Download or read book Rational Points and Arithmetic of Fundamental Groups written by Jakob Stix and published by Springer. This book was released on 2012-10-19 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.
Download or read book Rational Arithmetic written by George Pease Lord and published by . This book was released on 1920 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Birational Geometry Rational Curves and Arithmetic written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2013-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.
Download or read book Finite Precision Number Systems and Arithmetic written by Peter Kornerup and published by Cambridge University Press. This book was released on 2010-09-30 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive reference volume, suitable for graduate teaching, includes problems, exercises, solutions and an extensive bibliography.
Download or read book Algebraic Arithmetic written by Eric Temple Bell and published by American Mathematical Soc.. This book was released on 1927-12-31 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the Bocher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, elliptic and theta functions, Bernoulli numbers and functions, and the foundations of mathematics.
Download or read book The Rational Arithmetic written by James S. Russell and published by . This book was released on 1847 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rational Elementary Arithmetic written by Henry Holmes Belfield and published by . This book was released on 1898 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computer Arithmetic written by Earl E Swartzlander and published by World Scientific. This book was released on 2015-03-17 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the new edition of the classic book Computer Arithmetic in three volumes published originally in 1990 by IEEE Computer Society Press. As in the original, the book contains many classic papers treating advanced concepts in computer arithmetic, which is very suitable as stand-alone textbooks or complementary materials to textbooks on computer arithmetic for graduate students and research professionals interested in the field. Told in the words of the initial developers, this book conveys the excitement of the creators, and the implementations provide insight into the details necessary to realize real chips. This second volume presents topics on error tolerant arithmetic, digit on-line arithmetic, number systems, and now in this new edition, a topic on implementations of arithmetic operations, all wrapped with an updated overview and a new introduction for each chapter. This volume is part of a 3 volume set: Computer Arithmetic Volume I Computer Arithmetic Volume II Computer Arithmetic Volume III The full set is available for sale in a print-only version. Contents:Error Tolerant ArithmeticOn-Line ArithmeticVLSI Adder ImplementationsVLSI Multiplier ImplementationsFloating-Point VLSI ChipsNumber RepresentationImplementations Readership: Graduate students and research professionals interested in computer arithmetic. Key Features:It reprints the classic papersIt covers advanced arithmetic operationsIt does this in the words of the original creatorsKeywords:Computer Arithmetic;Fault Tolerant;Arithmetic;On-Line Arithmetic;Adder Implementations;Multiplier Implementations;Floating Point Chips;Number Representation;Implementations
Download or read book Rational Grammar School Arithmetic written by George William Myers and published by . This book was released on 1903 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Arithmetic of Dynamical Systems written by J.H. Silverman and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.
Download or read book Rational Points on Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Download or read book The Southworth Stone Arithmetic written by Gordon Augustus Southworth and published by . This book was released on 1904 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Real Analysis A Constructive Approach Through Interval Arithmetic written by Mark Bridger and published by American Mathematical Soc.. This book was released on 2019-07-05 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. For example, at the very beginning, the real numbers are shown to exist because they are constructed from the rationals using interval arithmetic. This approach, with its clear analogy to scientific measurement with tolerances, is taken throughout the book and makes the subject especially relevant and appealing to students with an interest in computing, applied mathematics, the sciences, and engineering. The first part of the book contains all the usual material in a standard one-semester course in analysis of functions of a single real variable: continuity (uniform, not pointwise), derivatives, integrals, and convergence. The second part contains enough more technical material—including an introduction to complex variables and Fourier series—to fill out a full-year course. Throughout the book the emphasis on rigorous and direct proofs is supported by an abundance of examples, exercises, and projects—many with hints—at the end of every section. The exposition is informal but exceptionally clear and well motivated throughout.
Download or read book Numbers Rational and Irrational written by Ivan Niven and published by . This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-study guide on the classification of numbers and the standards used to determine whether a number is rational or irrational.
Download or read book Arithmetic Geometry written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2009 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this tile is intended for graduate students and recent PhD's. It introduces readers to modern techniques and conjectures at the interface of number theory and algebraic geometry.
Download or read book Quantitative Arithmetic of Projective Varieties written by Timothy D. Browning and published by Springer Science & Business Media. This book was released on 2009-12-21 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties.
Download or read book Classical Theory of Arithmetic Functions written by R Sivaramakrishnan and published by Routledge. This book was released on 2018-10-03 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
