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Representation theory has applications to number theory, combinatorics and many areas of algebra. The aim of this text is to present some of the key results in the representation theory of finite groups. Professor Alperin concentrates on local representation theory, emphasizing module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. Exercises are provided at the end of most sections; the results of some are used later in the text.

• Sales Rank: #2929841 in Books
• Brand: Brand: Cambridge University Press
• Published on: 1993-09-24
• Original language: English
• Number of items: 1
• Dimensions: 8.98" h x .43" w x 5.98" l, .60 pounds
• Binding: Paperback
• 192 pages

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• Used Book in Good Condition

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0 of 3 people found the following review helpful.
great introduction
By David John Hemmer
This is a wonderfully written book, definitely suitable for a graduate student to study individually or as a text for a 1-semester class.

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The rapid spread of divorce since the 1960s has dramatically affected family life in Western society. Extensive research has been devoted to this recent period of change, and yet the long-term history of divorce has remained surprisingly obscure. Roderick Phillips, author of the highly acclaimed magisterial history of divorce, Putting Asunder, has now abridged his fascinating and wide-ranging study for a general readership. Encompassing religious and secular attitudes to divorce, the evolution of divorce laws, and changing responses to marriage breakdown, Untying the Knot offers a highly readable and thought-provoking history of the phenomenon, placed illuminatingly against a variety of social, economic, political and cultural backgrounds.

• Sales Rank: #2168059 in Books
• Published on: 1991-06-28
• Original language: English
• Number of items: 1
• Dimensions: 8.50" h x .63" w x 5.43" l, .60 pounds
• Binding: Paperback
• 280 pages

Review
'Roderick Phillips' new book is the first in the English language to attempt an overall view of the history of divorce in the West, from the Reformation to the present day, covering in some detail England, America and France. Putting Asunder is the result of a prodigious amount of research, and provides a clear, intelligent, scholarly, and dependable general account of the history of divorce.' Lawrence Stone, The New York Review of Books

'... in its originality of concept and thoroughness of execution his book must be called an outstanding achievement'. Peter Laslett, The Times Literary Supplement

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** Free Ebook LMSST: 24 Lectures on Elliptic Curves (London Mathematical Society Student Texts), by J. W. S. Cassels

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The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.

• Sales Rank: #16400283 in Books
• Published on: 1991-11-29
• Original language: English
• Dimensions: 9.33" h x .51" w x 6.18" l, .74 pounds
• Binding: Hardcover
• 143 pages

Review
'... an excellent introduction ... written with humour.' Monatshefte für Mathematik

About the Author
Biography of J.W.S. Cassels

J. W. S. Cassels (known to his friends by the Gaelic form "Ian" of his first name) was born of mixed English-Scottish parentage on 11 July 1922 in the picturesque cathedral city of Durham. With a first degree from Edinburgh, he commenced research in Cambridge in 1946 under L. J. Mordell, who had just succeeded G. H. Hardy in the Sadleirian Chair of Pure Mathematics. He obtained his doctorate and was elected a Fellow of Trinity College in 1949. After a year in Manchester, he returned to Cambridge and in 1967 became Sadleirian Professor. He was Head of the Department of Pure Mathematics and Mathematical Statistics from 1969 until he retired in 1984.
Cassels has contributed to several areas of number theory and written a number of other expository books:
- An introduction to diophantine approximations
- Rational quadratic forms
- Economics for mathematicians
- Local fields
- Lectures on elliptic curves
- Prolegomena to a middlebrow arithmetic of curves of genus 2 (with E. V. Flynn).

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@ Ebook Free Guicciardini: Dialogue on the Government of Florence (Cambridge Texts in the History of Political Thought), by Francesco Guicciardini

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This is the first English translation of Guicciardini's Dialogue on the Government of Florence, written in the 1520s. Like Machiavelli, his more famous contemporary and friend, Guicciardini rejects classical republican arguments in the name of the new political realism and acknowledges the important role of patronage and graft in contemporary politics and the illegitimacy of nearly all forms of political power, arguing for the priority of state interest over private morality and religion.

• Sales Rank: #1596057 in Books
• Brand: Brand: Cambridge University Press
• Published on: 1994-06-24
• Original language: English
• Number of items: 1
• Dimensions: 8.50" h x .59" w x 5.43" l, .61 pounds
• Binding: Paperback
• 256 pages

Features

• Used Book in Good Condition

Language Notes
Text: English (translation)
Original Language: Italian

From the Back Cover
This is the first translation into English of Guicciardini's Dialogue on the Government of Florence. This dialogue presents what is arguably the most searching and comprehensive analysis of the politics of his times.

About the Author
Alison Brown is a Senior Lecturer in the School of City & Regional Planning at Cardiff University, and an urban planning consultant specializing in international planning practice. She is course director for the MSc in International Planning & Development, and has undertaken extensive research and consultancy in the developing world--in Southern and West Africa, South Asia, and the Middle East. She has recently managed a Department for International Development-funded study on street trading and livelihoods on which the book is based.

Raymond Geuss is Lecturer in Philosophy at the University of Cambridge. He has taught widely in Germany and the United States, and has been an editor of the series of Cambridge Texts in the History of Political Thought since its inception. His previous books include The Idea of a Critical Theory (Cambridge, 1981, ISBN 0521 284228), Morality, Culture, and History (Cambridge, 1999, ISBN 0 521 635683), and Public Goods, Private Goods (Princeton, 2001). He has also published a collection of classical verse in his own English translations, Parrots, Poets, and Philosophers & Good Advice (London, 1999).

Quentin Skinner is Barber Beaumont Professor of the Humanities at Queen Mary, University of London. He is a Fellow of the British Academy and the Academia Europaea, and a foreign member of many other learned societies. His scholarship, which is available in more than twenty languages, has won him numerous awards, including the Wolfson Prize for History in 1979 and a Balzan Prize in 2006. His books include The Foundations of Modern Political Thought (2 volumes, 1978), Reason and Rhetoric in the Philosophy of Hobbes (1996), Liberty Before Liberalism (1998), Hobbes and Republican Liberty (2008), Forensic Shakespeare (2014) and a three-volume collection of essays, Visions of Politics (2002).

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1 of 1 people found the following review helpful.
overlooked but essential political theory reading
By Ovidius
Written between 1521-24, the book consists of a dialogue between four leading Florentine citizens in 1494, one of whom defends the old Medici regime and three of whom defend the new republican government (adding pathos to the dialogue is the fact that the main speaker and defender of the Medici regime, Bernardo del Nero, was in fact summarily executed by the new regime in 1497 for involvement with a planned Medici coup).

Part I is a profound (and still relevant) debate on the merits and demerits of both narrow government and republican government. It should be essential reading for anyone doing political theory.

Part II turns to Guicciardini's ideal constitutional arrangement for Florence (still in the form of a dialogue). Constitutional arrangement is an eminently practical topic but one I find laborious reading. There are many excellent and relevant parts in part II but when it comes to how many people should sit on one imaginary council and how many on another, etc., it makes dry reading. Part II, in implicit dialogue with Machiavelli, also defends the model of the Venetian constitution over the Roman constitution.

There are many relevant ideas in the _Dialogue_ but to give a taste of Guicciardini's late Renaissance thought, here is one on the relationship between equality and liberty:

"although the basis of a free city is equality, nonetheless one can't prevent citizens enjoying different status according to their different levels of intelligence, virtue and merit" (115).

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** Download New England's Generation: The Great Migration and the Formation of Society and Culture in the Seventeenth Century, by Virginia DeJohn Ande

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Through analyses of the process of migration and settlement and of the symbolic meaning that participants attached to their experiences, the book tells the story of New England's origins as one of dynamism and change. Focusing on the lives of nearly 700 emigrants, the narrative examines such topics as the settlers' motives for leaving England, their experience of the voyage, their patterns of settlement in the New World, and their search for economic security in a new land. The descendants of the founders erected the story of their "great" migration into early British America's only effective foundation myth--a record of achievement that succeeding generations could never match. Rich in detail and insight, this exploration of New England's founding examines both the lives of ordinary people and the transcendent meanings that those lives ultimately acquired.

