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This volume contains the expanded versions of the lectures given by the authors at the C. I. M. E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians. ... Read more

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This volume investigates interface interpretation within Phase Theory, the current stage of syntactic theorizing within the ´;Minimalist Program´, the generative research enterprise instigated by Noam Chomsky over 15 years ago. The collection brings together scholars who address architectural, conceptual, and interpretive issues in the grammar. In their investigations of the interpretive interfaces, Logical Form and Phonetic Form, the chapters provide novel analyses for both new and well-known facts, address theoretical issues for Phase Theory, and contribute insights from phonology and semantics. ... Read more

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What causes crime? This seemingly simple question is dauntingly complex and has yielded answers so diverse and numerous as to fill two volumes of the Encyclopedia of Criminological Theory. In discussing a criminology topic, lecturers and course textbooks often toss out names of theorists or make a sideways reference to a particular theory and move on, as if assuming their student audience possesses the necessary background to appreciate and integrate the reference. However, university reference librarians can tell you this is often far from the case. Students often approach them seeking a source to provide a quick overview of a particular theory or theorist with just the basics-the “who, what, where, how, and why,” if you will. And reference librarians often find it difficult to guide these students to a quick, one-stop source. It is the goal of this encyclopedia, available in both print and electronic formats, to provide that resource.

This work is designed to serve as a reference source for anyone interested in the roots of contemporary criminological theory. Drawing together a team of international scholars, it examines the global landscape of all the key theories and the theorists behind them, presenting them in the context needed to understand their strengths and weaknesses. In addition to interpretations of long-established theories, it also offers essays on cutting-edge research as one might find in a handbook. And, like an unabridged dictionary, it provides concise, to-the-point definitions of key concepts, ideas, schools, and figures. Coverage will include contexts and concepts in criminological theory, the social construction of crime, policy implications of theory, diversity and intercultural contexts, conflict theory, rational choice theories, conservative criminology, feminist theory, and more. ... Read more

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Part I. Introduction: Elementary matrices Stability $K_1(A[t])$ and unipotents Grothendieck and Whitehead groups of categories with exact sequences A Grothendieck style definition of $K_1(A)$ Homology, mapping cones, and Euler characteristics Resolution theorems Projective resolutions and regular rings Hilbert's syzygy theorem Appendix 1 Part II. Localisation, divissage and applications: The localisation sequence Categories of nilpotent endomorphisms $K_1(A[t,t^-1])$ Devissage Some calculations with the localisation sequence and $K_1$-Laurent theorem Computations with the Mayer-Vietoris sequence References ... Read more

Customer Reviews (1)

Short but adequate
Written for those who are not familiar to the subject, the author gives a brief but fairly effective overview of the subject of algebraic K-theory. Once thought to be of interest only to pure mathematicians, K-theory has now found applications to high energy physics and cryptography. Higher algebraic K-theory is not covered, the author realizing that very advanced technical machinery is needed for such material. The notes could be used though as an introduction to higher K-theory and Quillen's construction of K-groups for categories with exact sequences.

The author begins the lectures with stating the main goal of the book, namely for proving that for the polynomial ring A in N variables over the integers or integers modulo p, the general linear group of n by n matrices GL(n,A) over this ring is finitely generated for n greater than or equal to N + 3. To meet this goal he reviews the properties of elementary matrices in lecture 1. For a ring A, by considering the elementary subgroups E(n,A) of GL(n,A), these subgroups consisting of matrices satisfying certain relations, the author shows that for a surjective ring homomorphism between rings A and A', the homomorphism from E(n,A) to E(n,A') is surjective, even though it is not for GL(n,A) to GL(n,A'). E(n,A) is shown to be stable under transposition and shown to be commutator subgroup of GL(n,A) for large n. This is the origin of the stability issues in K-theory, and these are discussed in lecture 2. The author shows just why it is advantageous to consider taking the union GL(A) of GL(n,A) (and E(n,A)) for all n and why stability is important in the proof of the above result.

