Number theory

This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication.

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.

This book offers an organized and systematic approach to poset metrics and codes.

This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes.

Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic.

In this book, the author pays tribute to Bernhard Riemann (1826-1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc.

Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory.

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "e;down-to-earth"e; manner.

Many different fractal dimensions have been proposed for networks.

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history.

This unique collection of new and classical problems provides full coverage of algebraic inequalities.

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.

This book constitutes the refereed post-conference proceedings  of the First International Conference on Number-Theoretic Methods in Cryptology,  NuTMiC 2017, held in Warsaw, Poland, in September 2017.

This book develops the foundations of "e;summability calculus"e;, which is a comprehensive theory of fractional finite sums.

Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry.

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics.

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises).

This book is intended as a teacher's manual and as an independent-study handbook for students and mathematical competitors.

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 "e;Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory"e;, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016.

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "e;Automorphic Forms and L-Functions"e;, held at the University of Heidelberg in 2016.

This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions.

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory.

This book provides the first extensive survey of block ciphers following the Lai-Massey design paradigm.

This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging).

This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications.

This highly readable book aims to ease the many challenges of starting undergraduate research.

The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook.

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.

This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics.

This book contains selected papers based on talks given at the "e;Representation Theory, Number Theory, and Invariant Theory"e; conference held at Yale University from June 1 to June 5, 2015.

This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability.

This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory.

Important results surrounding the proof of Goldbach's ternary conjecture are presented in this book.

This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications.

This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author's personal and life-long study-inspired by Ramanujan-of aspects of this broad topic.

With a specific focus on the mathematical life in small undergraduate colleges, this book presents a variety of elementary number theory insights involving sequences largely built from prime numbers and contingent number-theoretic functions.

Theta functions were studied extensively by Ramanujan.

This volume is dedicated to Robert F.

Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year.

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Bedlewo, Poland in September 2015.

This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters.

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives.

This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut.

This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject.

The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic.

In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry.

The canonical way to establish the central limit theorem for i.

Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems.

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory.

Celebrating one of the leading figures in contemporary number theory - John H.