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Important results on the Hilbert modular group and Hilbert modular forms are introduced and described in this book. In recent times, this branch of number theory has been given more and more attention and thus the need for a comprehensive presentation of these results, previously scattered in research journal papers, has become obvious. The main aim of this book is to give a description of the singular cohomology and its Hodge decomposition including explicit formulae. The author has succeeded i...

Das Lehrbuch uber Codierungstheorie fur Mathematik- und Informatik-Studenten setzt ausser elementarem Grundwissen keine besonderen Kenntnisse voraus. Angesprochen werden Themen aus den Gebieten: Quellencodierung, Prufzeichenverfahren, fehlerkorrigierende Codes und Kryptosysteme. Begriffe, Methoden und Satze sind bis ins Detail ausfuhrlich dargestellt und durch viele einfache Beispiele erlautert. Erganzend zur 1. Auflage sind als Themen u.a. hinzugekommen: DVD-Datentrager, MDS-Codes und Bogen, Co...

This new ADVANTAGE SERIES of C. L. Johnston, Alden T. Willis, and Jeanne Lazaris' ESSENTIAL ARITHMETIC is a traditional, straight-forward, extremely popular book which is noted for its one-step, one-concept-at-a-time approach. All major topics are divided into small sections, each with its own examples and often with its own exercises--an approach that helps students master each section before proceeding to the next one. As part of the ADVANTAGE SERIES, this version will offer all the quality co...

This book discusses the theory of third-order differential equations. Most of the results are derived from the results obtained for third-order linear homogeneous differential equations with constant coefficients. M. Gregus, in his book written in 1987, only deals with third-order linear differential equations. These findings are old, and new techniques have since been developed and new results obtained. Chapter 1 introduces the results for oscillation and non-oscillation of solutions of third-...

Solutions to odd-numbered section exercises. - Solutions to every (even and odd) Mental Math exercise. - Solutions to every (even and odd) Practice Problem (margin exercise). - Solutions to every (even and odd) exercises found in the Chapter Pretests, Integrated Reviews (mid-chapter reviews), Chapter Reviews, Chapter Tests, Cumulative Reviews.

This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules.

Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equatio...

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters a...

This book is a translation of my book Suron Josetsu (An Introduction to Number Theory), Second Edition, published by Shokabo, Tokyo, in 1988. The translation is faithful to the original globally but, taking advantage of my being the translator of my own book, I felt completely free to reform or deform the original locally everywhere. When I sent T. Tamagawa a copy of the First Edition of the original work two years ago, he immediately pointed out that I had skipped the discussion of the class nu...

The student solutions manual provides worked-out solutions to the odd-numbered problems in the text. This manual also contains useful study tools, such as practice tests and key formulas and concepts summarized at the end of each chapter.