The "Whitehead group" K(1,A) is defined as GL(A)/E(A), and its use in the proof of the theorem results from the map GL(n,A)/E(n,A) to K(1,A) being a bijection for large n and that K(1,A) is finitely generated. Following this matrix characterization of K(1,A), the author reduces the proof of the theorem to showing that for a "regular" ring A, every unipotent element in GL(A) represents 0 in K(1,A), and that the rings in the theorem are indeed regular. Noting the analogy between determinants of matrices and determinants of endomorphisms of vector spaces, the author begins the proof of these assertions with a different description of K(1,A). This description involves the consideration of Grothendieck and Whitehead groups of categories with exact sequences.

The Whitehead group is now defined as the quotient of the Grothendieck group, the latter being the abelian group whose generators are essentially isomorphism classes of objects from an admissible Abelian category. The Whitehead group K(1,A) for a ring A is then related to the Whitehead group K(1,M) for an admissible category M. This definition is due to Grothendieck and involves showing that their is an isomorphism between K(1,A) and K(1, P(A)) where P(A) is the category of finitely generated projective A-modules. P(A) is not abelian, and therefore must be enlarged, without changing K(1,A), to one that is. The author shows that P(A) must be abelian in order to kill unipotents K(1,A). The enlarged P(A) is abelian as long as A is regular, the latter meaning that A is right Noetherian and that any finitely generated A-module has finite homological dimension. As the name implies, homological dimensions involves some discussion of homology theory, and is defined to the least n for which there is a projective resolution of the A-module of length n. The proof of the above theorem then follows, as the author shows, from Hilbert's syzygy theorem. ... Read more

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Most large firms are controlled by shareholders, who choose the board of directors and can replace the firms management.In rare instances, however, control over the firm rests with the workforce.Many explanations for the rarity of workers' control have been offered, but there have been few attempts to assess these hypotheses in a systematic way. This book draws upon economic theory, statistical evidence, and case studies to frame an explanation.The fundamental idea is that labor is inalienable, while capital can be freely transferred from one person to another.This implies that worker controlled firms typically face financing problems, encounter collective choice dilemmas, and have difficulty creating markets for control positions within the firm.Together these factors can account for much of what is known about the incidence, behavior, and design of worker- controlled firms.A policy proposal to encourage employee buyouts is developed in the concluding chapter.Gregory L. Dow is Professor and Chair of the Department of Economics at Simon Fraser University, British Columbia, Canada.He previously taught at the University of Alberta and Yale University, and has served as a visiting professor at the University of New South Wales, the Erasmus Institute for Philosophy and Economics, and the Swedish Collegium for Advanced Studies in the Social Sciences.Professor Dow is Associate Editor on the Journal of Economic Behavior and Organization and has published numerous articles on labor-managed firms and other topics in economic theory in leading journals such as the American Economic Review and the Journal of Political Economy. ... Read more

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A serious approach to employee control
Dow makes a thorough survey of the literature and establishes a solid theoretical framework for workers' control.In the end of the book after nearly 200 pages, he finally presents a formula for transferring control (and ownership) away from capital suppliers and to labor suppliers.It is a thoughtful book though perhaps existing more in the realm of theory than actual practice.The case for capital controlling the firm while not theoretically exclusive, remains empiracally dominant and I don't think he provides a strong enough argument why worker control is better.

In any case, a very thoughtful book with some insightful ideas, highly recommended! ... Read more

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This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for self-dual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated Seiberg-Witten invariants. The results described in this volume form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution. ... Read more

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Theory for Performance Studies: A Student's Guide is a clear and concise handbook to the key connections between performance studies and critical theory since the 1960s. Philip Auslander looks at the way the concept of performance has been engaged across a number of disciplines.

Beginning with four foundational figures – Freud, Marz, Nietzsche and Saussure – Auslander goes on to provide guided introductions to the major theoretical thinkers of the past century, from Althusser to Zizek. Each entry offers biographical, theoretical, and bibliographical information along with a discussion of each figure's relevance to theatre and performance studies and suggestions for future research.

Brisk, thoughtful, and engaging, this is an essential first volume for anyone at work in theatre and performance studies today.

Adapted from Theory for Religious Studies, by William E. Deal and Timothy K. Beal.

Customer Reviews (1)

2 Authors Say Routledge Recycled Their Work Without Credit
See the article in the Chronicle of Higher Education (Tuesday August 5, 2008) by Thomas Bartlett. http://chronicle.com/temp/email2.php?id=rxm56spWpttNRpgcmcfRbRVfcp6Rh6dx

"When William E. Deal casually flipped through Theory for Performance Studies: A Student's Guide, published this year by Routledge, he noticed a few familiar sentences. After taking a closer look, Mr. Deal, a professor of religious studies at Case Western Reserve University, discovered whole paragraphs and even entire pages that had been lifted directly from a book he co-wrote, Theory for Religious Studies, published by Routledge in 2004.

"My jaw dropped," he recalls. "My stomach turned flip-flops."

Mr. Deal and his co-author, Timothy K. Beal, a professor of religion at Case Western, estimated that roughly 80 percent of their book had been copied, word for word, without credit of any kind. Their names did not appear in the new book." ... Read more

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An analysis of criminal behavior from the perspectives of rational choice theory leading to suggestions for a criminal policy.

Previous edition sold 900 copies world wide since its release in June 2001.

Customer Reviews (2)

Towards a More Cooperative Society
I highly recommend this book and ask you to help me bring it to the attention of our law makers and legal authorities. This is an important book for our times, in my humble opinion, about the ironic reality that some of our laws create rational motives to commit crime in spite of any well meaning intention to the contrary. In essence, Sieberg contributes to the development of a field of social research which shows the way towards a more cooperative society, which is exactly what one Princeton University philosopher, Peter Singer, recently called for in his book, _A Darwinian Left: Politics, Evolution, and Cooperation_ (see pg. 47).

Sieberg is full of surprises. She ignores the emotional and moral aspects of a few select current issues, and goes straight to the rational self interested calculations of the hypothetical individual who is considering whether to be content to earn the going legal wage (perhaps slave wages), or to commit a potentially much more profitable crime. That list of current issues includes mandatory prison sentencing, the three strikes and you're out laws, the privatization of prisons, prostitution, drugs, gangs, and gun control. On the basis of this analysis she makes a few suggestions as to what may be better and more rational legal policy; for example, regarding prison sentencing and alternative means of punishing criminals, she concludes with the following:

"This analysis indicates that a hybrid policy of imprisoning violent criminals and imposing alternative sentences on nonviolent criminals would be superior in terms of fulfilling society's goals. The maintenance of the prisons for violent offenders would provide protection of the public, both by incapacitation of those who are violent and by deterring others from the use of violence. Alternative sentencing [such as community service and repaying the victim with the earnings] could yield an improvement over the current system in terms of retribution, rehabilitation, and deterrence - but only if done seriously and carefully. Importantly, this more positive form of sentencing [as opposed to imprisonment], involving some form of repayment, reduces the individual and social cost of crime."
--page 33.

This book appears to be an expansion of work the author began as a student of Donald Saari, who is currently perhaps the world's leading mathematician in the field of social choice theory. My personal interest in this book stems from reading Saari's latest book, _Decisions and Elections_ (Cambridge University Press, 2001), where he briefly describes the nature of some of Sieberg's results, and explains how those results are related to the unintended loss of crucial but available information or action, and how that screws up decision making processes and public policies.

Using the tools of theoretical economics and decision theory with some basic algebra and calculus, Sieberg helps us look at the decision making process of those who consider whether to commit this crime or that, or no crime at all. We see the world through the eyes of the rational criminal, or potential criminal, and are surprised to see how some laws actually create incentives for increased crime. Beginning with the famous "Prisoner's Dilemma," an important abstract model of decision making, Sieberg formalizes the rational strategic thinking of criminals and potential criminals, and shows how they may calculate the probable costs and benefits of their various legal and illegal options.

Consider the case of marijuana sales or prostitution, where Sieberg notes that both the buyer and seller are committing a crime. What happens if one of them is ripped off by the other? They don't have legal recourse, of course, given that they prefer to avoid imprisonment, public humiliation or a fine. Sieberg shows how this sort of situation arises throughout the underground economic world, and this creates a force which tends to create and grow criminal gangs, pimps, etc., to which they may turn for justice.It is widely recognized that the mafia in the US is largely a child of the underground economy which was created by the prohibition of alcohol. We were soon forced to recognize our mistake in that case, but we apparently haven't fully learned our lesson yet. According to Sieberg's analysis, the current prohibition of drugs and prostitution fosters a similar crime laden underground economy.

