Product Description
Over the past twenty-five years K-theory has become an integrated part of the study of C*-algebras. This book gives a very elementary introduction to this interesting and rapidly growing area of mathematics. The authors cover the basic properties of the functors K and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequence is derived. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject. ... Read more

Customer Reviews (2)

One of the best two introductory titles along with Wegge-Olsen
K-theory is a branch of algebraic topology originally concerned with the study of vector bundles by algebraic means. The first notions of the theory were put forward by Alexander Groethendieck in his work on the Riemann-Roch theorem in algebraic geometry, and early in the 60's it was developed into a branch of algebraic topology by M. Atiyah and F. Hirzebruch. From the analysis perspective, K-theory has a very natural link with the theory of Fredholm operators on a compact manifold and hence to the famous Atiyah-Singer index theorem. In the recent decades the theory has revolutionized the study of the structure theory of certain operator algebras. The procedure involves defining a collection of functors {K_n} from the category of C*-algebras to the category of abelian groups, satisfying the Eilenberg-Steenrod axioms for a homology theory. Bott periodicity as a handy feature then implies that there are only two such functors. In this nice text, the readers will find the needed material on C*-algebras, as well as an exposition of the K_0 and K_1 functors leading to the exploration of the Bott periodicity theorem and the six term exact sequence. As a graduate student a few years ago I attempted giving a seminar talk on this topic but was overwhelmed with the task of fitting the needed discussion into a 60-minute time span, specially in a way that the majority of the attendees could follow on. The exposition is indeed heavily algebraic in nature and hence anyone attempting to read and digest it properly will have to possess a strong background in the ideas and methods of basic algebraic topology.

Nice place to start...
It's a very clear book with virtually no typos/mistakes and lots of nice exercises (if you are willing to do them - highly recommended). Really an introductory text, so you might need to consult the more advanced books of Wegge-Olsen, Blackadar after this one for more information on the subject. Nice place to start, especially if it is for self-study. ... Read more

Product Description

This handbook presents the first compilation of techniques and results across much of the present state of the art in K-theory. Consisting of individual chapters, each an exposition of a particular subfield or line of development related to K-theory, written by an expert, it outlines fundamental ideas and techniques of the past, fundamental open problems, and exciting directions for future research. Much of the material presented here appears for the first time in book form. The intent of each chapter is present to the interested reader, be she an established K-theorist or someone interested in obtaining an overview of results, an exposition of both results and techniques in the literature as well as challenges for the future. The book should be especially useful for students and mathematicians interested in pursuing further research in this rapidly expanding field.

Customer Reviews (1)

Interesting overview of modern developments in K-theory
K-theory is now a highly developed but esoteric subject, and touches many different areas in mathematics, including operator theory and functional analysis, algebraic geometry, and geometric topology. In addition, it has found its way into theoretical physics, thanks to the advent of string theory and its more modern metamorphosis M-theory. Everything about K-theory is fascinating, and this two-volume set gives a general overview of the subject from the standpoint of a collection of researchers who have been involved in its development. It is not written for those who are interested in learning K-theory, since it emphasizes developments lying in the frontier of the subject. Students of K-theory, and non-experts (such as this reviewer) can still gain a lot however from its perusal, due to the clarity exhibited in each article along with the copious references at the end of each. Historians of mathematics who want to trace the history of K-theory will also find the volumes of great interest.

K-theory has been developed in both a topological and algebraic context, with the former being more easily grasped for newcomers. It is in the context of algebraic geometry where research in K-theory has shown the greatest activity. Earlier developments in K-theory emphasized its role in the classification and study of vector bundles, and these developments led many to find suitable formulations for algebraic varieties and general schemes. What is now called `motive theory' involves the study of how well known constructions in algebraic topology can be carried over to algebraic geometry. One article in this handbook that gives a good motivation for this study is the one by Daniel Grayson on the motivic spectral sequence. In the article Grayson discusses different approaches to finding a `motivic' version of the Atiyah-Hirzebruch spectral sequence, the latter of which relates topological K-theory to singular cohomology. The trick is not only to find a suitable spectral sequence but also one that is computable. The author shows various ways in which spectral sequences can be constructed, such as the use of long exact sequences in homotopy theory and by using filtrations of a spectrum (such as the familiar Postnikov tower of a space). These are well known in algebraic topology, but for (nonsingular) varieties or (regular) schemes in algebraic geometry one needs another approach that respects as much as possible the general ideas in algebraic topology. One of the approaches discussed is actually fairly intuitive, since it relates K-theory to chain complexes, the latter of which are constructed from direct-sum Grothendieck groups of commuting automorphisms. This approach reflects the well-known strategy of studying the behavior of groups by relating them to the homotopy of a particular space (the mathematician Daniel Quillen used this idea to arrive at his definition of the higher K-groups). Grayson also discusses another approach to obtaining motivic cohomology by using the higher Chow groups, and the work of the mathematician Vladimir Voevodsky on using (affine) homotopy theory of schemes. Voevodsky's work is also motivated by a familiar idea in algebraic topology, namely that of a simplicial space. Voevodsky replaces the simplices by affine spaces over a field, along with the smooth varieties over this field and the colimits of diagrams between these varieties. The colimits are presheaves on these varieties, which are then made into sheaves in a topology called the Nisnevich topology (which is finer than the Zariski topology but coarser than the etale topology). The affine simplices are contractible, and allow the usual techniques of algebraic topology to be applied. In particular, spectra can be defined, called `motivic spectra', and the algebraic K-theory of these spectra results in the motivic spectrum. The Voevodsky construction of a motivic spectral sequence uses a suitable filtration of this motivic spectrum, called the `slice filtration.' The slice filtration involves taking suspensions of the suspension spectra of smooth varieties. Grayson discusses the viability of this approach via the conjectures that were made by Voevodsky, one of which was proved when the field is assumed to have characteristic zero.

Jonathan Rosenberg writes another interesting article in the handbook on the use of K-theory in geometric topology. One immediately thinks of vector bundles in this context and indeed Rosenberg outlines the role of K-theory in the study of flat vector bundles. The K-theory spectrum of the complex numbers arises here, in that every class in this spectrum arises from some flat vector bundle over a homology n-sphere. Also discussed, and definitely a more contemporary topic, is the Waldhausen A-theory, which is a variant of algebraic K-theory, and is highly complex in both its formulation and the proof of its main results. Rosenberg shows how to define the Waldhausen A(X) when X is a pointed space in terms of the infinite loop space whose homotopy groups are the stable homotopy groups of the loop group of X. With multiplication defined by concatenation of loops, this loop space is a `homotopy ring' and if X is path-connected there is map from the loop space to the group ring of the first homotopy group of X. A(X) is then the K-theory space of the ring up to homotopy. The advantage of A(X) according to Rosenberg is that there is essentially a linear map from it to the K-group of the first homotopy group ring, which in some cases is an equivalence. For the case of compact smooth manifolds and its space of pseudo-isotopies, A(X) gives information on higher Whitehead and Reidemeister torsion. Rosenberg ends the article with a very brief discussion of the application of K-theory to symbolic dynamics. In this area of chaotic dynamical systems one is interested in what transition matrices will give equivalent symbolic dynamics. One can define an equivalence relation between them, called `shift equivalence.' K-theory assists in the study of shift equivalence by defining a C*-algebra associated to the shift, and studying the zeroth K-group of this C*-algebra. ... Read more

Product Description
This fourth edition of the classic book, Health Behavior and Health Education: Theory, Research, and Practice provides a comprehensive, highly accessible, and in-depth analysis of health behavior theories that are most relevant to health education. This essential resource includes the most current information on theory, research, and practice at individual, interpersonal, and community and group levels. This edition includes substantial new content on current and emerging theories of health communication, e-health, culturally diverse communities, health promotion, the impact of stress, the importance of networks and community, social marketing, and evaluation. ... Read more

Customer Reviews (21)

Excellent book.
Excellent book. All theories and constructs in Health Behaviour, beliefs and education are discussed with a complet approach.

Health Behavior review
The book was in the condition as stated before I placed the order, when I received it.

in good condition
book was in good condition when i received it. some of the plastic on the cover was peeling off, but other than that, it was fine. it's too bad the book took over 2 weeks to be shipped to me.

Lovely
Shipping took a while, but it did arrive sooner than promised. Received in great condition.

Health Behavior and Health Education
The book is in great condition and I received it within several days of my order! ... Read more

Product Description
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory. ... Read more

Customer Reviews (1)

Solid introduction;but..
You'd think, at these notorious prices, that the publisher would havemade a solid effort to cast these notes in a more engaging and readable form (i.e. to have them beautifully typeset, and dothem somejusticelong after they were first published), as this still istheauthoritative reference on the subject.

Shame, really.
... Read more

Product Description
This book introduces students to optimization theory and its use in economics and allied disciplines.The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified.The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming.A preliminary chapter and three appendices are designed to keep the book mathematically self-contained. ... Read more

Customer Reviews (12)

topics covered are great but loses 3 stars because of ...
glaring mistakes all over the book.
i've found at least 3 wrong definition of convexity in the book. some contradicing within a paragraph. wow do some proof reading?
along with wrong definition for implicit function theorem in chapter 1 - missing minus sign in front.
and look at page where they talk about epigraph and subgraph. and ... you get the point.

i can't believe it has such basic definitions wrong.
not to mention uncommon notations used for some analysis...
not happy with the book.
for optimization stick with Stephen Boyd, Bertsekas, or Luenberger.
and for applying optimization tech to economics get simon, and blume

2 stars might not seem a big deal to you but look at my rating history.
i rarely go under 4 stars.

stay away from this book. although if the author fixes those deluge of stupid mathematical mistakes this book has a potential to be 5 stars.

A nice treatment for econ grad, but lots of typos.. so be careful
I am a student at Penn econ. The book fits the requirement of the department very well. It is a nice treatment of the topic, both on the theoretical and applied sides. However, there're a considerable amount of typos in it. For instance, the statement of the Lagrange's Theorem takes the function g(i) to R(k), which should be R(1), etc.. So be careful. Mine is 15th printing version, but no revisions so far.. I think the press has earned enough from the book and should consider a second edition, right? haha..

A must-have reference
If you're a graduate student in economics, or perhaps computer science, buy this book as soon as possible. It will make your life much, much easier. Lagrangeans and Kuhn-Tucker optimization are the bread and butter of microeconomics, and yet few professors will bother to go into them in detail. This book succeeds in making these abstract mathematical procedures feel tangible and intuitive, defining them rigorously, explaining their usefulness and providing examples. This is one of very few books that I keep on my shelf for reference.

For a broader (and equally necessary) introduction to the math that you'll need for advanced study in economics, I recommend Simon and Blume's Mathematics for Economists.

Very self contained
This is a very readable introduction to optimisation that should appeal to a wide audience, althouh it is mainly aimed at economics students.
The subject is presented from very elementatry notions up, so if you have gaps in your calculus, this book is very likely to fill them.
The author bends over backwards to make the proofs clear.
It must be stressed that this is just an introduction, so people looking for an explanation of numerical methods such as Newton's method or derived methods won't find them here.

I originally got a book with missing pages near the end and found this out rather late. The publisher replaced my copy.

Great Review of Optimization for Graduates
This book is a great review prior to starting graduate study in economics. Its accessible even if you've never studied optimization before, and covers many of the main optimization concepts used in first semester graduate coursework. ... Read more

Product Description
K-theory is often considered a complicated mathematical theory for specialists only. This book is an accessible introduction to the basics and provides detailed explanations of the various concepts required for a deeper understanding of the subject.Some familiarity with basic C*algebra theory is assumed.The book then follows a careful construction and analysis of the operator K-theory groups and proof of the results of K-theory, including Bott periodicity. Of specific interest to algebraists and geometrists, the book aims to give full instruction. No details are left out in the presentation and many instructive and generously hinted exercises are provided. Apart from K-theory, this book offers complete and self contained expositions of important advanced C*-algebraic constructions like tensor products, multiplier algebras and Hilbert modules. ... Read more

Customer Reviews (2)

Great for beginners in the subject
This book is wonderful for beginners in K-theory of operator algebras because it also covers some fundamentals from other subjects that are needed. The proofs are always very clear. The best of it are theexcercises! Very many details of K-theory and its applications become clearwhen you do the excercises.

Great introduction to the subjects!
This book is a rarity in mathematics - a technical book on a difficult subject that remains entirely readable, even to non-specialists. Rather than the usual 300 pages of dense text and inscrutable proofs, the authorgives examples, straightforward proofs, and a writing style that borders onthe (gasp!) conversational. Highly recommended, especially fornon-mathematicians needing to learn K-theory. :) ... Read more

Product Description
In the discussion of architecture, the prevailing sentiment of the pastthree decades has been that cultural production can no longer beunderstood to arise spontaneously, as a matter of social course, but isconstructed through ever more self-conscious theoretical procedures. Thedevelopment of interpretive modes of various stripes--poststructuralist,Marxian, phenomenological, psychoanalytic, as well as others dissentingor eccentric--has given scholars a range of tools for rethinkingarchitecture in relation to other fields and for reassertingarchitecture's general importance in intellectual discourse.

This long-awaited anthology is in some sense a sequel to JoanOckman's Architecture Culture 1943-1968, A Documentary Anthology (1993).It presents forty-seven of the primary texts of contemporaryarchitecture theory, introducing each by detailing the concepts andcategories necessary for its understanding and evaluation. It alsopresents twelve documents of projects or events that had majortheoretical repercussions for the period. Several of the essays appearhere in English for the first time. ... Read more

Customer Reviews (5)

Great for learning more in depth about architecture theory
A bit of a tough read though.

Woa!
I'm a graduate student in architecture, and for a theory course we read selections from this book, and two other similar theory anthologies, Kate Nesbitt's "Theorizing a New Agenda for Architecture," and Niel Leach's "Rethinking Architecture." All books attempt to do roughly the same thing, and I have to say the Hays (this one) was the one I got the least out of.

I'll start with one minor criticism, which wouldn't condemn the book, but is extremely infuriating: the page numbers are printed on the inside upper corners of the pages near the spine, not the outside upper corners as is standard practice in books. This makes it difficult to flip through and find what you're looking for, and is just sort of a mind-bogglingly idiotic thing to do. Compounding the problem, many pages are simply not numbered!

That little complaint aside, I guess Hays does do a pretty good job with his selection of essays. If anything it illustrates how much the discourse has obfuscated itself over the last 30+ years. To give you the the flavor of the book, here are a few selections:

"The concept of architecture is itself an inhabited constructum, a heritage wich comprehends us even before we could submit it to thought. Certain invariables remain, constant, through all the mutations of architecture. Impassable, imperturbable, an axiomatic traverses the whole history of architecture. An axiomatic, that is to say, an organized ensemble of fundamental and always presupposed evaluations. This hierarchy has fixed itself in stone; henceforth, it informs the entirety of social space."
(Jacques Derrida)

"The combination of the system theory of the urban realm with its dynamic interpretation as a pressurized field gives rise to an assembly language based on impregnation, with system elements existing simultaneously, and at least virutally, everywhere, emerging to actualization only within nodes (conjunctions) of mutually interfering systems."
(Stanford Kwinter)

"This suggests the idea of architecture as "writing" as opposed to architecture as image. What is being "written" is not the object itself - its mass and volume - but the act of massing. This idea gives a metaphoric body to the act of architecture. It then signals its reading through an other system of signs, called traces. Traces are not the be read literally, since the have no other value than to signal the idea that three is a reading event and that reading should take place; trace signals the idea to read. Thus a trace is a partial or fragmentary signal; it has no objecthood."
(Peter Eisenman)

They are not all quite like that of course, but most will not find this 'easy' reading. Learning to read english like this is a skill that takes some time to develop. Hays's little blurbs preceding each writer are decent enough, grounding you a little before you take on the selection, but they are not spectacular.

I simply cannot recommend this book to anyone other than students forced to read it or those with a highly devoted interest in contemporary architectural theory. Anybody else will find it useless. (The Nesbitt and Leach were somewhat better)

Greatest Hits
This is a great book for students and professionals alike.As a collogue once said, "A Hayes book is like buying a greatest hits CD, all the good things are there".Hayes compilation saves time by retrieving the most influential articles since 1968 and places them in one place, most with a preface to the article.Must have for any student.Pages are also east to underline and annotate in the margins.

No House of Cards
I praise Michael Hayes for his succinct and accurate notation and massive inter-article references. This text is the bible of a discipline that ostensibly began in the twentieth century, as self-conscious writing began to absorb architecture as a theme or subject.

Each successive wave of theorization about architecture contains similar elements of concern and patterns of approach, each multivalent through time or the pen of the author. Hayes gathers the contentious groups and individuals who have jumped into the fray of Architectural Theory and presents them neatly, their most salient essays all within one binding.

