Mathematics
Number Theory


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The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics
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The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics
by Marcus Du Sautoy

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In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change the history of mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not...
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The Beginner's Guide to Construction: Mathematical Archetypes of Nature, Art, and Science, the
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The Beginner's Guide to Construction: Mathematical Archetypes of Nature, Art, and Science, the
by Michael Schneider

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< P> < CENTER> < B> The Universe May Be a Mystery, < br> But It's No Secret< /B> < /CENTER> < /P> < P> Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through...
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E : Story of a Number (94 Edition)
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E : Story of a Number (94 Edition)
by Eli Maor

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The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number "e". In this informal and engaging history, mathematician Eli Maor...
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Number Theory (Dover Books on Advanced Mathematics)
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Number Theory (Dover Books on Advanced Mathematics)
by George E. Andrews

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Includes bibliographical references (p. [230]-232) and indexes....
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How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics
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How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics
by James D. Stein

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In How Math Explains the World, mathematician Stein reveals how seemingly arcane mathematical investigations and discoveries have led to bigger, more world-shaking insights into the nature of our world. In the four main sections of the book, Stein tells...
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The Fabulous Fibonacci Numbers
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The Fabulous Fibonacci Numbers
by Alfred S. Posamentier and Ingmar Lehmann

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The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5...
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Progress in Mathematics #900: Eisenstein Series and Applications
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Progress in Mathematics #900: Eisenstein Series and Applications
by Wee Teck (edt) Gan

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Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together...
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The Golden Ratio and Fibonacci Numbers
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The Golden Ratio and Fibonacci Numbers
by R. A. Dunlap

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In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and...
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Problems in Algebraic Number Theory 2ND Edition
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Problems in Algebraic Number Theory 2ND Edition
by M Ram Murty

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Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an important role in training the mind of a researcher. It would not be an...
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Invitation to the Mathematics of Fermat-Wiles
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Invitation to the Mathematics of Fermat-Wiles
by Yves Hellegouarch

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"To decompose a cube into two other cubes, a fourth power, and generally an arbitrary power into two of the same powers above the second power, is an impossible thing and I have certainly found its admirable proof. This narrow margin would not contain it....
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Contributions to the Founding of the Theory of Transfinite Numbers
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Contributions to the Founding of the Theory of Transfinite Numbers
by Georg Cantor

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The famous articles, 1895-7, that founded a new branch of mathematics. Covers addition, multiplication and exponentiation of cardinal numbers, smallest transfinite cardinal numbers, ordinal types of simple ordered aggregates, more. Translated with...
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Progress in Mathematics #184: New Horizons in Pro- P Groups
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Progress in Mathematics #184: New Horizons in Pro- P Groups
by Marcus Du Sautoy

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The impetus for current research in pro-p groups comes from four main directions: from new applications in number theory, which continue to be a source of deep and challenging problems; from the traditional problem of classifying finite p-groups; from...
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Sphere Packings Lattices & Groups 3RD Edition
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Sphere Packings Lattices & Groups 3RD Edition
by John Horton Conway

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The third edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related...
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Basic Quadratic Forms
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Basic Quadratic Forms
by Larry J Gerstein

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This rich branch of number theory is useful to group theory, topology, cryptography and coding theory. Gerstein (mathematics, U. of California at Santa Barbara) works from his graduate-level courses to develop his material from the theoretical and...
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Continued Fractions
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Continued Fractions
by Doug Hensley

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The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre. While our understanding of continued fractions and related methods for simultaneous...
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Primes of the Form X + NY: Fermat, Class Field Theory, and Complex Multiplication (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
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Primes of the Form X + NY: Fermat, Class Field Theory, and Complex Multiplication (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
by David A. Cox

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Now available in paperback, this book explains how Fermat's work gave birth to the quadratic reciprocity and the genus of quadratic forms. It goes on to show how the results of Euler and Gauss can be fully understood in the context of classical field...
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Elements of Number Theory (Dover Phoenix Editions)
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Elements of Number Theory (Dover Phoenix Editions)
by I M Vinogradov

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"A very welcome addition to books on number theory."--Bulletin, American Mathematical Society Clear and detailed in its exposition, this text can be understood by readers with no background in advanced mathematics; only a small part requires a working...
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Riemann S Zeta Function
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Riemann S Zeta Function
by Harold M. Edwards

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Superb study of one of the most influential classics in mathematics examines the landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude, " and traces developments in theory inspired by it. Topics include Riemann's main...
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Reciprocity Laws (Springer Monographs in Mathematics)
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Reciprocity Laws (Springer Monographs in Mathematics)
by Franz Lemmermeyer

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This book is about the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory...
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P Adic Numbers P Adic Analysis Zeta 2ND Edition
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P Adic Numbers P Adic Analysis Zeta 2ND Edition
by Neal Koblitz

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Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu. I...
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