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Elementary Number Theory Group Theory And Ramanujan Graphs
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Book Synopsis Elementary Number Theory, Group Theory and Ramanujan Graphs by : Giuliana Davidoff
Download or read book Elementary Number Theory, Group Theory and Ramanujan Graphs written by Giuliana Davidoff and published by Cambridge University Press. This book was released on 2003-01-27 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Four Faces of Number Theory by : Kathrin Bringmann
Download or read book Four Faces of Number Theory written by Kathrin Bringmann and published by European Mathematical Society. This book was released on 2015 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arose from courses given at an International Summer School organized by the number theory group of the Department of Mathematics at the University of Wurzburg. It consists of four essentially self-contained chapters and presents recent research results highlighting the strong interplay between number theory and other fields of mathematics, such as combinatorics, functional analysis and graph theory. The book is addressed to undergraduate students who wish to discover various aspects of number theory. Remarkably, it demonstrates how easily one can approach frontiers of current research in number theory by elementary and basic analytic methods. Kathrin Bringmann gives an introduction to the theory of modular forms and, in particular, so-called Mock theta-functions, a topic which had been untouched for decades but has obtained much attention in the last years. Yann Bugeaud is concerned with expansions of algebraic numbers. Here combinatorics on words and transcendence theory are combined to derive new information on the sequence of decimals of algebraic numbers and on their continued fraction expansions. Titus Hilberdink reports on a recent and rather unexpected approach to extreme values of the Riemann zeta-function by use of (multiplicative) Toeplitz matrices and functional analysis. Finally, Jurgen Sander gives an introduction to algebraic graph theory and the impact of number theoretical methods on fundamental questions about the spectra of graphs and the analogue of the Riemann hypothesis.
Book Synopsis Number Theory, Fourier Analysis and Geometric Discrepancy by : Giancarlo Travaglini
Download or read book Number Theory, Fourier Analysis and Geometric Discrepancy written by Giancarlo Travaglini and published by Cambridge University Press. This book was released on 2014-06-12 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of geometric discrepancy, which provides a framework for quantifying the quality of a distribution of a finite set of points, has experienced significant growth in recent decades. This book provides a self-contained course in number theory, Fourier analysis and geometric discrepancy theory, and the relations between them, at the advanced undergraduate or beginning graduate level. It starts as a traditional course in elementary number theory, and introduces the reader to subsequent material on uniform distribution of infinite sequences, and discrepancy of finite sequences. Both modern and classical aspects of the theory are discussed, such as Weyl's criterion, Benford's law, the Koksma–Hlawka inequality, lattice point problems, and irregularities of distribution for convex bodies. Fourier analysis also features prominently, for which the theory is developed in parallel, including topics such as convergence of Fourier series, one-sided trigonometric approximation, the Poisson summation formula, exponential sums, decay of Fourier transforms, and Bessel functions.
Book Synopsis A Guide to Elementary Number Theory by : Underwood Dudley
Download or read book A Guide to Elementary Number Theory written by Underwood Dudley and published by American Mathematical Soc.. This book was released on 2009-12-31 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory guide to elementary number theory for advanced undergraduates and graduates.
Book Synopsis Number Theory in the Spirit of Liouville by : Kenneth S. Williams
Download or read book Number Theory in the Spirit of Liouville written by Kenneth S. Williams and published by Cambridge University Press. This book was released on 2011 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.
Book Synopsis Analytic and Elementary Number Theory by : Krishnaswami Alladi
Download or read book Analytic and Elementary Number Theory written by Krishnaswami Alladi and published by Springer. This book was released on 2013-12-21 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. Audience: Researchers and students of number theory, analysis, combinatorics and modular forms will find this volume to be stimulating.
Book Synopsis The Block Theory of Finite Group Algebras by : Markus Linckelmann
Download or read book The Block Theory of Finite Group Algebras written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.
Book Synopsis The Block Theory of Finite Group Algebras: Volume 2 by : Markus Linckelmann
Download or read book The Block Theory of Finite Group Algebras: Volume 2 written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
Book Synopsis Random Graphs, Geometry and Asymptotic Structure by : Michael Krivelevich
Download or read book Random Graphs, Geometry and Asymptotic Structure written by Michael Krivelevich and published by Cambridge University Press. This book was released on 2016-04-25 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
Book Synopsis Graph Theory and Additive Combinatorics by : Yufei Zhao
Download or read book Graph Theory and Additive Combinatorics written by Yufei Zhao and published by Cambridge University Press. This book was released on 2023-07-31 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
Book Synopsis Concise Encyclopedia of Coding Theory by : W. Cary Huffman
Download or read book Concise Encyclopedia of Coding Theory written by W. Cary Huffman and published by CRC Press. This book was released on 2021-03-26 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
Book Synopsis Introduction to Compact Riemann Surfaces and Dessins D'Enfants by : Ernesto Girondo
Download or read book Introduction to Compact Riemann Surfaces and Dessins D'Enfants written by Ernesto Girondo and published by Cambridge University Press. This book was released on 2012 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.
Book Synopsis Representation Theory of Finite Groups by : Benjamin Steinberg
Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Book Synopsis Introduction to Analysis on Graphs by : Alexander Grigor’yan
Download or read book Introduction to Analysis on Graphs written by Alexander Grigor’yan and published by American Mathematical Soc.. This book was released on 2018-08-23 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk (Markov chain) on finite graphs. For infinite graphs, a study of the heat kernel allows to solve the type problem—a problem of deciding whether the random walk is recurrent or transient. This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs and their application to the type problem. The book is suitable for beginners in the subject and accessible to undergraduate and graduate students with a background in linear algebra I and analysis I. It is based on a lecture course taught by the author and includes a wide variety of exercises. The book will help the reader to reach a level of understanding sufficient to start pursuing research in this exciting area.
Book Synopsis Surveys in Combinatorics 2019 by : Allan Lo
Download or read book Surveys in Combinatorics 2019 written by Allan Lo and published by Cambridge University Press. This book was released on 2019-06-27 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains eight survey articles based on the invited lectures given at the 27th British Combinatorial Conference, held at the University of Birmingham in July 2019. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, cryptography, matroids, incidence geometries and graph limits. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.
Book Synopsis An Introduction to the Representation Theory of Groups by : Emmanuel Kowalski
Download or read book An Introduction to the Representation Theory of Groups written by Emmanuel Kowalski and published by American Mathematical Society. This book was released on 2014-08-28 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.
Download or read book Regular Graphs written by Zoran Stanić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-24 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates possible applications. Finally, the author also includes some conjectures and open problems to promote further research. Contents Spectral properties Particular types of regular graph Determinations of regular graphs Expanders Distance matrix of regular graphs