• Sales Rank: #847909 in Books
• Brand: Brand: CAMBRIDGE UNIVERSITY PRESS (PRINT ON DEMAND)
• Published on: 1992-11-27
• Original language: English
• Number of items: 1
• Dimensions: 8.98" h x .55" w x 5.98" l, .70 pounds
• Binding: Paperback
• 248 pages

Features

• Used Book in Good Condition

Review
"As the title suggests, this is a scholarly book, yet there's much here to interest general readers of American history. Anderson's mission is to examine the reasons for the stability of early New England." Providence Journal

"Historian Virginia DeJohn Anderson studied 693 settlers who came here on seven ships between 1635 and 1638... in careful prose, Anderson refracts their psychological makeup in a way that makes them understandable to us." The Boston Globe

"...besides being beautifully written, the book is both original and highly useful in linking so many issues so intelligently through collective biography....It is an apt depiction of the socioeconomic context within which much of the cultural and intellectual drama of New England was played." Richard P. Gildrie, William and Mary Quarterly

From the Back Cover
Through analyses of the process of migration and settlement and of the symbolic meaning that participants attached to their experiences, the book tells the story of New England's origins as one of dynamism and change. Focusing on the lives of nearly 700 emigrants, the narrative examines such topics as the settlers' motives for leaving England, their experience of the voyage, their patterns of settlement in the New World, and their search for economic security in a new land.

About the Author
Virginia DeJohn Anderson is Associate Professor of History at the University of Colorado, Boulder. She is the author of New England's Generation and co-author (with David Goldfield, et al.) of The American Journey: A History of the United States.

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18 of 18 people found the following review helpful.
Beautifully written, well argued
By P. Baldwin
This book was a fascinating exposure of the "Great Migration", as it has been called, the New England immigration, that lastest less than 10 years, from 1630 to 1640. This migration was "great" in the minds of the people who made the journey, even though it was the smaller in duration and numbers of people, than any other region of American colonization. It was "great" in their minds because of the religious motivations. The follows the immigrants from the decision to immigrate, the trip over, settling in the new country, and continues on to the the second generation and the desire of the first generation to impress on them the values that they had come over with. The book is a fascinating look at what life was like for these early immigrants, illustrated with real life people, including a few of my ancestors. The book is well documented with a combination of historical and genealogical sources. The book is engaging and extremely well written.

2 of 2 people found the following review helpful.
Great historical analysis of Puritan migration to New England
By Betty Ann
I found this to be excellent background material to read while working on my family genealogy of this period. It gave a third dimension to my understanding of who these people were and what they sought in the New World.

1 of 1 people found the following review helpful.
Interesting and Well Researched.
By David G. Burrell
Anyone interested in the Great Migration will find this book informative and well researched. Documentation on various families is especially good, based on the author's doctoral dissertation.

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## Free Ebook Status Epilepticus: Its Clinical Features and Treatment in Children and Adults, by Simon Shorvon

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• Sales Rank: #5122548 in Books
• Published on: 1994-08-26
• Original language: English
• Number of items: 1
• Dimensions: 8.98" h x 1.38" w x 5.98" l, .17 pounds
• Binding: Hardcover
• 400 pages

Review
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>> Ebook Cambridge English for Schools 2 Student's book (Bk. 2), by Andrew Littlejohn, Diana Hicks

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Cambridge English for Schools offers an exciting approach to English for students from eleven to sixteen years old. This five-level course for young students has won worldwide praise for its innovative approach that really works. It was the first course to be fully based on CLIL (Content and Language Integrated Learning) principles. Cambridge English for Schools features a communicative, task-based approach where the content and concepts reflect students' own lives and interests. There is a clearly-structured, active approach to grammar with regular revision and evaluation. This course is effective with mixed-ability classes and emphasises learner choice, decision-making and autonomy. Level 2 contains 32 units and 80+ hours of class work.

• Sales Rank: #5587777 in Books
• Brand: Brand: Cambridge University Press
• Published on: 1996-04-26
• Original language: English
• Number of items: 1
• Dimensions: 10.87" h x .43" w x 8.66" l, 1.05 pounds
• Binding: Paperback
• 160 pages

Features

• Used Book in Good Condition

Review
'Imaginative, thorough, sustained with some novel features - especially good is the 'Parcel of English' idea.' The English Speaking Union

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^ Download Ebook Rethinking Religion: Connecting Cognition and Culture, by E. Thomas Lawson, Robert N. McCauley

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This book develops a cognitive approach to religion. Focusing particularly on ritual action, it borrows analytical methods from linguistics and other cognitive sciences. The authors provide a lucid, critical review of established approaches to the study of religion, and make a strong plea for the combination of interpretation and explanation. Often represented as competitive approaches, they are, rather, complementary and equally vital to the study of symbolic systems. Rethinking Religion deals with the relationship between cognition and culture in a novel manner, and introduces a method of analysis that will have many applications.

• Sales Rank: #2371162 in Books
• Color: Blue
• Published on: 1993-01-29
• Released on: 1993-01-14
• Original language: English
• Number of items: 1
• Dimensions: 8.98" h x .47" w x 5.98" l, .66 pounds
• Binding: Paperback
• 208 pages

Review
"[The authors] do a splendid job of demonstrating how such a theory would have interpretive and explanatory capabilities that previous theories have lacked....their analysis truly connects the cognitive and cultural dimensions involved in all religious ritual systems." A. Javier Trevino, Sociological Analysis

"One certainly hopes that this impressive book will set the tone for future discussions of this topic. It provides an important theoretical framework that the anthropology of religion cannot possibly ignore." Pascal Boyer, American Anthropologist

"Lawson and McCauley's Rethinking Religion is a creative and carefully crafted book that both defends a general approach to explaining religious systems and develops in embryo a substantive theory of religious ritual. The book cuts across disciplines in a fruiful way, making contributions to anthropology, cogitive psychology and philosophy as well as religious studies more generally." Harold Kincaid, Annals of Scholarship

From the Back Cover
This book is an ambitious attempt to develop a cognitive approach to religion. Focusing particularly on ritual action, it borrows analytical methods from linguistics and other cognitive sciences. The theory's central feature is a set of universal principles of religious ritual structure. The authors, a philosopher of science and a scholar of comparative religion, provide a lucid critical review of established approaches to religion, and make a strong plea for the combination of interpretation and explanation. Often represented as competitive approaches, they are, rather, complementary, equally vital to the study of symbolic systems.

About the Author
E. THOMAS LAWSON is Professor of Comparative Religion at Western Michigan University and executive editor of the Journal of Cognition and Culture.

ROBERT N. MCCAULEY is Professor of Philosophy and Director of the Emory College Center for Teaching and Curriculum, Emory University.

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4 of 4 people found the following review helpful.
Foundational for study of culture & cognition
By Brian Malley
First, a confession: I was a student of Tom Lawson's when this book first came out, and I came to it with a favorable predisposition and was willing to put in the work required to master its contents. Only someone very well educated to begin with would find this an easy read, but it repays close study.

This book has remained one of my favorites, however, because it lays out--better than I have seen anywhere else--the philosophical and methodological considerations involved in studying the interaction of individual minds with social/cultural systems. The authors really make three major points:
(1) Explanation and interpretation are complementary endeavors in the study of human behavior.
(2) One way of illuminating cultural systems is by studying their representation in individual minds.
(3) There are some rather unexpected universal principles of religious ritual that play a vital role in structuring how people think about rituals.
Lawson & McCauley's Ritual form hypothesis (as they later named it) has held up (surprisingly) well under subsequent empirical study.

I find that when I need to think about these issues, this book is a key resource. McCauley & Lawson have since published a further development of this theory, in Bringing Ritual to Mind (2002), but I still find Rethinking Religion, where they lay out the foundations, to be my go-to resource for the theory.

Note: There are some really significant omissions in the rules they provide for the action-representation system. If you look carefully at them, you will notice that some of them omit possibilities that other rules imply. They did not develop these rules further elsewhere, so take the ones in the book as illustrative only.