There is room for criticism, of course. The author takes issue after issue, and argues that a consequence of prohibiting that product or activity will likely be to foster a black market. This may be true, it seems to me, but aren't there cases where there is no better alternative to prohibiting it? How about the case of human slavery, or the sale of the flesh of chimpanzees and other nonhuman great apes in gourmet restaurants? What is the difference between slavery and alcohol, which makes one (apparently) immune to the black market argument, but not the other? Isn't there a similar argument that the prohibition of slavery or chimpanzee dinners creates a black market incentive? I suppose that the difference is that there are some extenuating circumstances that need to taken into account, whatever they may be, which clearly tip the scale in favor of the prohibition of slavery or chimpanzee steaks, but not alcohol. I suspect that the relevant differences lie in the "victimless crime nature of prostitution, drugs and alcohol, on the one hand, and in the overridingly strong interest of vulnerable individuals, on the other hand, against being legally categorized and treated as mere property. That is, I suppose the essential difference is in the relative strength of the interests of the victim and the offender, which relates back to Saari's book and his analysis of (1998 Nobel Laureate) Amartya Sen's important theorem that individual and societal rights are incompatible.

Towards a More Cooperative Society
I highly recommend this book and ask you to help me bring it to the attention of our law makers and legal authorities. This is an important book for our times, in my humble opinion. It is about the ironic reality that some of our laws create rational motives to commit crime, in spite of any well meaning intention to reduce crime. In essence, Sieberg contributes to the development of a field of social research which shows the way towards a more cooperative society, which is exactly what one Princeton University philosopher, Peter Singer, recently called for in his book, _A Darwinian Left: Politics, Evolution, and Cooperation_ (see pg. 47).

Sieberg is full of surprises. She ignores the emotional and moral aspects of a few select c urrent issues, and goes straight to the rational self interested calculations of the hypothetical individual who is considering whether to be content to earn the going legal wage (perhaps slave wages), or to commit a potentially much more profitable crime. That list of current issues includes mandatory prison sentencing, the three strikes and you're out laws, the privatization of prisons, prostitution, drugs, gangs, and gun control. On the basis of this analysis she makes a few suggestions as to what may be better and more rational legal policy; for example, regarding prison sentencing and alternative means of punishing criminals, she concludes with the following:

This analysis indicates that a hybrid policy of imprisoning violent criminals and imposing alternative sentences on nonviolent criminals would be superior in terms of fulfilling society's goals. The maintenance of the prisons for violent offenders would provide protection of the public, both by incapacitation of those who are violent and by deterring others from the use of violence. Alternative sentencing such as community service and repaying the victim with the earnings could yield an improvement over the current system in terms of retribution, rehabilitation, and deterrence - but only if done seriously and carefully. Importantly, this more positive form of sentencing [as opposed to imprisonment], involving some form of repayment, reduces the individual and social cost of crime.--page 33.

This book appears to be an expansion of work the author began as a student of Donald Saari, who is currently perhaps the world's leading mathematician in the field of social choice theory. My personal interest in this book stems from reading Saari's latest book, _Decisions and Elections_ (Cambridge University Press, 2001), where he briefly describes the nature of some of Sieberg's results, and explains how those results are related to the unintended loss of crucial but available information or action, and how that screws up decision making processes and public policies - the main theme of Saari's book.

Using the tools of theoretical economics and decision theory, Sieberg helps us look at the decision making process of those who consider whether to commit this crime or that, or no crime at all. We see the world through the eyes of the rational criminal, or potential criminal, and are surprised to see how some laws actually create incentives for increased crime. Beginning with the famous Prisoner's Dilemma, an important abstract model of decision making, Sieberg formalizes the rational strategic thinking of criminals and potential criminals, and shows how they may calculate the probable costs and benefits of their various legal and illegal options.

Consider the case of marijuana sales or prostitution, where both the buyer and seller are committing a crime. What happens if one of them is ripped off by the other? They don't have legal recourse, of course, given that they prefer to avoid imprisonment, public humiliation or a fine. This sort of situation arises throughout the underground economic world, and this creates a force which tends to create and grow criminal gangs, pimps, etc., to which they may turn for justice.It is widely recognized that the mafia in the US is largely a child of the underground economy which was created by the prohibition of alcohol. We were soon forced to recognize our mistake in that case, but we haven't fully learned our lesson yet. The current prohibition of drugs and prostitution fosters a similar crime laden underground economy, but those bad policies remain with us to this day.

There is room for criticism, of course. The author takes issue after issue, and argues that a consequence of prohibiting that product or activity will likely be to foster a black market. This may be true, it seems to me, but aren't there cases where there is no better alternative to prohibiting it? How about the case of human slavery, or the sale of the flesh of chimpanzees and other nonhuman great apes in gourmet restaurants? What is the difference between slavery and alcohol, which makes one (apparently) immune to the black market argument, but not the other? Isn't there a similar argument that the prohibition of slavery or chimpanzee dinners creates a black market incentive? I suppose that the difference is that there are some extenuating circumstances that need to taken into account, whatever they may be, which clearly tip the scale in favor of the prohibition of slavery or chimpanzee steaks, but not alcohol. I suspect that the relevant differences lie in the "victimless crime nature of prostitution, drugs and alcohol, on the one hand, and in the overridingly strong interest of vulnerable individuals, on the other hand, against being legally categorized and treated as mere property. That is, I suppose the essential difference is in the relative strength of the interests of the victim and the offender, which relates back to Saari's book and his analysis of Amartya Sen's Theorem regarding the conflict between individual and societal rights. ... Read more

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The authors's primary objective in this book is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider audience, much of the relevant background material from nonlinear functional analysis and the qualitative theory of differential equations is presented in detail. Two distinct aspects of bifurcation theory are discussed - static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. Dynamic bifurcation theory is concerned with the changes that occur in the structure of the limit sets of solutions of differential equations as parameters in the vector field are varied. This second printing contains extensive corrections and revisions throughout the book. ... Read more

Customer Reviews (1)

Excellent book!!!
This is an excellent and comprehensive book on bifurcation theory for agraduate-level course on this subject. It is also a very useful resourcefor research on nonlinear bifurcations. I strongly recommend this book. ... Read more

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Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy. ... Read more

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This book serves not only as an introduction, but also as an advanced text and reference source in the field of deterministic optimal control systems governed by ordinary differential equations. It also includes an introduction to the classical calculus of variations.

An important feature of the book is the inclusion of a large number of examples, in which the theory is applied to a wide variety of economics problems. The presentation of simple models helps illuminate pertinent qualitative and analytic points, useful when confronted with a more complex reality. These models cover: economic growth in both open and closed economies, exploitation of (non-) renewable resources, pollution control, behaviour of firms, and differential games. A great emphasis on precision pervades the book, setting it apart from the bulk of literature in this area. The rigorous techniques presented should help the reader avoid errors which often recur in the application of control theory within economics.

... Read more

Customer Reviews (1)

Still the best guide ever to Optimal Control for Economists
There are a number of standard textbooks in optimal control theory for economists. This is the textbook for the guys that wrote the other textbooks. Both the Calculus of Variations and Optimal Control Theory is presented in a rigorous manner. The authors are however not wedded to rigour as they often present "rough" arguments when they suspect that presenting the results rigourously would exceed the proficiency one could reasonably expect from their economist readers.

When the book was written it was not only a textbook but also an important piece of research. The reprint, appearing 10 years later, still presents the ideas with remarkable freshness. The discussion of transversality conditions in infinite horizon models should be read by all economists using these models and corrects some other textbooks where the topic has been bungled. The discussion of jump controls is superb. ... Read more

Customer Reviews (2)

Book Nitty-Gritty
A handsome production from the University of Washington Press: large format trade paperback, 298 pp with something like 375 b&w illustrations. 12 p Bibliography. Index and Notation Index.

