to Geometry written by D.J. Collins and published by Springer Science & Business Media. This book was released on 1998-03-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

Group Theory

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Publisher : Courier Corporation
ISBN 13 : 0486140164
Total Pages : 512 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Group Theory by : W. R. Scott

Download or read book Group Theory written by W. R. Scott and published by Courier Corporation. This book was released on 2012-05-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.

Combinatorial Group Theory

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Publisher :
ISBN 13 : 9781139884334
Total Pages : pages
Book Rating : 4.8/5 (843 download)

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Book Synopsis Combinatorial Group Theory by : Daniel E. Cohen

Download or read book Combinatorial Group Theory written by Daniel E. Cohen and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: