Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.
The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.
A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.
Let p p be a prime and S S a finite p p-group. A p p-fusion system on S S is a category whose objects are the subgroups of S and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory. The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
In around 1980, G. Mason announced the classification of a subclass of an important class of finite simple groups known as 'quasithin groups'. In the main theorem of this two-part work the authors provide a proof of a stronger theorem classifying a larger class of groups independently of Mason's research.
A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathematics, including graph theory, number theory and topology. Various generalisations have been studied in more recent years, with a particular focus on the existence of derangements with special properties. Written for academic researchers and postgraduate students working in related areas of algebra, this introduction to the finite classical groups features a comprehensive account of the conjugacy and geometry of elements of prime order. The development is tailored towards the study of derangements in finite primitive classical groups; the basic problem is to determine when such a group G contains a derangement of prime order r, for each prime divisor r of the degree of G. This involves a detailed analysis of the conjugacy classes and subgroup structure of the finite classical groups.
How the internet and powerful online tools are democratizing and accelerating scientific discovery Reinventing Discovery argues that we are living at the dawn of the most dramatic change in science in more than three hundred years. This change is being driven by powerful cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business, the workplace, or government. But this is the first book about something much more fundamental: how the internet is transforming our collective intelligence and our understanding of the world. From the collaborative mathematicians of the Polymath Project to the amateur astronomers of Galaxy Zoo, Reinventing Discovery tells the exciting story of the unprecedented new era in networked science. It will interest anyone who wants to learn about how the online world is revolutionizing scientific discovery—and why the revolution is just beginning.
The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.
Combinatorial Designs for Authentication and Secrecy Codes is a succinct in-depth review and tutorial of a subject that promises to lead to major advances in computer and communication security. This monograph provides a tutorial on combinatorial designs, which gives an overview of the theory. Furthermore, the application of combinatorial designs to authentication and secrecy codes is described in depth. This close relationship of designs with cryptography and information security was first revealed in Shannon's seminal paper on secrecy systems. We bring together in one source foundational and current contributions concerning design-theoretic constructions and characterizations of authentication and secrecy codes.
Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.
In Volume III, as in Volumes I and II, the classic topics of reading are included--from vocabulary and comprehension to reading instruction in the classroom--and, in addition, each contributor was asked to include a brief history that chronicles the legacies within each of the volume's many topics. However, on the whole, Volume III is not about tradition. Rather, it explores the verges of reading research between the time Volume II was published in 1991 and the research conducted after this date. The editors identified two broad themes as representing the myriad of verges that have emerged since Volumes I and II were published: (1) broadening the definition of reading, and (2) broadening the reading research program. The particulars of these new themes and topics are addressed.
A collection of the total range of scholarly and popular writing on English as spoken from Maryland to Texas and from Kentucky to Florida The only book-length bibliography on the speech of the American South, this volume focuses on the pronunciation, vocabulary, grammar, naming practices, word play, and other aspects of language that have interested researchers and writers for two centuries. Compiled here are the works of linguists, historians, anthropologists, sociologists, and educators, as well as popular commentators. With over 3,800 entries, this invaluable resource is a testament to the significance of Southern speech, long recognized as a distinguishing feature of the South, and the abiding interest of Southerners in their speech as a mark of their identity. The entries encompass Southern dialects in all their distinctive varieties—from Appalachian to African American, and sea islander to urbanite.
This book proposes and explores the idea that the forced union of the aleatory and epistemic aspects of probability is a sterile hybrid, inspired and nourished for 300 years by a false hope of formalizing inductive reasoning, making uncertainty the object of precise calculation. Because this is not really a possible goal, statistical inference is not, cannot be, doing for us today what we imagine it is doing for us. It is for these reasons that statistical inference can be characterized as a myth. The book is aimed primarily at social scientists, for whom statistics and statistical inference are a common concern and frustration. Because the historical development given here is not merely anecdotal, but makes clear the guiding ideas and ambitions that motivated the formulation of particular methods, this book offers an understanding of statistical inference which has not hitherto been available. It will also serve as a supplement to the standard statistics texts. Finally, general readers will find here an interesting study with implications far beyond statistics. The development of statistical inference, to its present position of prominence in the social sciences, epitomizes a number of trends in Western intellectual history of the last three centuries, and the 11th chapter, considering the function of statistical inference in light of our needs for structure, rules, authority, and consensus in general, develops some provocative parallels, especially between epistemology and politics.
Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.
Many middle school teachers across the United States use student science notebooks as part of their daily classroom instruction. Many others would like to but are not sure exactly how to start. Following his bestselling Using Science Notebooks in Elementary Classrooms, Michael Klentschy now examines how the student science notebook can be an invaluable tool at the middle school level. --
The characterization of combinatorial or geometric structures in terms of their groups of automorphisms has attracted considerable interest in the last decades and is now commonly viewed as a natural generalization of Felix Klein’s Erlangen program(1872).Inaddition,especiallyfor?nitestructures,importantapplications to practical topics such as design theory, coding theory and cryptography have made the ?eld even more attractive. The subject matter of this research monograph is the study and class- cation of ?ag-transitive Steiner designs, that is, combinatorial t-(v,k,1) designs which admit a group of automorphisms acting transitively on incident point-block pairs. As a consequence of the classi?cation of the ?nite simple groups, it has been possible in recent years to characterize Steiner t-designs, mainly for t=2,adm- ting groups of automorphisms with su?ciently strong symmetry properties. For Steiner 2-designs, arguably the most general results have been the classi?cation of all point 2-transitive Steiner 2-designs in 1985 by W. M. Kantor, and the almost complete determination of all ?ag-transitive Steiner 2-designs announced in 1990 byF.Buekenhout,A.Delandtsheer,J.Doyen,P.B.Kleidman,M.W.Liebeck, and J. Saxl. However, despite the classi?cation of the ?nite simple groups, for Steiner t-designs witht> 2 most of the characterizations of these types have remained long-standing challenging problems. Speci?cally, the determination of all ?- transitive Steiner t-designs with 3? t? 6 has been of particular interest and object of research for more than 40 years.
Across the land communities are questioning the role of schools and the community's expectations of parents, students, and teachers. Increasingly, educators struggle to convince administrators, parents, students, and community members that teaching strategies have strengthened and that students are improving. Yet, teachers consistently share their concerns about the lack of parent and community involvement in education. Parents indicate their desire to improve the connections between the classroom and the community, but are unsure how to initiate such relationships. In Authentic Learning, Michael L. Slavkin provides parents and educators the opportunity to understand why best practices, constructivism, student-centered practices, student choice, and democratic classrooms are effective because they result in a variety of environmental experiences. Such experiences have often been thought to be the environmental foundation that supports and nurtures a creative and challenged brain: guiding children to think in a variety of ways, providing the flexibility of thought that is critical in the 21st century world. With this text these two groups will discover ways they can work together to create meaningful learning experiences at home and school. For parents, students, and preservice and inservice teachers.