All texts of postmodernism in one book
This book, which is very beautifully printed, shows us all the relevant texts of the post-modernarchitecture debate. Although this debate is very difficult to understand, all the texts are introduced by a very cleartext. References and literature is everywhere and exhaustive. ... Read more

Product Description
It has been over a decade since scholars in education began to apply the CRT framework from legal studies to the complex issues of race and racism in education. Yet, the picture of what it would mean to "do" CRT in educational research remains unclear. This edited volume brings together several scholars from both law and education to provide some clarity on the current status and future directions of Critical Race Theory, answering key questions regarding the "what' and "how" of the application of CRT to education. The contributors to the book return to the roots of CRT, interweaving the legal scholarship from which CRT originated with the new growth of CRT in education. The authors succeed at both pushing the boundaries of race-related theory in education, while at the same time remaining true to the original tenets of CRT in the law. As such, the book can serve as a primer for emerging scholars interested CRT and a reader for established CRT scholars in education and the social sciences. ... Read more

Product Description
K-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to a subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the theory.This book is the only comprehensive treatment of K-theory for operator algebras, and is intended to help students, non specialists, and specialists learn the subject. This first paperback printing has been revised and expanded and contains an updated reference list. This book develops K-theory, the theory of extensions, and Kasparov's bivariant KK-theory for C*-algebras. Special topics covered include the theory of AF algebras, axiomatic K-theory, the Universal Coefficient Theorem, and E-theory. Although the book is technically complete, motivation and intuition are emphasized. Many examples and applications are discussed. ... Read more

Customer Reviews (2)

A well-written book on a difficult subject
K-theory is a challenging subject; Kasparov's KK-theory even more so. But Bruce Blackadar's textbook manages to present both of these in a clear and coherent fashion, readable both by mathematicians and physicists. The ideal reader of this book will already be familiar with the basics of operator algebras and will have had some exposure to K-theory (perhaps through Wegge-Olsen's remarkable book) and noncommutative geometry; but an extensive background is not needed.

One especially good feature of this book is the wealth of examples it contains, especially those examples of most relevance to string theory. (Where K-theory is finding some of its most interesting applications today) A wide range of subjects such as "topological" K-theory (the K-theory of gauge fields) and supersymmetry (referred to as "grading," following mathematicians' notation) round out this presentation of one of the most exciting subjects on the border of mathematics and physics.

A difficult book on a difficult subject
The books covers not only K-theory but also KK-theory that was introduced by G. G. Kasparov. The original article by Kasparov are very hard to read because of the generality of his approach. Furthermore the theory was muchsimplified by Skandalis et al. The second part of the book offers a veryreadable introduction to KK-theory. Now the new edition even contains ashort exposition of E-theory.

"Elements of KK-theory" by K. K.Jensen and K. Thomsen is good introduction too. ... Read more

Product Description

This book examines interactions of polyhedral discrete geometry and algebra. What makes this book different from others is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory. The only prerequisite for the reader is a background in algebra. The basics of polyhedral geometry have been included as background material in Chapter 1.

The text will be of interest to graduate students and mathematicians. Included are numerous exercises, historical background, and notes throughout the chapters.

Product Description
Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory. ... Read more

Customer Reviews (1)

Very effective and understandable overview of K-theory
Speaking somewhat loosely, algebraic K-theory could be viewed as an attempt to generalize the invariants of linear algebra (such as determinants and canonical forms) to the case of projective modules. In modern mathematical classification, it is to be distinguished from topological K-theory, although both have a lot in common in terms of the general mathematical machinery used and were motivated from similar research interests. This book gives a superb overview of algebraic K-theory, and could be read by anyone who has taken a course in commutative algebra or a course in the theory of rings.The reader will see a common theme throughout algebraic K-theory, namely that of abelianization, which is very prevalent throughout modern mathematics.

In chapter 1, the author begins the construction of K0. After defining projective modules (over a ring R with a unit), and he characterizes finitely generated projective R-modules. The isomorphism classes of finitely generated projective R-modules form an abelian semigroup, the completion of which is the well-known Grothendieck group, and which is defined to be K0(R). The author also develops an alternative approach to K0 using idempotent matrices, thus making a connection with the general linear group. He shows both approaches are essentially equivalent, via the well-known "Morita invariance." Several examples of K0 are discussed, such as when R is a principal ideal domain, a local ring, and a Dedekind domain. The author also discusses to what extent K-theory can be viewed as a "homology for rings". This is relative K-theory, which is defined for two-sided ideals in R. Also, he gives the reader a taste of topological K-theory.

Just as one studies linear transformations of vector spaces and their invariants in linear algebra, the study of automorphisms of free and projective modules is done in K-theory, particularly via the construction of the K1 functor. In chapter 3, the author constructs K1 via the use of matrices, with a more categorical approach delayed until chapter 4. The group of "elementary matrices" for a ring R is defined, and K1(R) is defined to be GL(R)/E(R). The vanishing of K1(R) is equivalent to saying that every matrix in GL(R) and be row or column reduced to the identity matrix. When R is a field, the calculation of K1(R) reduces to ordinary linear algebra via the use of the determinant, and as a consequence K1(R) becomes trivial. When R is a local ring, then there exists a generalization of the determinant, which induces an isomorphism between K1(R) and the matrix group of its units modulo its commutator. When R is a Euclidean ring, K1(R) is isomorphic to its group of units, but when R is a principal ideal domain or a Dedekind domain, the author shows that K1(R) is not so elementary. He again gives a brief discussion of the application of K-theory, via the K1 functor, to topology. The relative K1 theory is also discussed.

Chapter 4 is an overview of how to construct K-theory for categories, instead of just rings. The categories considered are those that are ones wherein it is sensible to speak of an object as being constructed from more elementary objects, and are "abelian" categories, i.e. those that allow such homological results as the Five-Lemma. For a ring R, such categories include those of the category of finitely generated R-modules, the category of R-modules with a finite-type projective resolution, as well as of course the category of finitely generated projective R-modules. After discussing the connection between K0(R), K1(R) and K1 of the Laurent polynomial ring in R (the Bass-Heller-Swan theorem), the author introduces the notion of "negative K-theory", which gives the construction of an exact sequence of an ideal "arbitrarily far to the right", and thus allows the computation of K0(R/I) given information about R and I.

In chapter 5 the author describes the construction of the K2 functor as accomplished by the mathematician John Milnor. This entails a review of the theory of universal central extensions, which the author does in the first section. Following up on the idea that the K-theory of rings measures in some sense the abelian invariants of the non-abelian group GL(R), for a ring R, K2(R) is related to central extensions of E(R) by abelian groups: K2(R) is the kernel of the map of the universal extension of E(R), called the Steinberg group, to E(R). Some examples of the calculation of K2(R) are given, such as for the case where R is a field, wherein K2(R) is generated by the "Steinberg symbols." If R is a finite field, then K2(R) is zero. The lengthy concentration on the case where R is a field is done in order to point out the connection of K2 with number theory. When R is a field, the well-known Brauer group relates K2(R) to finite-dimensional non-abelian division algebras over R, and the author discusses this is fair detail.

The construction of the higher algebraic K-functors, i.e. Ki(R) for i greater than or equal to 3, is done in chapter 5 using the +-construction due to Daniel Quillen. It is here that topological considerations are brought to the forefront, since the Quillen approach is to construct the higher K-functors in terms of the homotopy groups of a particular space, called the classifying space. In particular, the (higher) K-theory of a ring R is defined as the product of the group of units of the classifying space of R and K0(R). The author shows that this definition of K-theory does coincide with that of K0 and K1 done earlier in the book. A brief but interesting survey (with proofs omitted) of the applications of the higher K-groups ends the chapter.

I did not read the last chapter on cyclic homology, and so its review will be omitted. ... Read more

Product Description
This concise introduction to ring theory, module theory and number theory is ideal for a first year graduate student, as well as being an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains. It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups. About 200 exercises complement the text and introduce further topics. This book provides the background material for the authors' forthcoming companion volume Categories and Modules. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory. ... Read more

Customer Reviews (2)

Accessible and easy to read
I believe this introductory textbook is a rare-bird in that it treats both non-commutative Artininan semisimple rings and commutative Dedekind domains from the view point of projective modules.I recall a similar book on ring theory by Jacob Barshay (written some thirty-seven years ago) which "falls short" in its treatment of the subject.The book by Berrick and Keating nicely covers many subjects that Barshay doesn't (important ones that come into my mind includes BINs and the fact that rings of integers of number fields form Dedekind domains.)And their writing style is quite accessible and easy to read.If you are majoring in algebra, you may have to go on to Lam's books, but otherwise this book may be sufficient most of(if not all) the time.

