Surveys in Geometry and Number Theory

Reports on Contemporary Russian Mathematics
Author: Nicholas Young
Publisher: Cambridge University Press
ISBN: 0521691826
Category: Mathematics
Page: 318
View: 4157

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A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.

Two-Dimensional Homotopy and Combinatorial Group Theory


Author: Cynthia Hog-Angeloni,Wolfgang Metzler,Allan J. Sieradski
Publisher: Cambridge University Press
ISBN: 9780521447003
Category: Mathematics
Page: 412
View: 9935

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Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.

Series

AAAS to Intro Handbks
Author: N.A
Publisher: N.A
ISBN: 9780835221061
Category:
Page: 1444
View: 1735

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Prospects in Mathematics. (AM-70)


Author: Friedrich Hirzebruch,Lars Hörmander,John Milnor,Jean-Pierre Serre,I. M. Singer
Publisher: Princeton University Press
ISBN: 1400881692
Category: Mathematics
Page: 185
View: 3942

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Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.

Trends in Contemporary Mathematics


Author: Vincenzo Ancona,Elisabetta Strickland
Publisher: Springer
ISBN: 3319052543
Category: Mathematics
Page: 307
View: 2650

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The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.

Transactions of the Moscow Mathematical Society


Author: American Mathematical Society,Moscow Mathematical Society
Publisher: American Mathematical Soc.
ISBN: 9780821895245
Category: Mathematics
Page: 283
View: 4609

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Among the topics explored are categories of Banach spaces, semisimple algebraic groups, linear elliptic differential equations, the Poincare boundary value problem, and pseudodifferential operators

Operator Theory in Function Spaces


Author: Kehe Zhu
Publisher: American Mathematical Soc.
ISBN: 0821839659
Category: Mathematics
Page: 348
View: 7087

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This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Combinatorial Geometry and Its Algorithmic Applications

The Alcalá Lectures
Author: János Pach,Micha Sharir
Publisher: American Mathematical Soc.
ISBN: 0821846914
Category: Mathematics
Page: 235
View: 3501

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Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. "Combinatorial Geometry and Its Algorithmic Applications" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography.

Proof and Computation


Author: Helmut Schwichtenberg
Publisher: Springer Science & Business Media
ISBN: 3642793614
Category: Computers
Page: 470
View: 9638

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Logical concepts and methods are of growing importance in many areas of computer science. The proofs-as-programs paradigm and the wide acceptance of Prolog show this clearly. The logical notion of a formal proof in various constructive systems can be viewed as a very explicit way to describe a computation procedure. Also conversely, the development of logical systems has been influenced by accumulating knowledge on rewriting and unification techniques. This volume contains a series of lectures by leading researchers giving a presentation of new ideas on the impact of the concept of a formal proof on computation theory. The subjects covered are: specification and abstract data types, proving techniques, constructive methods, linear logic, and concurrency and logic.

Introduction to Analytic and Probabilistic Number Theory


Author: Gérald Tenenbaum
Publisher: American Mathematical Soc.
ISBN: 082189854X
Category: Number theory
Page: 629
View: 4881

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This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. --Mathematical Reviews

The Survival of a Mathematician

From Tenure-track to Emeritus
Author: Steven George Krantz
Publisher: American Mathematical Soc.
ISBN: 0821846299
Category: Mathematics
Page: 310
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"One of the themes of the book is how to have a fulfilling professional life. In order to achieve this goal, Krantz discusses keeping a vigorous scholarly program going and finding new challenges, as well as dealing with the everyday tasks of research, teaching, and administration." "In short, this is a survival manual for the professional mathematician - both in academics and in industry and government agencies. It is a sequel to the author's A Mathematician's Survival Guide."--BOOK JACKET.

Naming Infinity

A True Story of Religious Mysticism and Mathematical Creativity
Author: Loren Graham,Jean-Michel Kantor
Publisher: Harvard University Press
ISBN: 0674032934
Category: History
Page: 239
View: 3467

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Looks at the competition between French and Russian mathematicians over the nature of infinity during the twentieth century.

Choice


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Academic libraries
Page: N.A
View: 4169

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Surveys on Surgery Theory

Papers Dedicated to C.T.C. Wall
Author: Sylvain E. Cappell,Charles Terence Clegg Wall,Andrew Ranicki,Jonathan R​osenberg
Publisher: Princeton University Press
ISBN: 9780691049380
Category: Mathematics
Page: 448
View: 4532

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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.