2012, Approx. 400 p. 1 illus. in color.
Hardcover
ISBN 978-3-642-30978-6
Due: September 23, 2012
Latest research results in Combinatorics, Computer Algebra, and Number Theory
Contributions by the foremost researchers in the areas
Foreword by D.E.Knuth (tentative)
This book is a proceedings of the conference which attracted the top combinatorialists worldwide. The conference is intended to honour the influence and achievements of Herbert S. Wilf who has authored several classical textbooks and research monographs pertaining to the conference themes, namely Combinatorics, Number Theory, and Computer Algebra.
Content Level ≫ Research
Keywords ≫ combinatorics - computational algebra - enumerative combinatorics - generating functions - number theory
Related subjects ≫ Computational Science & Engineering - Number Theory and Discrete Mathematics
Series: Springer Proceedings in Mathematics & Statistics, Vol. 25
2012, 2012, V, 360 p. 3 illus.
Hardcover
ISBN 978-1-4614-4564-7
Due: September 30, 2012
Recent Advances in Harmonic Analysis and Applications is dedicated to the 65th birthday of Konstantin Oskolkov and features contributions from analysts around the world.
The volume contains expository articles by leading experts in their fields, as well as selected high quality research papers that explore new results and trends in classical and computational harmonic analysis, approximation theory, combinatorics, convex analysis, differential equations, functional analysis, Fourier analysis, graph theory, orthogonal polynomials, special functions, and trigonometric series.
Numerous articles in the volume emphasize remarkable connections between harmonic analysis and other seemingly unrelated areas of mathematics, such as the interaction between abstract problems in additive number theory, Fourier analysis, and experimentally discovered optical phenomena in physics. Survey and research articles provide an up-to-date account of various vital directions of modern analysis and will in particular be of interest to young researchers who are just starting their career. This book will also be useful to experts in analysis, discrete mathematics, physics, signal processing, and other areas of science.
Content Level ≫ Research
Keywords ≫ Approximation Theory - Compressive Sensing - Harmonic - Orthogonal Polynomials - Sparse Representation - Trigonometric Series
Related subjects ≫ Analysis - Computational Science & Engineering - Dynamical Systems & Differential Equations - Number Theory and Discrete Mathematics
Series: Applied and Numerical Harmonic Analysis
2013, XVI, 468 p. 33 illus., 18 in color.
lHardcover
ISBN 978-0-8176-8372-6
Due: October 31, 2012
First book on the topic
Unified presentation across all contributions to the volume
Comprehensive coverage of theory and applications of finite frames
Useful for a wide range of mathematicians, computer scientists, and engineers
Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject.
Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including:
* Finite Frame Constructions;
* Optimal Erasure Resilient Frames;
* Quantization of Finite Frames;
* Finite Frames and Compressed Sensing;
* Group and Gabor Frames;
* Fusion Frames.
Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory.
With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.
Introduction.- Constructing Finite Frames with a Given Spectrum.-Spanning and Independence Properties of Finite.-Alegebraic Geometry and Finite Frames.- Group Frames.- Gabor Framses in Finite Dimensions.- Frames as Codes.- Quantization and Finite Frames.- Finite Frames for Sparse Signal Processing.- Finite Frames and Filter Banks.- Finite Frame theory in Pure Mathematics.- Probabilitstic Frames.- Fusion Frames.
Series: Springer Undergraduate Mathematics Series
2013, 2013, XVI, 320 p. 34 illus. With online files/update.
Softcover
ISBN 978-1-4471-4407-6
Accessible to students of a quantitative subject such as such as economics or physics as well as undergraduates in the final years of a mathematics degree
Includes a complete treatment of no-arbitrage pricing for both European and American derivatives in incomplete markets as well as Black-Scholes theory
Although focusing on the theory of derivative pricing in models with discrete time, the book also provides an understanding of the more advanced theory of continuous-time models
Derivatives are financial entities whose value is derived from the value of other more concrete assets such as stocks and commodities. They are an important ingredient of modern financial markets. This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative. To keep the mathematics as simple as possible, while explaining the basic principles, only discrete time models with a finite number of possible future scenarios are considered. The theory examines the simplest possible financial model having only one time step, where many of the fundamental ideas occur, and are easily understood. Proceeding slowly, the theory progresses to more realistic models with several stocks and multiple time steps, and includes a comprehensive treatment of incomplete models. The emphasis throughout is on clarity combined with full rigour. The later chapters deal with more advanced topics, including how the discrete time theory is related to the famous continuous time Black-Scholes theory, and a uniquely thorough treatment of American options. The book assumes no prior knowledge of financial markets, and the mathematical prerequisites are limited to elementary linear algebra and probability. This makes it accessible to undergraduates in mathematics as well as students of other disciplines with a mathematical component. It includes numerous worked examples and exercises, making it suitable for self-study.
Derivative Pricing and Hedging.- A Simple Market Model.- Single-Period Models.- Multi-Period Models: No-Arbitrage Pricing.- Multi-Period Models: Risk-Neutral Pricing.- The Cox-Ross-Rubinstein model.- American Options.- Advanced Topics.
Series: Universitext
2013, 2013, XII, 252 p.
Softcover
ISBN 978-1-4471-4434-2
Due: October 31, 2012
presents an elementary introduction that requires only few pre-requisites
introduces a host of different techniques such as representation theory, adeles and ideles, and the methods of Tate's thesis
combines the classical and analytical viewpoint and the modern representation-theoretic approach and reveals their interplay
Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem.
This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers.
Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Doubly periodic functions.-Modular forms for SL2(Z).-Representations of SL2(R).-p-adic numbers.-Adeles and ideles.-Tate’s thesis.-Automorphic representations of GL2(A).-Automorphic L-functions.