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~~ Download Risk and Protective Factors in the Development of PsychopathologyFrom Brand: Cambridge University Press

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This important volume presents a definitive review of the origins and implications of developmental psychopathology and what has been learned about the phenomenon of psychosocial resilience in diverse populations at risk.

• Sales Rank: #3133285 in Books
• Brand: Brand: Cambridge University Press
• Published on: 1993-01-29
• Original language: English
• Number of items: 1
• Dimensions: 9.21" h x 1.26" w x 6.14" l, 1.73 pounds
• Binding: Paperback
• 572 pages

Features

• Used Book in Good Condition

Review
"Clinicians who wish to broaden their horizons will find selective reading within this volume to be both rewarding and sobering, sometimes puzzling, but nearly always thought provoking." Lyman C. Wynne, Journal of Nervous and Mental Disease

"What makes this volume particularly important is the number of significant contributors to the study of developmental psychopathology....given its scope and importance, the volume makes a valuable contribution to our growing understanding." Michael Lewis, American Scientist

"It promises to enhance both our understanding of developmental processes as well as our understanding of psychopathology. This volume is one of several recent ones that begins to tackle this problem, and given its scope and importance, the volume makes a valuable contribution to our growing understanding." American Scientist

"This volume is much more than a tribute to Garmezy; its level of excellence makes it required reading for all psychologists interested in psychopathology, whether they are scientists, practitioners, or scientist-practitioner." Contemporary Psychology

About the Author
Ann S. Masten, PhD, Distinguished McKnight University Professor in the Institute of Child Development, University of Minnesota, is internationally known for her research on competence, risk and resilience in human development. She is currently President of the Society for Research in Child Development and serves on the Board of Children, Youth, and Families of the US Institute of Medicine/National Academies. She directs the Project Competence studies of risk and resilience, including studies of normative populations and high-risk children exposed to the stress of migration, homelessness, war and natural disasters.

Mark L. Howe is a Professor of Psychology and a Research Chair in Developmental Psychology at Lancaster University, Lancaster UK. Dr. Howe is also Co-director of the Centre for Research in Human Development at Lancaster University. His research concerns children's memory development including
children's false memories, autobiographical memory, and long-term retention of information. He is a Fellow of the American Psychological Association as well as the Association for Psychological Science.
Gail S. Goodman is Professor of Psychology and Director of the Center for Public Policy Research at the University of California, Davis, and Professor of Forensic Psychology at the University of Oslo, Norway. Her research concerns children's memory development and forensic developmental psychology.
Dr. Goodman has received many awards for her research, including two Distinguished Contributions awards in 2005 from the American Psychological Association (the Distinguished Contributions to Research in Public Policy Award, as well as the Distinguished Professional Contributions to Applied Research
Award). Dr. Goodman obtained her Ph.D. in Developmental Psychology from UCLA and conducted postdoctoral research at the University of Denver and the Universite Rene Descartes in Paris, France.
Dante Cicchetti is McKnight Presidential Chair of Child Psychology in the Institute of Child Development and in the Department of Psychiatry, University of Minnesota. He also is Professor of Psychology at the University of Minnesota. From 1985 to 2005, he directed the Mt. Hope Family Center at the
University of Rochester. Dr. Cicchetti has published 30 books including volumes on developmentalpsychopathology, child development, emotional development, Down syndrome, attachment beyond infancy, self development, risk and protective factors in the development of psychopathology, neurodevelopment
and psychopathology, and stress and development.

Most helpful customer reviews

6 of 6 people found the following review helpful.
diverse take-offs on a central theme
By A Customer
Here are 23 chapters combining theoretical and empirical work on risk and reslience. Contributors include the most well-known names in the field. The focus on resilience ("protective factors") as well as risk is a big plus.
Infancy, childhood, adolescence and adulthood are all given some attention here. Topics taken up for analysis include depression, divorce, maternal stress, and eating disorders. It's a diverse collection of articles all sharing one question: when two people face the same circumstances, why does this one develop psychopathology and this one not?
Important reading. A central book for those seriously interested in the development of psychopathology.

