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Communication Theory

Communication Theory Author Charles M. Goldie
ISBN-10 0521406064
Release 1991-11-07
Pages 210
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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.

Fourier Analysis on Finite Groups and Applications

Fourier Analysis on Finite Groups and Applications Author Audrey Terras
ISBN-10 0521457181
Release 1999-03-28
Pages 442
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A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.

Presentations of Groups

Presentations of Groups Author D. L. Johnson
ISBN-10 0521585422
Release 1997-05-15
Pages 216
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The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied.This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.

Set Theory

Set Theory Author A. Hajnal
ISBN-10 1107362555
Release 2014-05-14
Pages 325
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This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.

LMSST 24 Lectures on Elliptic Curves

LMSST  24 Lectures on Elliptic Curves Author John William Scott Cassels
ISBN-10 0521425301
Release 1991-11-21
Pages 137
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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.

Undergraduate Commutative Algebra

Undergraduate Commutative Algebra Author Miles Reid
ISBN-10 0521458897
Release 1995-11-30
Pages 153
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In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.

Classical Invariant Theory

Classical Invariant Theory Author Peter J. Olver
ISBN-10 0521558212
Release 1999-01-13
Pages 280
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The book is a self-contained introduction to the results and methods in classical invariant theory.

A Brief Guide to Algebraic Number Theory

A Brief Guide to Algebraic Number Theory Author H. P. F. Swinnerton-Dyer
ISBN-10 0521004233
Release 2001-02-22
Pages 146
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Broad graduate-level account of Algebraic Number Theory, including exercises, by a world-renowned author.

An Introduction to the Theory of Graph Spectra

An Introduction to the Theory of Graph Spectra Author Dragoš Cvetković
ISBN-10 0521134080
Release 2009-10-15
Pages 378
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This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many new developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

An Introduction to K Theory for C Algebras

An Introduction to K Theory for C  Algebras Author M. Rørdam
ISBN-10 0521789443
Release 2000-07-20
Pages 242
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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

Undergraduate Algebraic Geometry

Undergraduate Algebraic Geometry Author Miles Reid
ISBN-10 0521356628
Release 1988-12-15
Pages 129
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.

Riemann Surfaces and Algebraic Curves

Riemann Surfaces and Algebraic Curves Author Renzo Cavalieri
ISBN-10 9781316798935
Release 2016-09-26
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Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Hyperbolic Geometry

Hyperbolic Geometry Author Birger Iversen
ISBN-10 9780521435086
Release 1992-12-17
Pages 298
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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

Dynamical Systems and Ergodic Theory Author Mark Pollicott
ISBN-10 0521575990
Release 1998-01-29
Pages 179
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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).

Set Theory for the Working Mathematician

Set Theory for the Working Mathematician Author Krzysztof Ciesielski
ISBN-10 0521594650
Release 1997-08-28
Pages 236
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Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Linear Analysis

Linear Analysis Author Béla Bollobás
ISBN-10 0521655773
Release 1999-03-04
Pages 240
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Revised and updated introduction to functional analysis.

An Introduction to Noncommutative Noetherian Rings

An Introduction to Noncommutative Noetherian Rings Author K. R. Goodearl
ISBN-10 0521545374
Release 2004-07-12
Pages 344
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This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.