Author : Derek F. Holt
Publisher : CRC Press
Page : 532 pages
File Size : 17,72 MB
Release : 2005-01-13
Category : Mathematics
ISBN : 1420035215
The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
Author : Luise-Charlotte Kappe
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 28,34 MB
Release : 2010-04-08
Category : Mathematics
ISBN : 0821848054
This volume consists of contributions by researchers who were invited to the Harlaxton Conference on Computational Group Theory and Cohomology, held in August of 2008, and to the AMS Special Session on Computational Group Theory, held in October 2008. This volume showcases examples of how Computational Group Theory can be applied to a wide range of theoretical aspects of group theory. Among the problems studied in this book are classification of p-groups, covers of Lie groups, resolutions of Bieberbach groups, and the study of the lower central series of free groups. This volume also includes expository articles on the probabilistic zeta function of a group and on enumerating subgroups of symmetric groups. Researchers and graduate students working in all areas of Group Theory will find many examples of how Computational Group Theory helps at various stages of the research process, from developing conjectures through the verification stage. These examples will suggest to the mathematician ways to incorporate Computational Group Theory into their own research endeavors.
Author : Luise-Charlotte Kappe
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 39,27 MB
Release : 2008
Category : Computers
ISBN : 0821843656
"The power of general purpose computational algebra systems running on personal computers has increased rapidly in recent years. For mathematicians doing research in group theory, this means a growing set of sophisticated computational tools are now available for their use in developing new theoretical results." "This volume consists of contributions by researchers invited to the AMS Special Session on Computational Group Theory held in March 2007. The main focus of the session was on the application of Computational Group Theory (CGT) to a wide range of theoretical aspects of group theory. The articles in this volume provide a variety of examples of how these computer systems helped to solve interesting theoretical problems within the discipline, such as constructions of finite simple groups, classification of $p$-groups via coclass, representation theory and constructions involving free nilpotent groups. The volume also includes an article by R. F. Morse highlighting applications of CGT in group theory and two survey articles." "Graduate students and researchers interested in various aspects of group theory will find many examples of Computational Group Theory helping research and will recognize it as yet another tool at their disposal."--BOOK JACKET.
Author : Klaus Lux
Publisher : Cambridge University Press
Page : 471 pages
File Size : 34,12 MB
Release : 2010-07-01
Category : Mathematics
ISBN : 1139489186
The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from www.gap-system.org and readers can download source code and solutions to selected exercises from the book's web page.
Author : Robert Fitzgerald Morse
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 27,20 MB
Release : 2010
Category : Computational complexity
ISBN : 0821858378
Author : Luise-Charlotte Kappe
Publisher :
Page : 200 pages
File Size : 21,25 MB
Release : 2010
Category :
ISBN : 9780821848050
Author : Charles M. Quinn
Publisher : Elsevier
Page : 198 pages
File Size : 28,4 MB
Release : 2010-07-26
Category : Science
ISBN : 0080455204
Modern Computational Quantum Chemistry is indispensable for research in the chemical sciences. Computational Quantum Chemistry II - The Group Theory Calculator describes the group theory that the authors have developed in the past twenty-five years and illustrates how this approach, known as the 'Spherical Shell' method, can be applied to solve a variety of problems that benefit from a group theory analysis. To complement the theory, the book is supplied with a CD-ROM (Windows TM application), on which interactive files, based on EXCEL spreadsheet technology controlled by Visual Basic code, can be used to perform straightforwardly group-theory analyses for direct application to the simplification of physical problems in Chemistry, Physics and even Engineering Science.The Group Theory Calculator Web page is located at http://www.chemistry.nuim.ie/gt_calculator.htm. The primary purpose of this Web page is to identify and resolve any problems encountered while using the MS EXCEL files on the CD-ROM (included with the book). The Web page is maintained by Charles M. Quinn and allows readers to gain updates and news relating to this publication.* A comprehensive description of the authors' revolutionary group theory and structural chemistry methodology* A unique reference/ teaching work together with a CD-ROM filled with powerful interactive files that can be applied to solve group theory problems* Valuable companion for instructors, designers and students* Contains powerful calculators that are simple to use and do not require detailed knowledge for their application
Author : Matt Clay
Publisher : Princeton University Press
Page : 456 pages
File Size : 25,20 MB
Release : 2017-07-11
Category : Mathematics
ISBN : 1400885396
Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.
Author : Sean Cleary
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 26,59 MB
Release : 2002
Category : Mathematics
ISBN : 0821828223
This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 41,23 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461243726
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.
