Geometry, Algebra, Number Theory, and Their Information Technology Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry, Algebra, Number Theory, and Their Information Technology Applications write by Amir Akbary. This book was released on 2018-09-18. Geometry, Algebra, Number Theory, and Their Information Technology Applications available in PDF, EPUB and Kindle. This volume contains proceedings of two conferences held in Toronto (Canada) and Kozhikode (India) in 2016 in honor of the 60th birthday of Professor Kumar Murty. The meetings were focused on several aspects of number theory: The theory of automorphic forms and their associated L-functions Arithmetic geometry, with special emphasis on algebraic cycles, Shimura varieties, and explicit methods in the theory of abelian varieties The emerging applications of number theory in information technology Kumar Murty has been a substantial influence in these topics, and the two conferences were aimed at honoring his many contributions to number theory, arithmetic geometry, and information technology.
From Great Discoveries in Number Theory to Applications
From Great Discoveries in Number Theory to Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook From Great Discoveries in Number Theory to Applications write by Michal Křížek. This book was released on 2021-09-21. From Great Discoveries in Number Theory to Applications available in PDF, EPUB and Kindle. This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Number Theory and Geometry: An Introduction to Arithmetic Geometry
Number Theory and Geometry: An Introduction to Arithmetic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Number Theory and Geometry: An Introduction to Arithmetic Geometry write by Álvaro Lozano-Robledo. This book was released on 2019-03-21. Number Theory and Geometry: An Introduction to Arithmetic Geometry available in PDF, EPUB and Kindle. Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Noncommutative Geometry and Number Theory
Noncommutative Geometry and Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Noncommutative Geometry and Number Theory write by Caterina Consani. This book was released on 2007-12-18. Noncommutative Geometry and Number Theory available in PDF, EPUB and Kindle. In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
Number Theory for Computing
Number Theory for Computing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Number Theory for Computing write by Song Y. Yan. This book was released on 2013-03-09. Number Theory for Computing available in PDF, EPUB and Kindle. Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.
