Stable Groups
Author: Frank Olaf Wagner
Publisher: Cambridge University Press
Published: 1997-08-21
Total Pages: 326
ISBN-13: 9780521598392
DOWNLOAD EBOOKIn this book the general theory of stable groups is developed from the beginning.
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Stable Groups
Author: Bruno Poizat
Publisher: American Mathematical Soc.
Published: 2001
Total Pages: 145
ISBN-13: 0821826859
DOWNLOAD EBOOKThis is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the model-theoretic study of groups, i.e., into what can be said about groups, and for that matter, about all the traditional algebraic objects. The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then, whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described. The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic.
Complex Cobordism and Stable Homotopy Groups of Spheres
Author: Douglas C. Ravenel
Publisher: American Mathematical Soc.
Published: 2003-11-25
Total Pages: 418
ISBN-13: 082182967X
DOWNLOAD EBOOKSince the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.
Groups and Model Theory
Author: Olga Kharlampovich
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2021-05-10
Total Pages: 250
ISBN-13: 3110719762
DOWNLOAD EBOOKThis monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .
Essential Stability Theory
Author: Steven Buechler
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 368
ISBN-13: 1107168392
DOWNLOAD EBOOKSince their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Stability theory was introduced and matured in the 1960s and 1970s. Today stability theory influences and is influenced by number theory, algebraic group theory, Riemann surfaces, and representation theory of modules. There is little model theory today that does not involve the methods of stability theory. In this volume, the fourth publication in the Perspectives in Logic series, Steven Buechler bridges the gap between a first-year graduate logic course and research papers in stability theory. The book prepares the student for research in any of today's branches of stability theory, and gives an introduction to classification theory with an exposition of Morley's Categoricity Theorem.
Finite Groups
Author: Daniel Gorenstein
Publisher: American Mathematical Soc.
Published: 2007
Total Pages: 546
ISBN-13: 0821843427
DOWNLOAD EBOOK"The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups. The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem. This book would be a valuable companion text for a graduate group theory course."--Publisher's website
Group Privacy
Author: Linnet Taylor
Publisher: Springer
Published: 2016-12-28
Total Pages: 249
ISBN-13: 3319466089
DOWNLOAD EBOOKThe goal of the book is to present the latest research on the new challenges of data technologies. It will offer an overview of the social, ethical and legal problems posed by group profiling, big data and predictive analysis and of the different approaches and methods that can be used to address them. In doing so, it will help the reader to gain a better grasp of the ethical and legal conundrums posed by group profiling. The volume first maps the current and emerging uses of new data technologies and clarifies the promises and dangers of group profiling in real life situations. It then balances this with an analysis of how far the current legal paradigm grants group rights to privacy and data protection, and discusses possible routes to addressing these problems. Finally, an afterword gathers the conclusions reached by the different authors and discuss future perspectives on regulating new data technologies.
Effective Group Work in Primary School Classrooms
Author: Peter Kutnick
Publisher: Springer Science & Business Media
Published: 2013-06-22
Total Pages: 224
ISBN-13: 9400769911
DOWNLOAD EBOOKThis book offers a challenge to traditional approaches to classroom teaching and pedagogy. The SPRinG (Social Pedagogic Research into Groupwork) project, part of a larger research programme on teaching and learning funded by the Economic and Social Research Council (ESRC), was developed to enhance the learning potential of pupils working in classroom groups by actively involving teachers in a programme designed to raise levels of group work during typical classroom learning activities. Internationally, the SPRinG project is the largest evaluation of effective group working methods in comparison to traditional teaching, with findings that show raised levels of pupil achievement and a doubling of sustained, active engagement in learning. The opening chapters present arguments regarding the relationship of social interaction and children’s cognitive development and examine theories that explain why social interactional processes should be integrated into primary school pedagogic practices. Next, the book describes the conceptual and methodological basis for the SPRinG studies, especially its focus on the relational approach, the type of involvement of teachers and classroom planning. Further chapters present key results and describe the background and methods used to establish SPRinG-based effects on pupil progress in mathematics, literacy and science, including both macro and micro assessments; how the SPRinG approach affected pupil-pupil interactions and teacher-pupil interactions, as measured by systematic on-the-spot observations and analyses of videotapes of groups working on specially designed tasks work; and effects on pupil self-completed measures of motivation and attitudes to group work. The book also analyses reflections of teachers who have worked with SPRinG: moving from theory to practice as well as adding insights associated with implementing SPRinG principles in schools. Drawing upon developmental psychological, social psychological and classroom research, it develops a new and ambitious social pedagogic approach to classroom learning, with a stress on group work, which will be of interest to researchers, teachers and policy-makers. This book includes contributions from Andrew Tolmie and Ed Baines, who were also involved in the ScotSPRinG and SPRinG projects.
A Guide to Classical and Modern Model Theory
Author: Annalisa Marcja
Publisher: Springer Science & Business Media
Published: 2012-09-10
Total Pages: 377
ISBN-13: 9400708122
DOWNLOAD EBOOKThis volume is easily accessible to young people and mathematicians unfamiliar with logic. It gives a terse historical picture of Model Theory and introduces the latest developments in the area. It further provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The book is for trainees and professional model theorists, and mathematicians working in Algebra and Geometry.
Algebra
Author: Yu. L. Ershov
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2017-03-06
Total Pages: 320
ISBN-13: 3110813416
DOWNLOAD EBOOKThe series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