The ideal school is closer than you think. This high school of your dreams is a dynamic place that promotes aspirations and meaningful learning—and each aspect of its success exists in a school today, drawn from research, observations, focus groups, and interviews. Whether you’re a policymaker or district leader who can build from the ground up or an educator aiming for incremental change, you’ll find your next steps, including: A whole new way to work with all stakeholders Research and action for best practices, from physical layout to curriculum Principles for designing practices that encourage student aspirations Messages from thought leaders inside and outside the field of education
Don’t start from scratch! Learn what works—and what doesn’t—in providing education to off-campus students! This unique compilation presents practical advice on how to set up distance learning programs that effectively serve the needs of students who don’t have access to the campus. The book examines issues surrounding development, implementation, teacher training, time management, and other important aspects of distance education. Distance Education: What Works Well brings you lessons garnered from real-life experiences at several institutions to help you explore the pros and cons of distance education—and what it takes to implement a distance program that really works. In the first half of Distance Education: What Works Well you’ll examine: the development of a digital high school—from the early stages through “rookie camp” experiences practical recommendations on how to design successful online high school programs what has worked well—and what has not—in terms of distance education in the rural K-12 environment the successful and not-so-successful aspects of an innovative distance education project that encourages collaboration between high schools and middle schools The second half of this informative book presents practical advice to help you set up distance learning programs that make the most of available technology. You’ll learn: how to train faculty to effectively use distance education techniques the importance of student-teacher and student-student interaction in a distance education setting—and how to build active online communities that keep students and faculty in touch the roles and functions of moderators in online education—and the skills they need to be effective six effective tactics designed to optimize online time how to decide whether distance education is the right choice for you
This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following: 1. Curves with many rational points. Several articles describe main approaches to the construction of such curves: the Drinfeld modules and fiber product methods, the moduli space approach, and the constructions using classical curves. 2. Monodromy groups of characteristic $p$ covers. A number of authors presented the results and conjectures related to the study of the monodromy groups of curves over finite fields. In particular, they study the monodromy groups from genus 0 covers, reductions of covers, and explicit computation of monodromy groups over finite fields. 3. Zeta functions and trace formulas. To a large extent, papers devoted to this topic reflect the contributions of Professor Bernard Dwork and his students. This conference was the last attended by Professor Dwork before his death, and several papers inspired by his presence include commentaries about the applications of trace formulas and L-function. The volume also contains a detailed introduction paper by Professor Michael Fried, which helps the reader to navigate the material presented in the book.
One of the more frustrating aspects of buying a new digital video camera for consumers is trying to discover not only how it works, but how to shoot good movies with it right away. For most of us, we just want to turn on the camera and go, without spending too much time sorting through dense jargon and video editing software manuals. Here to guide the troubled newcomer to the exciting world of digital video is The Little Digital Video Book, 2e. This friendly, approachable guide will teach users the basics of shooting, organizing, and editing their own footage, with short examples so they can practice the techniques as they read through the book. This revised edition of the bestselling book on digital video is now in full color and completely updated for the modern beginning videographer. Users get a thorough grounding in the basics of digital video, but without all the jargon. Michael Rubin explains in under 200 pages all users need to know to get great shots, add sound, organize the footage, and use basic editing techniques. They will learn how to start and actually finish that video project they had in mind--in less than a day.
Health, Illness, and Optimal Aging: Biological and Psychosocial Perspectives, Third Edition shows the continuity and advancements in our understanding of human life-span development... It offers a solid foundation for exploring the art and science of successful aging.- Robert M. Kaplan, Stanford University
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
In this monograph p-adic period domains are associated to arbitrary reductive groups. Using the concept of rigid-analytic period maps the relation of p-adic period domains to moduli space of p-divisible groups is investigated. In addition, non-archimedean uniformization theorems for general Shimura varieties are established. The exposition includes background material on Grothendieck's "mysterious functor" (Fontaine theory), on moduli problems of p-divisible groups, on rigid analytic spaces, and on the theory of Shimura varieties, as well as an exposition of some aspects of Drinfelds' original construction. In addition, the material is illustrated throughout the book with numerous examples.
Introduces the reader to qualitative approaches--a major development in the field of evaluation during the last decade. This volume presents an introduction to the approach--differentiates it in the method and philosophy from more traditional quantitative methods; specifies the kinds of evaluation questions for which it is most appropriate; and explains the design decisions and sampling strategies which underlie its implementation. Step-by-step guides for planning and conducting fieldwork and observations; doing in-depth interviewing; analyzing, interpreting and reporting results; and many examples--from a wide range of disciplines and professions--clarify the use of qualitative methods in evaluations.
& Best-selling author and Hollywood veteran Michael Rubin teaches home and corporate videomakers video editing. & & Apple's new Final Cut Express offers a hefty portion of a professional video editor's toolkit for a fraction of the price of Final Cut Pro. & & Companion DVD includes all of the files and images readers need to turn raw footage into a polished dramatic scene.
A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.
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