The study of elliptic curves by algebraists, algebraic geometers and number theorists dates back to the middle of the nineteenth century. There now exists an extensive literature that describes the beautiful and elegant properties of these marvelous objects. In 1984, Hendrik Lenstra described an ingenious algorithm for factoring...
This text organizes a range of results in chromatic homotopy theory, running a single thread through theorems in bordism and a detailed understanding of the moduli of formal groups. It emphasizes the naturally occurring algebro-geometric models that presage the topological results, taking the reader through a pedagogical development of the...
The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic...
This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the...
Over the last 50 years there have been an increasing number of applications of algebraic tools to solve problems in communications, in particular in the fields of error-control codes and cryptography. More recently, broader applications have emerged, requiring quite sophisticated algebra - for example, the Alamouti scheme in MIMO...
This book resulted from lectures given at the University of Erlangen– Nuremberg and at the University of Magdeburg. On these occasions we often had to deal with the problem of a heterogeneous audience composed of students of mathematics and of different natural or engineering sciences.
Presentation of the main approaches developed for a posteriori error estimation in various problems.
Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of...
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to...
This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the...
There are many surprising connections between the theory of numbers, which is one of the oldest branches of mathematics, and computing and information theory. Number theory has important applications in computer organization and security, coding and cryptography, random number generation, hash functions, and graphics. Conversely, number theorists...
This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as...
This unique book is designed to provide the reader with an exposition of interesting aspects -- encompassing both rudimentary and advanced knowledge -- of oscillation theory of partial differential equations, which dates back to the publication in 1955 of a paper by Ph Hartman and A Wintner. The objective of oscillation theory is to acquire...
