Tag: Arithmetic

Free Download John Gustafson, "Next Generation Arithmetic: Third International Conference, CoNGA 2022, Singapore, March 1-3, 2022, Revised Selected Pap"
English | ISBN: 3031097785 | 2022 | 144 pages | PDF | 5 MB
This book constitutes the refereed proceedings of the Third International Conference on Next Generation Arithmetic, CoNGA 2022, which was held in Singapore, during March 1-3, 2022. The 8 full papers included in this book were carefully reviewed and selected from 12 submissions. They deal with emerging technologies for computer arithmetic focusing on the demands of both AI and high-performance computing.

Free Download Arithmetic Geometry by Gary Cornell, Joseph H. Silverman
English | PDF | 1986 | 359 Pages | ISBN : 0387963111 | 31.3 MB
This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt ings’ seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.

Free Download Trilogy of Numbers and Arithmetic: History of Numbers and Arithmetic: An Information Perspective by Mark Burgin
English | June 8, 2022 | ISBN: 9811236836 | 372 pages | MOBI | 2.85 Mb
The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.

Free Download Masanori Morishita, "Knots and Primes: An Introduction to Arithmetic Topology"
English | 2011 | pages: 202 | ISBN: 1447121570 | EPUB | 2,7 mb
This is a foundation for arithmetic topology – a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry. ​

Free Download Local Systems in Algebraic-Arithmetic Geometry
English | 2023 | ISBN: 303140839X | 94 Pages | PDF EPUB (True) | 6 MB
The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci.

Free Download Computer Arithmetic in Practice; Exercises and Programming; 1
by Gryś Sławomir
English | 2023 | ISBN: 1032425652 | 213 pages | True PDF | 5.8 MB
Computer Arithmetic in Practice: Exercises and Programming is a simple, brief introductory volume for undergraduate and graduate students at university courses interested in understanding the foundation of computers. It is focused on numeric data formats and capabilities of computers to perform basic arithmetic operations. It discusses mainly such topics as:

Free Download Arithmetic of Higher-Dimensional Algebraic Varieties by Bjorn Poonen, Yuri Tschinkel
English | PDF | 2004 | 292 Pages | ISBN : 081763259X | 22.1 MB
One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory.

Free Download Charles Favre, "The Arithmetic of Polynomial Dynamical Pairs: (AMS-214) "
English | ISBN: 0691235465 | 2022 | 252 pages | PDF | 6 MB
New mathematical research in arithmetic dynamics

Free Download Field Arithmetic
English | 2023 | ISBN: 3031280199 | 839 Pages | PDF (True) | 15 MB
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.

Free Download Volker Diekert, "Discrete Algebraic Methods: Arithmetic, Cryptography, Automata and Groups "
English | ISBN: 3110413329 | 2016 | 356 pages | EPUB | 29 MB
The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups