Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation.
Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs.
Methods Used to Solve Discrete Math ProblemsInteresting examples highlight the interdisciplinary nature of this areaPearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures.
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.
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory.
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject.
Although much literature exists on the subject of RSA and public-key cryptography, until now there has been no single source that reveals recent developments in the area at an accessible level.
Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field.
Introduction to Modern Cryptography, the most relied-upon textbook in the field, provides a mathematically rigorous yet accessible treatment of this fascinating subject.
A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus, called the Monster Lie algebra.
The power and properties of numbers, from basic addition and sums of squares to cutting-edge theoryWe use addition on a daily basis-yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity?
In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups.
The remarkable properties of the numbers one through nineIn Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics.
A look at one of the most exciting unsolved problems in mathematics todayElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics-the Birch and Swinnerton-Dyer Conjecture.
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view.
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.
This volume offers an English translation of all ten extant books of Diophantus of Alexandria's Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary.
Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory.
A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing.
Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.
Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.
Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations.
Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations.
Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics.
Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics.
