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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.



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.



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.



Logic Induction and Sets

Logic  Induction and Sets Author Thomas Forster
ISBN-10 0521533619
Release 2003-07-21
Pages 234
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This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the center of his exposition resulting in a treatment of well established topics that is fresh and insightful. The presentation is engaging, but always great care is taken to illustrate difficult points. Understanding is also aided by the inclusion of many exercises. Little previous knowledge of logic is required of the reader, and only a background of standard undergraduate mathematics is assumed.



Potential Theory in the Complex Plane

Potential Theory in the Complex Plane Author Thomas Ransford
ISBN-10 0521466547
Release 1995-03-16
Pages 232
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Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the sharp quantitative form of Runge's theorem. In addition, there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.



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.



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.



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.



Notes on Logic and Set Theory

Notes on Logic and Set Theory Author P. T. Johnstone
ISBN-10 0521336929
Release 1987-10-08
Pages 110
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A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.



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 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.



Equilibrium States in Ergodic Theory

Equilibrium States in Ergodic Theory Author Gerhard Keller
ISBN-10 0521595347
Release 1998-01-22
Pages 178
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This book provides a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems. It starts with a chapter on equilibrium states on finite probability spaces which introduces the main examples for the theory on an elementary level. After two chapters on abstract ergodic theory and entropy, equilibrium states and variational principles on compact metric spaces are introduced emphasizing their convex geometric interpretation. Stationary Gibbs measures, large deviations, the Ising model with external field, Markov measures, Sinai-Bowen-Ruelle measures for interval maps and dimension maximal measures for iterated function systems are the topics to which the general theory is applied in the last part of the book. The text is self contained except for some measure theoretic prerequisites which are listed (with references to the literature) in an appendix.



Potential Theory in the Complex Plane

Potential Theory in the Complex Plane Author Thomas Ransford
ISBN-10 0521466547
Release 1995-03-16
Pages 232
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Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the sharp quantitative form of Runge's theorem. In addition, there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics and gives a flavor of some recent research in the area.



An Introduction to Twistor Theory

An Introduction to Twistor Theory Author S. A. Huggett
ISBN-10 0521456894
Release 1994
Pages 178
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This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics.



Riemann Surfaces and Algebraic Curves

Riemann Surfaces and Algebraic Curves Author Renzo Cavalieri
ISBN-10 9781316798935
Release 2016-09-26
Pages
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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.