See all 1 customer reviews...

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# Download Introduction to Analytic and Probabilistic Number Theory (Cambridge Studies in Advanced Mathematics), by G. Tenenbaum

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This book is a systematic introduction to analytic methods in number theory, and assumes as a prerequisite only what is taught in a standard undergraduate course. The author aids readers by including a section of bibliographic notes and detailed exercises at the end of each chapter. Tenenbaum has emphasized methods rather than results, so readers should be able to tackle more advanced material than is included here. Moreover, he covers developments on many new and unpublished topics, such as: the Selberg-Delange method; a version of the Ikehara-Ingham Tauberian theorem; and a detailed exposition of the arithmetical use of the saddle-point method.

• Sales Rank: #2910346 in Books
• Brand: Brand: Cambridge University Press
• Published on: 1995-06-30
• Original language: English
• Number of items: 1
• Dimensions: 8.98" h x 1.14" w x 5.98" l, 1.69 pounds
• Binding: Hardcover
• 468 pages

Features

• Used Book in Good Condition

Review
"Gerald Tenenbaum has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate."
H.G. Diamond, Mathematical Reviews

"It contains clear and well written text, and enough exercises. I can recommend this book for students, researchers and professors, for studying and teaching."
Mehdi Hassani, MAA Reviews

Language Notes
Text: English (translation)
Original Language: French

About the Author
Professeur a l'Institut Elie Cartan, Universite de Lorraine. Outre des ouvrages de mathematiques, G. Tenenbaum a aussi publie un ouvrage de jeunesse, une piece de theatre et plusieurs romans, dont l'un, "L'Ordre des jours", a recu le prix Erckmann-Chatrian 2008.

Bela Bollobas has taught at Cambridge University's Department of Pure Maths and Mathematical Statistics for over 25 years and has been a fellow of Trinity College for 30 years. Since 1996, he has held the unique Chair of Excellence in the Department of Mathematical Sciences at the University of Memphis. Bollobas has previously written over 250 research papers in extremal and probabilistic combinatorics, functional analysis, probability theory, isoperimetric inequalities and polynomials of graphs.

Most helpful customer reviews

6 of 7 people found the following review helpful.
takes on number theory where Hardy and Wright left it
By Gilles Benson
I am very much in tune with everything that has already been written on this book although I don't feel that the text is that conventional; the author has chosen to separate every chapter in three parts: 1) theorems and proofs according to the chapter's title; 2) notes on the chapter which may contain additional theorems and proofs. 3) exercices enhancing the first part. It is said (I did not try them...) that the exercices are really challenging; this can be expected since the main subject of this book is very challenging: arithmetic functions are notoriously very bad behaving functions with very erratic asymptotic properties (for example: the Euler phi-function). One good news is that a solution book exists (although written in french) which can be found on the site of the SMF (Société mathématiques de france); another good news is that a third vastly augmented edition can also be found on French book sites at a much cheaper price than Cambridge's: Introduction à la théorie analytique et probabiliste des nombres (Belin 2008). And mathematical french is not that daunting.
The text is rather self-contained since the main tools of the trade are given in the first chapters and there is a whole chapter on Euler Gamma function with a view towards Mellin transform and Stirling formula.
As a reward for all the "hard work" needed to grovel through the book, one can find a whole chapter discussing Riemann's long standing hypothesis; one of the main reference on the subject; earlier works that I would suggest are "Arithmetical functions" by Chandrasekharan (Springer 1970) and "Les nombres premiers" by W.J. Ellison (Hermann 1975) which has been translated in english in 1985.

7 of 12 people found the following review helpful.
Analytic Number Theory for those who love maths...
By Satanas
Gerald Tenenbaum's lucid writing style provides a comprehensive, yet non-painful introduction to the subject. This book focuses on methods, which once learned are of utility both to the expert and novice. The beautiful---and sometimes obscure results---chosen as exercises enhance the appeal of the book. A must for number theorists and a text for anyone wanting to explore applications of analysis in an arithmetic setting.

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