An Excellent Introduction
This is a very nice introduction to rings and modules.The text is well written and pedagogical, and the exercises are both informative and do-able.Beginning at a level appropriate for advanced undergraduates, this book builds up the theory of rings and modules in a concise manner without sacrificing clarity.Although not as in depth as some other texts (i.e., fewer full proofs), the reader is given enough guidance to fill in the missing proofs for herself.This, together with their other text on categories andRosenberg's book on algebraic K-theory, gives a solid introduction to algebraic K-theory. ... Read more

Product Description

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. This new edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience.

A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers “Higher Algebraic K-Theory, I, II.” A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained. An applications is also given to modules of finite length and finite projective dimension over the local ring of a normal surface singularity. These results lead the reader to some interesting conclusions regarding the Chow group of varieties.

Product Description

This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales.

From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

Customer Reviews (5)

Probability
Did not recieve the item in two days when I paid extra for expedited shipping.Recieved it 3 weeks later

A very good book indeed
A reviewer who has given this book 2 stars below says "It was the only math textbook that I really struggled with". That tells me this guy shouldn't have been in a maths course in the first place; stick to drama or English dude, they may be a little taxing for your brain. There should be a rule on Amazon against letting idiots review books of substance.

Chung's book is rich in historical notes, motivation and intuitive development of the subject. Chung is a world-renowned probabilst and also is a gifted writer. This book was followed in my undergraduate days and I still have fond memories of it.

My only gripe is that the new edition has added stuff by another author on finance. There was no need for this whatsoever.

best textbook for elementary probability theory
As a professor in computer science, I am teaching a seminar course in which I wanted to cover basic probability theory in a week.I read at least a half dozen textbooks in the university library and found this book to be far better than others for my purpose.In particular, the material I used was the derivation from the binomial distribution (a coin toss) to the normal and the Poisson distributions, which I covered in two classes.Students liked the many interesting, real-life examples in the book. In addition, I taught the two proofs for the law of large numbers.The second one from Chebyshev was more powerful (applies to non-identical distributions), stronger (guaratees the speed of convergence), simpler and shorter (half a page with no need of mathematical analysis).It eclipsed the theories of other mathematicians in the previous 200 years.The Chebyshev's theorem was new to me and to all the people I mentioned this to.

Of the books I know, this is the best entry level textbook for probability theories.I did not read the chapters on mathematical finance.

Great thoughts in every page
I just read the review by another reader, I would say unfortunately he was wrong. This book is one of the greatest probability book I have ever seen. If you want high-school level combination problem, this book is not for you. But if you want the essence of probability theory, this will be the perfect book for the entry. Actually I'm annoied by the comments of the other reviewer. I think he needs to review himself if he is not competent enough to take such course.

painful... even by undergraduate math textbook standards
I remember this ghastly nightmare from my undergraduate days. It was the only math textbook that I really struggled with. Part of that was probably due to having an inordinately lousy professor, but part of it is because the book reads more like a quick review for people who already know the subject matter than as an actual tool for learning.

As a contrast, check out what people are saying about "A Book of Abstract Algebra" by Pinter -- they're right, THAT is everything a math textbook should be. My class never quite finished it, but I had no trouble reading the later chapters on my own. I still have a copy of Chung's book, but it only has one remotely interesting thing in it that I remember, which was Laplace's calculation of the probability that the sun will rise tomorrow.

Bottom line: if you're unfortunate enough to end up with a professor who is still using Chung's book (I used it in 1997) ... run! ... Read more

Product Description

Engaging Organizational Communication Theory and Research: Multiple Perspectives is a book unlike any in the field. Each chapter is written by a prominent scholar who presents a theoretical perspective and discusses how he or she "engages" with it, personally examining what it means to study organizations. Rejecting the traditional model of a "reader," this volume demonstrates the intimate connections among theory, research, and personal experience. Engaging Organizational Communication Theory and Research is an indispensable resource for anyone wishing to be familiar with current trends in the field of organizational communication.

Product Description

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing.

Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques.

Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping.

The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.