Friedlander, J.B., Heath-Brown, D.R., Iwaniec, H., Kaczorowski, J.

Analytic Number Theory
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11-18, 2002

Series: Lecture Notes in Mathematics Vol. 1891
Subseries: Fondazione C.I.M.E., Firenze ,
2006, Approx. 220 p., Softcover.
ISB: 3-540-36363-7
Due: August 17, 2006

About this book

The four contributions collected in this volume deal with several advanced results in analytic number theory. Friedlander’s paper contains some recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials. Heath-Brown's lecture notes mainly deal with counting integer solutions to Diophantine equations, using among other tools several results from algebraic geometry and from the geometry of numbers. Iwaniec’s paper gives a broad picture of the theory of Siegel’s zeros and of exceptional characters of L-functions, and gives a new proof of Linnik’s theorem on the least prime in an arithmetic progression. Kaczorowski’s article presents an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg, with a detailed exposition of several recent results.

Table of contents

Preface.- J. B. Friedlander: Producing Prime Numbers via Sieve Methods.- D. R. Heath-Brown: Counting Rational Points on Algebraic Varieties.- H. Iwaniec: Conversations on the Exceptional Character.- J. Kaczorowski: Axiomatic Theory of L-Functions: the Selberg Class.

Bachman, David

A Geometric Approach to Differential Forms

2006, XVIII, 142 p., 39 illus., Softcover.
ISBN: 0-8176-4499-7
Due: September 2006

About this textbook

The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the sophomore undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually.

Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember.

The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in sophomore-level vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, covering more advanced topics such as Maxwell's equations, foliation theory, and cohomology.

Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks.

Table of contents

Preface.-Guide to the Reader.-Multivariable Calculus.-Parameterizations.-Introduction to Forms.-Forms.-Differential Forms.-Differentiation of Forms.-Stokes' Theorem.-Applications.-Manifolds.-Non-linear Forms.-References.-Index.-Solutions.

Elkadi, Mohamed; Mourrain, Bernard; Piene, Ragni (Eds.)

Algebraic Geometry and Geometric Modeling

Series: Mathematics and Visualization
2006, XII, 252 p., Hardcover.
ISBN: 3-540-33274-X
Due: August 17, 2006

About this book

Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects.

Written for:

Graduate students and researchers in Computer Aided Geometric Design, Geometric Modeling,Computer Science, Effective Algebraic Geometry and Symbolic Computation

Hazewinkel, Michiel, Gubareni, Nadiya, Kirichenko, V.V.

Algebras, Rings and Modules, Volume 2, 2nd ed.

Series: Mathematics and Its Applications , Vol. 575
2006, Approx. 350 p., Hardcover.
ISBN: 1-4020-5140-9
Due: September 2006

About this book

As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras.

Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius,right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined.

The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provides the theory of semiprime Noetherian semiperfect and semidistributive rings.

Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest.

Table of contents

Preface.- Groups and group representations.- Quivers and their representations.- Representations of posets and finite dimensional algebras.- Frobenius algebras and quasi-Frobenius rings.- Right serial rings.- Tiled orders over discrete valuation rings.- Gorenstein matrices.- Suggestions for further reading.- Index.- Name Index.

Heidergott, Bernd F.

Max-Plus Linear Stochastic Systems and Perturbation Analysis

Series: The International Series on Discrete Event Dynamic Systems , Vol. 15
2006, XII, 319 p., Hardcover.
ISBN: 0-387-35206-6
Due: September 2006

About this book

During the last decade, the area of stochastic max-plus linear systems has witnessed a rapid development, which created a growing interest in this area. This book provides a thorough treatment of the theory of stochastic max-plus linear systems. Max-plus algebra is an algebraic approach to discrete event systems (DES), like queuing networks that are prone to synchronization. Perturbation analysis studies the sensitivity of the performance of DES with respect to changes in a particular system parameter.

The first part of the book addresses modeling issues and stability theory for stochastic max-plus systems. The second part of the book treats perturbation analysis of max-plus systems: a calculus for differentiation of max-plus systems is developed. This calculus leads to numerical evaluations of performance indices of max-plus linear stochastic systems, such as the Lyapunov exponent or waiting times.

Table of contents

Part I.- Max-Plus Linear Stochastic Systems.- Queueing Systems.- Ergodic Theory.- Part II.- Perturbation Analysis.- A Max-Plus Differential Calculus.- Higher-Order Derivatives.- Taylor Series Expansions.- Appendix.