Geometry Algebra Number Theory And Their Information Technology Applications PDF Download
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| Author | : Amir Akbary |
| Publisher | : Springer |
| Total Pages | : 528 |
| Release | : 2018-09-18 |
| Genre | : Mathematics |
| ISBN | : 3319973797 |
Download Geometry, Algebra, Number Theory, and Their Information Technology Applications Book 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.
| Author | : Michal Křížek |
| Publisher | : Springer Nature |
| Total Pages | : 342 |
| Release | : 2021-09-21 |
| Genre | : Mathematics |
| ISBN | : 3030838994 |
Download From Great Discoveries in Number Theory to Applications Book 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.
| Author | : Martyn R. Dixon |
| Publisher | : John Wiley & Sons |
| Total Pages | : 544 |
| Release | : 2011-07-15 |
| Genre | : Mathematics |
| ISBN | : 9780470640531 |
Download Algebra and Number Theory Book in PDF, ePub and Kindle
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
| Author | : Lin Weng |
| Publisher | : World Scientific |
| Total Pages | : 414 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 981256814X |
Download Arithmetic Geometry and Number Theory Book in PDF, ePub and Kindle
Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.
| Author | : Diane L. Herrmann |
| Publisher | : CRC Press |
| Total Pages | : 446 |
| Release | : 2012-10-18 |
| Genre | : Mathematics |
| ISBN | : 1466554649 |
Download Number, Shape, & Symmetry Book in PDF, ePub and Kindle
Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
| Author | : Cem Y. Yildrim |
| Publisher | : CRC Press |
| Total Pages | : 364 |
| Release | : 2020-03-06 |
| Genre | : Mathematics |
| ISBN | : 1000657418 |
Download Number Theory and Its Applications Book in PDF, ePub and Kindle
This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey.
| Author | : Victor Shoup |
| Publisher | : Cambridge University Press |
| Total Pages | : 544 |
| Release | : 2005-04-28 |
| Genre | : Computers |
| ISBN | : 9780521851541 |
Download A Computational Introduction to Number Theory and Algebra Book in PDF, ePub and Kindle
This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.
| Author | : Song Y. Yan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 470 |
| Release | : 2002-04-24 |
| Genre | : Computers |
| ISBN | : 9783540430728 |
Download Number Theory for Computing Book in PDF, ePub and Kindle
This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.
| Author | : Gabor Toth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 466 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387224556 |
Download Glimpses of Algebra and Geometry Book in PDF, ePub and Kindle
Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems
| Author | : Christian Perwass |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 389 |
| Release | : 2009-02-11 |
| Genre | : Computers |
| ISBN | : 3540890688 |
Download Geometric Algebra with Applications in Engineering Book in PDF, ePub and Kindle
The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms. This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation. Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.
