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The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied.This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
Book Synopsis Presentations of Groups by : D. L. Johnson
Download or read book Presentations of Groups written by D. L. Johnson and published by Cambridge University Press. This book was released on 1997-05-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied.This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.
Book Synopsis Topics in the Theory of Group Presentations by : D. L. Johnson
Download or read book Topics in the Theory of Group Presentations written by D. L. Johnson and published by Cambridge University Press. This book was released on 1980-07-31 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.
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.
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.
The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.
Book Synopsis The Bounded and Precise Word Problems for Presentations of Groups by : S. V. Ivanov
Download or read book The Bounded and Precise Word Problems for Presentations of Groups written by S. V. Ivanov and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Book Synopsis Visual Group Theory by : Nathan Carter
Download or read book Visual Group Theory written by Nathan Carter and published by American Mathematical Soc.. This book was released on 2021-06-08 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
This outstanding new book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.
Book Synopsis Groups, Graphs and Trees by : John Meier
Download or read book Groups, Graphs and Trees written by John Meier and published by Cambridge University Press. This book was released on 2008-07-31 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding new book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.
Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.
Book Synopsis Computation with Finitely Presented Groups by : Charles C. Sims
Download or read book Computation with Finitely Presented Groups written by Charles C. Sims and published by Cambridge University Press. This book was released on 1994-01-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.
Presentation Patterns is the first book on presentations that categorizes and organizes the building blocks (or patterns) that you’ll need to communicate effectively using presentation tools like Keynote and PowerPoint. Patterns are like the lower-level steps found inside recipes; they are the techniques you must master to be considered a master chef or master presenter. You can use the patterns in this book to construct your own recipes for different contexts, such as business meetings, technical demonstrations, scientific expositions, and keynotes, just to name a few. Although there are no such things as antirecipes, this book shows you lots of antipatterns—things you should avoid doing in presentations. Modern presentation tools often encourage ineffective presentation techniques, but this book shows you how to avoid them. Each pattern is introduced with a memorable name, a definition, and a brief explanation of motivation. Readers learn where the pattern applies, the consequences of applying it, and how to apply it. The authors also identify critical antipatterns: clichés, fallacies, and design mistakes that cause presentations to disappoint. These problems are easy to avoid—once you know how. Presentation Patterns will help you Plan what you’ll say, who you’ll say it to, how long you’ll talk, and where you’ll present Perfectly calibrate your presentation to your audience Use the storyteller’s “narrative arc” to full advantage Strengthen your credibility—and avoid mistakes that hurt it Hone your message before you ever touch presentation software Incorporate visuals that support your message instead of hindering it Create highly effective “infodecks” that work when you’re not able to deliver a talk in person Construct slides that really communicate and avoid “Ant Fonts,” “Floodmarks,” “Alienating Artifacts,” and other errors Master 13 powerful techniques for delivering your presentation with power, authority, and clarity Whether you use this book as a handy reference or read it from start to finish, it will be a revelation: an entirely new language for systematically planning, creating, and delivering more powerful presentations. You’ll quickly find it indispensable—no matter what you’re presenting, who your audiences are, or what message you’re driving home.
Book Synopsis Presentation Patterns by : Neal Ford
Download or read book Presentation Patterns written by Neal Ford and published by Addison-Wesley. This book was released on 2012-08-15 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presentation Patterns is the first book on presentations that categorizes and organizes the building blocks (or patterns) that you’ll need to communicate effectively using presentation tools like Keynote and PowerPoint. Patterns are like the lower-level steps found inside recipes; they are the techniques you must master to be considered a master chef or master presenter. You can use the patterns in this book to construct your own recipes for different contexts, such as business meetings, technical demonstrations, scientific expositions, and keynotes, just to name a few. Although there are no such things as antirecipes, this book shows you lots of antipatterns—things you should avoid doing in presentations. Modern presentation tools often encourage ineffective presentation techniques, but this book shows you how to avoid them. Each pattern is introduced with a memorable name, a definition, and a brief explanation of motivation. Readers learn where the pattern applies, the consequences of applying it, and how to apply it. The authors also identify critical antipatterns: clichés, fallacies, and design mistakes that cause presentations to disappoint. These problems are easy to avoid—once you know how. Presentation Patterns will help you Plan what you’ll say, who you’ll say it to, how long you’ll talk, and where you’ll present Perfectly calibrate your presentation to your audience Use the storyteller’s “narrative arc” to full advantage Strengthen your credibility—and avoid mistakes that hurt it Hone your message before you ever touch presentation software Incorporate visuals that support your message instead of hindering it Create highly effective “infodecks” that work when you’re not able to deliver a talk in person Construct slides that really communicate and avoid “Ant Fonts,” “Floodmarks,” “Alienating Artifacts,” and other errors Master 13 powerful techniques for delivering your presentation with power, authority, and clarity Whether you use this book as a handy reference or read it from start to finish, it will be a revelation: an entirely new language for systematically planning, creating, and delivering more powerful presentations. You’ll quickly find it indispensable—no matter what you’re presenting, who your audiences are, or what message you’re driving home.
Advanced Presentations by Design overturns much of the conventional wisdom and practice for creating presentations. Based on over 200 research studies from the fields of communication, marketing, psychology, multimedia, and law, it provides fact-based answers to critical questions about presentation design, including how to adapt your presentation to different audience personality preferences, what role your data should play and how much of it you need, how to turn your data into a story, and how to design persuasive yet comprehensible visual layouts.
Book Synopsis Advanced Presentations by Design by : Andrew Abela
Download or read book Advanced Presentations by Design written by Andrew Abela and published by John Wiley & Sons. This book was released on 2008-08-20 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Presentations by Design overturns much of the conventional wisdom and practice for creating presentations. Based on over 200 research studies from the fields of communication, marketing, psychology, multimedia, and law, it provides fact-based answers to critical questions about presentation design, including how to adapt your presentation to different audience personality preferences, what role your data should play and how much of it you need, how to turn your data into a story, and how to design persuasive yet comprehensible visual layouts.
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.
Book Synopsis Complexity and Randomness in Group Theory by : Frédérique Bassino
Download or read book Complexity and Randomness in Group Theory written by Frédérique Bassino and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