TABLE OF CONTENTS HIGHLIGHTS
I. History and Theory of Plane Pattern Analysis
- Crystallographic and Mathematical History
- Applications of Geometry to Design
- Symmetry Analysis in Anthropological Perspective

II. Mathematical Principles and Terminologies
- Symmetries of the Plane: the Four Motions
- Designs, Repeated Patterns, and Dimension
- Recapitulation
- Notation for One-Color Designs and Patterns

III. Color Symmetry
IV. One-Dimensional Patterns
V. Two-Dimensional Patterns
VI. Finite Designs
VII. Problems in Classification

Conclusion
Appendices 1-3

Extensive scholarship!
Washburn is a mathematician and Crowe is an antrophologist. The book gives a very good description of both the mathematical ideas and the context around the art. The illustrations are great! As examples of the quality of the book, it gives the best description I've seen anywhere of the difference between p31m and p3m1 and a very interestig history of the study of patterns.

Only one minor complaint: On page 5 they mention that in 1987, all the 17 groups were finally found at Alhambra, but they do not give a reference. The place to go is J.M. Montesinos: Classical Tessellations and Three-Manifolds. ... Read more

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The book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. To make the book self-contained, the authors have included necessary geometric material (C*-algebras and their K-theory, cyclic homology, etc.).

Product Description
This book deals with algebraic topology, homotopy theory andsimple homotopy theory of infinite CW-complexes with ends. Contrary to most other works on these subjects, the current volumedoes not use inverse systems to treat these topics. Here, the homotopytheory is approached without the rather sophisticated notion ofpro-category. Spaces with ends are studied only by using appropriateconstructions such as spherical objects of CW-complexes in thecategory of spaces with ends, and all arguments refer directly to thiscategory. In this way, infinite homotopy theory is presented as anatural extension of classical homotopy theory. In particular, thisbook introduces the construction of the proper groupoid of a spacewith ends and then the cohomology with local coefficients is definedby the enveloping ringoid of the proper fundamental groupoid. This volume will be of interest to researchers whose work involvesalgebraic topology, category theory, homological algebra, generaltopology, manifolds, and cell complexes. ... Read more

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Algebraic K-theory is a modern branch of algebra whichhas many important applications in fundamental areas of mathematicsconnected with algebra, topology, algebraic geometry, functionalanalysis and algebraic number theory. Methods of algebraicK-theory are actively used in algebra and related fields,achieving interesting results.
This book presents the elements of algebraic K-theory, basedessentially on the fundamental works of Milnor, Swan, Bass, Quillen,Karoubi, Gersten, Loday and Waldhausen. It includes all principalalgebraic K-theories, connections with topologicalK-theory and cyclic homology, applications to the theory ofmonoid and polynomial algebras and in the theory of normed algebras.
This volume will be of interest to graduate students and researchmathematicians who want to learn more about K-theory.
... Read more

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These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences. ... Read more

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The book gives a comprehensive account of the basic algebraic properties of the classical groups over rings. Much of the theory appears in book form for the first time, and most proofs are given in detail. The book also includes a revised and expanded version of Dieudonné's classical theory over division rings. The authors analyse congruence subgroups, normal subgroups and quotient groups, they describe their isomorphisms and investigate connections with linear and hermitian K-theory. A first insight is offered through the simplest case of the general linear group. All the other classical groups, notably the symplectic, unitary and orthogonal groups, are dealt with uniformly as isometry groups of generalized quadratic modules. New results on the unitary Steinberg groups, the associated K2-groups and the unitary symbols in these groups lead to simplified presentation theorems for the classical groups. Related material such as the K-theory exact sequences of Bass and Sharpe and the Merkurjev-Suslin theorem is outlined. From the foreword by J. Dieudonné: "All mathematicians interested in classical groups should be grateful to these two outstanding investigators for having brought together old and new results (many of them their own) into a superbly organized whole. I am confident that their book will remain for a long time the standard reference in the theory." ... Read more

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This volume of research papers is an outgrowth of the Manin Seminar at Moscow University, devoted to K-theory, homological algebra and algebraic geometry. The main topics discussed include additive K-theory, cyclic cohomology, mixed Hodge structures, theory of Virasoro and Neveu-Schwarz algebras. ... Read more