Books Core
Posted: October 28th, 2007, 4:56pm CET by Swat

Jing-Song Huang, Pavle Pandzic, “Dirac Operators in Representation Theory ”
Birkhäuser Boston; 1 edition (July 27, 2006) | ISBN 0817632182 | 199 pages | PDF | 1,4 Mb
This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a far-reaching generalization that connects index theory in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective.
Key topics covered include:
* Proof of Vogan’s conjecture on Dirac cohomology
* Simple proofs of many classical theorems, such as the Bott–Borel–Weil theorem and the Atiyah–Schmid theorem
* Dirac cohomology, defined by Kostant’s cubic Dirac operator, along with other closely related kinds of cohomology, such as n-cohomology and (g,K)-cohomology
* Cohomological parabolic induction and $A_q(lambda)$ modules
* Discrete series theory, characters, existence and exhaustion
* Sharpening of the Langlands formula on multiplicity of automorphic forms, with applications
* Dirac cohomology for Lie superalgebras
An excellent contribution to the mathematical literature of representation theory, this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.
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Posted: October 28th, 2007, 4:54pm CET by Swat
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Posted: October 28th, 2007, 4:49pm CET by Swat

Sorin Dragomir, Giuseppe Tomassini, “Differential Geometry and Analysis on CR Manifolds”
Birkhäuser Boston; 1 edition (March 17, 2006) | ISBN: 0817643885 | 487 pages | PDF | 2,6 Mb
The study of CR manifolds lies at the intersection of three main mathematical disciplines: partial differential equations, complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has recently been made to understand the differential geometric side of the subject.
This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy–Riemann equations. It presents the major differential geometric acheivements in the theory of CR manifolds, such as the Tanaka–Webster connection, Fefferman’s metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang–Mills fields on CR manifolds, to name a few. It also aims at explaining how certain results from analysis are employed in CR geometry.
Motivated by clear exposition, many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory, this monograph is suitable for researchers and graduate students in differential geometry, complex analysis, and PDEs.
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Posted: October 28th, 2007, 4:43pm CET by Swat

Efstathios Vassiliou, ” Geometry of Principal Sheaves ”
Springer; 1 edition (2005) | ISBN: 1402034156 | 444 pages | PDF | 8,2 Mb
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities.
Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated.
The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.
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Posted: October 28th, 2007, 4:37pm CET by Swat

Tom Roeper “The Prism of Grammar: How Child Language Illuminates Humanism”
MIT Press (April 2007) | ISBN 0262182521 | 372 Pages | PDF | 2.2 Mb
Every sentence we hear is instantly analyzed by an inner grammar; just as a prism refracts a beam of light, grammar divides a stream of sound, linking diverse strings of information to different domains of mind–memory, vision, emotions, intentions. In The Prism of Grammar, Tom Roeper brings the abstract principles behind modern grammar to life by exploring the astonishing intricacies of child language. Adult expressions provide endless puzzles for the child to solve. The individual child’s solutions (”Don’t uncomfortable the cat” is one example) may amuse adults but they also reveal the complexity of language and the challenges of mastering it. The tiniest utterances, says Roeper, reflect the whole mind and engage the child’s free will and sense of dignity.
He offers numerous and novel “explorations”–many at the cutting edge of current work–that anyone can try, even in conversation around the dinner table. They elicit how the child confronts “recursion”–the heartbeat of grammar–through endless possessives (”John’s mother’s friend’s car”), mysterious plurals, contradictory adjectives, the marvels of ellipsis, and the deep obscurity of reference (”there it is, right here”). They are not tests of skill; they are tools for discovery and delight, not diagnosis. Each chapter on acquisition begins with a commonsense look at how structures work–moving from the simple to the complex–and then turns to the literary and human dimensions of grammar. One important human dimension is the role of dialect in society and in the lives of children. Roeper devotes three chapters to the structure of African-American English and the challenge of responding to linguistic prejudice.
Written in a lively style, accessible and gently provocative, The Prism of Grammar is for parents and teachers as well as students–for everyone who wants to understand how children gain and use language–and anyone interested in the social, philosophical, and ethical implications of how we see the growing mind emerge.
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Posted: October 28th, 2007, 4:31pm CET by Swat
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Posted: October 28th, 2007, 4:28pm CET by Swat

Erikson on Development in Adulthood: New Insights from the Unpublished Papers
publisher Oxford University Press | 16 November, 2001 | ISBN:0195131754 | CHM | 224 Pages | 2 Mb
Book Description:
Erik Erikson (1902-1994) was one of the most eminent and prolific psychologists of the 20th century. Over his long career he published a dozen books, including classics such as Childhood and Society; Identity, Youth, and Crisis; and Young Man Luther . He was awarded the Pulitzer Prize and the National Book Award in 1970 for his biography Gandhi’s Truth. It was also in 1970, when he retired from Harvard University, that Erikson began to rethink his earlier theories of development. He became increasingly occupied with the conflicts and challenges of adulthood–a shift from his earlier writings on the “identity crises� of adolescence. For the past twenty years, Carol Hoare has written extensively on various aspects of Erikson’s work. She has been aided by access to Erikson’s unpublished papers at Harvard, as well as cooperation with Joan Erikson, the psychologist’s wife and longtime collaborator. By reconstructing Erikson’s theory of adulthood from his unpublished papers, Hoare provides not only a much-needed revision of Erikson’s work, but also a glimpse into the mind of one of the 20th century’s most profound thinkers.
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Posted: October 28th, 2007, 4:25pm CET by Swat
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Posted: October 28th, 2007, 4:23pm CET by Swat

Jeffrey Jensen Arnett, “Encyclopedia of Children, Adolescents, and the Media”
Sage Publications, Inc (December 14, 2006) | ISBN: 1412905303 | 1104 pages | 9,5 Mb
*Starred Review* As media of all kinds become more pervasive, their effect on children and adolescents is much discussed and debated. This encyclopedia pulls together research on topics related to young people’s daily media experience. Editor Arnett is a research professor at Clark University in Worchester, Massachusetts, and the author of Emerging Adulthood: The Winding Road from the Late Teens through the Twenties (2004). More than 400 contributors from universities and organizations, primarily from the U.S., supplied the 463 entries. Broad areas of coverage (as outlined in the Reader’s Guide) include advertising; advocacy groups; computers and electronic media; gender and sexuality; movies, music, and television; public policy; and violence and aggression, among others. Although some entries discuss benefits, the weight of opinion in the entries in the encyclopedia is decidedly in the direction of the concerns and potential negative effects of media. Examples of entries include Cigarette use in television and movies; Gender roles in music; Internet use, psychological effects of; Manga (Japanese comic books); and Viral marketing. The relationship between food advertising and obesity; the portrayal of women in hip-hop; the cognitive effects of electronic games; the sexual information available in teen magazines; and media use in Asia, Europe, and Latin American are all the subjects of entries. A number of entries provide historical perspective, showing how comic strips or children’s television programming, for example, have evolved over the years. Others discuss academic theories such as mean world syndrome and the super peer. Each signed entry is from one to several pages in length and offers a list of further readings and cross-references. The index, more than 70 pages long and repeated in each volume, is invaluable for locating information on Dawson’s Creek, Grand Theft Auto, Madonna, and MySpace. A decision was made to exclude specific characters, performers, and media products as topics for entries in part because they come and go, and entries on them would already seem dated by the time the encyclopedia was published. Although the cost is substantial, this resource should be valuable at both academic institutions and large public libraries since there is no other like it. Libraries with online book collections should watch for it as part of the Gale Virtual Reference Library. Highly recommended. Shonrock, Diana
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Posted: October 28th, 2007, 4:20pm CET by Swat

Karen Christensen, David Levinson , “Encyclopedia of Community : From the Village to the Virtual World”
SAGE Publications; 1 edition (June 23, 2003) | ISBN: 0761925988 | 2000 pages | PDF | 18,2 Mb
Subject encyclopedias generally cover a well-defined academic area, historical period, or topic. The Encyclopedia of Community focuses on the hard-to-define concept of community and works to explore and position that concept within many disciplines and contexts. Entries such as Apartheid, Blogs, County fairs, Eugenics, Gangs, Shtetls, Social Darwinism, and Third places display the wide scope that the editors and contributors give to the notion of community.
Experienced reference book editors Christensen and Levinson (Encyclopedia of Modern Asia [Scribner, 2002] and Encyclopedia of World Sport [Oxford, 1999], among others) have assembled an international group of scholars to produce a set containing 500 signed entries, arranged in alphabetical order, with bibliographies and cross-references where appropriate. Some 266 of the entries are supplemented with sidebars that contain additional information, much of which comes from primary sources. An example is Emma Goldman’s address to the jury during her trial as a sidebar to the entry Anarchism. The encyclopedia opens with lists of entries, sidebars, and contributors. A “Reader’s Guide” groups the entries into 20 general categories, offering a thematic alternative to the alphabetical arrangement.
There are four potentially useful appendixes. “Resource Guides” offers 21 broad subject areas (not the same as those in the “Reader’s Guide” mentioned above), each with a definition, list of applicable entries, books and Web sites for further research, journals, and organizations. “Libraries Build Community” is designed to assist librarians by describing different kinds of outreach activities. “Community in Popular Culture” lists books, movies, television programs, and other resources on the theme of community, and the “Master Bibliography of Community” compiles most of the works cited in the articles. The entries themselves are clearly written and intended for a general researcher.
In spite of all the positive aspects of this work, it is necessary to question how essential it might be to a general academic or public collection. As most of the topics can be found in other subject encyclopedias, unless the focus on “community” matches a specific need, this may not be worth the price. For collections supporting community studies programs, as well as for comprehensive collections in sociology, urban planning, and the like, it is a good choice.
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