Number theory

This two-volume set collects and presents some fundamentals of mathematics in an entertaining and performing manner.

This book is an autobiographical interview with Chinese Academician Yuan Wang on his experience in mathematical research.

Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.

Alan Baker''s systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

This book highlights the many ideas and algorithms that Peter L.

This book offers an introduction to cryptology, the science that makes secure communications possible, and addresses its two complementary aspects: cryptography---the art of making secure building blocks---and cryptanalysis---the art of breaking them.

Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers.

This is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integration.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades.

This book is the first integrated treatment of sequences generated by finite automata and their generalizations.

Ergodic Theory and Topological Dynamics

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This unique volume presents a fruitful and beautiful mathematical world hidden in Caianiello's neuronic equations, which describe the instantaneous behavior of a model of a brain or thinking machine.

The International Conference on Modern Mathematics and the International Symposium on Differential Geometry, in honor of Professor Su Buchin on the centenary of his birth, were held in September 2001 at Fudan University, Shanghai, China.

Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science.

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 develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained.

"e;In order to become proficient in mathematics, or in any subject,"e; writes Andre Weil, "e;the student must realize that most topics in- volve only a small number of basic ideas.

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.

As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E.

The topic of this book is the theory of degenerations of abelian varieties and its application to the construction of compactifications of moduli spaces of abelian varieties.

This book based on lectures given by James Arthur discussesthe trace formula of Selberg and Arthur.

The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety.

Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina.

Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.

This book contains a number of elementary ideas on numbers, their representations, interesting arithmetical problems and their analytical solutions, fundamentals of computers and programming plus programming solutions as an alternative to the analytical solutions and much more.

Cryptology, for millennia a "e;secret science"e;, is rapidly gaining in practical importance for the protection of communication channels, databases, and software.

The first comprehensive introduction to the powerful moment approach for solving global optimization problems.

Chord Transformations in Higher-Dimensional Networks proposes an in-depth formal framework for generalized Tonnetze.

This book is a concise, self-contained treatise on abstract algebra with an introduction to number theory, where students normally encounter rigorous mathematics for the first time.

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.

This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields.

This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses.

Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms.

"e;A complete introduction to the geometric code of nature, written and illustrated by the most perceptive of its modern investigators.

A self-contained account of a new approach to the subject.

This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level.

This is the first extensive biography of the influential German mathematician, Peter Gustav Lejeune Dirichlet (1805 - 1859).

A central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold.

This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory' at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

This book is the result of research initiatives formed during the workshop "e;Low Dimensional Topology and Number Theory XIII"e; at Kyushu University in 2022.

This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24-28, 2019.

Model theory is one of the central branches of mathematical logic.

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

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