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Communication Theory

Author: Charles M. Goldie
Publisher: Cambridge University Press
ISBN: 9780521406062
Size: 11.35 MB
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This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.

Lmsst 24 Lectures On Elliptic Curves

Author: John William Scott Cassels
Publisher: Cambridge University Press
ISBN: 9780521425308
Size: 32.50 MB
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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.

A Brief Guide To Algebraic Number Theory

Author: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
ISBN: 9780521004237
Size: 66.39 MB
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Broad graduate-level account of Algebraic Number Theory, including exercises, by a world-renowned author.

Classical Invariant Theory

Author: Peter J. Olver
Publisher: Cambridge University Press
ISBN: 9780521558211
Size: 12.50 MB
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The book is a self-contained introduction to the results and methods in classical invariant theory.

An Introduction To K Theory For C Algebras

Author: M. Rørdam
Publisher: Cambridge University Press
ISBN: 9780521789448
Size: 65.49 MB
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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

Hyperbolic Geometry

Author: Birger Iversen
Publisher: Cambridge University Press
ISBN: 0521435080
Size: 22.87 MB
Format: PDF
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Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.

Dynamical Systems And Ergodic Theory

Author: Mark Pollicott
Publisher: Cambridge University Press
ISBN: 9780521575997
Size: 27.33 MB
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This book is essentially a self-contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a master's level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der Waerden's theorem and Szemerdi's theorem).