The Classification of the Finite Simple Groups, Number 3 PDF Download
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Author: Daniel Gorenstein
Publisher: American Mathematical Soc.
ISBN: 9780821803912
Category : Finite simple groups
Languages : en
Pages : 446
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Book Description
Examines the internal structure of the finite simple groups of Lie type, the finite alternating groups, and 26 sporadic finite simple groups, as well as their analogues. Emphasis is on the structure of local subgroups and their relationships with one another, rather than development of an abstract theory of simple groups. A foundation is laid for the development of specific properties of K-groups to be used in the inductive proof of the classification theorem. Highlights include statements and proofs of the Breol-Tits and Curtis-Tits theorems, and material on centralizers of semisimple involutions in groups of Lie type. For graduate students and research mathematicians. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Daniel Gorenstein
Publisher: American Mathematical Soc.
ISBN: 9780821803912
Category : Finite simple groups
Languages : en
Pages : 446
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Book Description
Examines the internal structure of the finite simple groups of Lie type, the finite alternating groups, and 26 sporadic finite simple groups, as well as their analogues. Emphasis is on the structure of local subgroups and their relationships with one another, rather than development of an abstract theory of simple groups. A foundation is laid for the development of specific properties of K-groups to be used in the inductive proof of the classification theorem. Highlights include statements and proofs of the Breol-Tits and Curtis-Tits theorems, and material on centralizers of semisimple involutions in groups of Lie type. For graduate students and research mathematicians. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Jean Gallier
Publisher: Springer Science & Business Media
ISBN: 3642343643
Category : Mathematics
Languages : en
Pages : 184
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Book Description
This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.
Author: Geoffrey C. Bowker
Publisher: MIT Press
ISBN: 0262522950
Category : Science
Languages : en
Pages : 390
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Book Description
A revealing and surprising look at how classification systems can shape both worldviews and social interactions. What do a seventeenth-century mortality table (whose causes of death include "fainted in a bath," "frighted," and "itch"); the identification of South Africans during apartheid as European, Asian, colored, or black; and the separation of machine- from hand-washables have in common? All are examples of classification—the scaffolding of information infrastructures. In Sorting Things Out, Geoffrey C. Bowker and Susan Leigh Star explore the role of categories and standards in shaping the modern world. In a clear and lively style, they investigate a variety of classification systems, including the International Classification of Diseases, the Nursing Interventions Classification, race classification under apartheid in South Africa, and the classification of viruses and of tuberculosis. The authors emphasize the role of invisibility in the process by which classification orders human interaction. They examine how categories are made and kept invisible, and how people can change this invisibility when necessary. They also explore systems of classification as part of the built information environment. Much as an urban historian would review highway permits and zoning decisions to tell a city's story, the authors review archives of classification design to understand how decisions have been made. Sorting Things Out has a moral agenda, for each standard and category valorizes some point of view and silences another. Standards and classifications produce advantage or suffering. Jobs are made and lost; some regions benefit at the expense of others. How these choices are made and how we think about that process are at the moral and political core of this work. The book is an important empirical source for understanding the building of information infrastructures.
Author: Shmuel Weinberger
Publisher: University of Chicago Press
ISBN: 9780226885674
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
Author: Konstantinos V. Katsikopoulos
Publisher: MIT Press
ISBN: 0262361957
Category : Language Arts & Disciplines
Languages : en
Pages : 208
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Book Description
Rules for building formal models that use fast-and-frugal heuristics, extending the psychological study of classification to the real world of uncertainty. This book focuses on classification--allocating objects into categories--"in the wild," in real-world situations and far from the certainty of the lab. In the wild, unlike in typical psychological experiments, the future is not knowable and uncertainty cannot be meaningfully reduced to probability. Connecting the science of heuristics with machine learning, the book shows how to create formal models using classification rules that are simple, fast, and transparent and that can be as accurate as mathematically sophisticated algorithms developed for machine learning.
Author: Inna Capdeboscq
Publisher: American Mathematical Society
ISBN: 1470464373
Category : Mathematics
Languages : en
Pages : 520
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Book Description
This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of $p$-type for a suitable odd prime $p$. It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
ISBN: 082183410X
Category : Mathematics
Languages : en
Pages : 496
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Book Description
The first of two volumes, this text offers results that are used in the proof of the main theoremthat lies behind quasithin groups, an class of finite simple groups. Some results are gathered from existing mathematical literature, but many are proven for the first time.
Author: J. Wilkins
Publisher: Springer
ISBN: 1137318120
Category : Science
Languages : en
Pages : 329
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Book Description
Discussing the generally ignored issue of the classification of natural objects in the philosophy of science, this book focuses on knowledge and social relations, and offers a way to understand classification as a necessary aspect of doing science.
Author: Ciro Ciliberto
Publisher:
ISBN: 9783037192108
Category :
Languages : en
Pages :
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Book Description
Author: Vanda Broughton
Publisher: Facet Publishing
ISBN: 1783300310
Category : Language Arts & Disciplines
Languages : en
Pages : 433
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Book Description
Classification is a crucial skill for all information workers involved in organizing collections. This new edition offers fully revised and updated guidance on how to go about classifying a document from scratch. Essential Classification leads the novice classifier step by step through the basics of subject cataloguing, with an emphasis on practical document analysis and classification. It deals with fundamental questions of the purpose of classification in different situations, and the needs and expectations of end users. The reader is introduced to the ways in which document content can be assessed, and how this can best be expressed for translation into the language of specific indexing and classification systems. Fully updated to reflect changes to the major general schemes (Library of Congress, LCSH, Dewey and UDC) since the first edition, and with new chapters on working with informal classification, from folksonomies to tagging and social media, this new edition will set cataloguers on the right path. Key areas covered are: - The need for classification - The variety of classification - The structure of classification - Working with informal classification - Management aspects of classification - Classification in digital space. This guide is essential reading for library school students, novice cataloguers and all information workers who need to classify but have not formally been taught how. It also offers practical guidance to computer scientists, internet and intranet managers, and all others concerned with the design and maintenance of subject tools.
