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  • Arithmetic Geometry, Number Theory, and Computation

    Series series Springer Nature Proceedings excluding Computer Science
    This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces ... Read more

    $242.99 USD

  • Quaternion Algebras

    by John Voight ...
    Series series Mathematics and Statistics (R0)
    This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while ... Read more

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    An accessible and fascinating exploration of how Alan Turing’s mathematical theory gave rise to modern computer science and applications—from the desktops to cell phonesIn 1936, when he was just 24 years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms ... Read more

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  • Numerical Analysis

    Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this ... Read more

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  • Concrete Mathematics

    A Foundation for Computer Science

    This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer ... Read more

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  • The Higher Arithmetic

    An Introduction to the Theory of Numbers

    by H. Davenport ...
    The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth ... Read more

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  • Computational Aspects of Modular Forms and Galois Representations

    How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime

    Series Book 176 - Annals of Mathematics Studies
    Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special ... Read more

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  • Algebra, Logic And Combinatorics

    Series Book 3 - Ltcc Advanced Mathematics Series
    This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.Algebra, Logic and Combinatorics ... Read more

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  • Real Analysis

    Modern Techniques and Their Applications

    Series series Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
    An in-depth look at real analysis and its applications-now expanded and revised.This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of ... Read more

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  • Weyl Group Multiple Dirichlet Series

    Type A Combinatorial Theory

    Series Book 175 - Annals of Mathematics Studies
    Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be ... Read more

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  • Explorations In Numerical Analysis: Python Edition

    This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those ... Read more

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  • Prime Numbers and Computer Methods for Factorization

    by Hans Riesel ...
    Series series Mathematics and Statistics (R0)
    From the original hard cover edition:In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number ... Read more

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