Geometry Algebra Number Theory And Their Information Technology Applications

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Geometry, Algebra, Number Theory, and Their Information Technology Applications

Amir Akbary,Sanoli Gun
Geometry Algebra Number Theory and Their Information Technology Applications Book PDF

Author : Amir Akbary,Sanoli Gun
Publisher : Springer
Page : 528 pages
File Size : 45,8 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9783319973791

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Geometry, Algebra, Number Theory, and Their Information Technology Applications by Amir Akbary,Sanoli Gun Pdf

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

Michal Křížek,Lawrence Somer,Alena Šolcová
From Great Discoveries in Number Theory to Applications Book PDF

Author : Michal Křížek,Lawrence Somer,Alena Šolcová
Publisher : Springer Nature
Page : 342 pages
File Size : 55,8 Mb
Release : 2021-09-21
Category : Mathematics
ISBN : 9783030838997

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From Great Discoveries in Number Theory to Applications by Michal Křížek,Lawrence Somer,Alena Šolcová Pdf

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.

Algebra and Number Theory

Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Algebra and Number Theory Book PDF

Author : Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin
Publisher : John Wiley & Sons
Page : 544 pages
File Size : 43,7 Mb
Release : 2011-07-15
Category : Mathematics
ISBN : 0470640537

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Algebra and Number Theory by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin Pdf

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.

Arithmetic Geometry and Number Theory

Lin Weng,Iku Nakamura
Arithmetic Geometry and Number Theory Book PDF

Author : Lin Weng,Iku Nakamura
Publisher : World Scientific
Page : 414 pages
File Size : 40,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812568144

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Arithmetic Geometry and Number Theory by Lin Weng,Iku Nakamura Pdf

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.

Number, Shape, & Symmetry

Diane L. Herrmann,Paul J. Sally, Jr.
Number Shape Symmetry Book PDF

Author : Diane L. Herrmann,Paul J. Sally, Jr.
Publisher : CRC Press
Page : 446 pages
File Size : 52,6 Mb
Release : 2012-10-18
Category : Mathematics
ISBN : 9781466554641

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Number, Shape, & Symmetry by Diane L. Herrmann,Paul J. Sally, Jr. Pdf

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.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Gebhard Böckle,Wolfram Decker,Gunter Malle
Algorithmic and Experimental Methods in Algebra Geometry and Number Theory Book PDF

Author : Gebhard Böckle,Wolfram Decker,Gunter Malle
Publisher : Springer
Page : 753 pages
File Size : 53,6 Mb
Release : 2018-03-22
Category : Mathematics
ISBN : 9783319705668

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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by Gebhard Böckle,Wolfram Decker,Gunter Malle Pdf

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Algebraic Geometry and Number Theory

Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin
Algebraic Geometry and Number Theory Book PDF

Author : Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin
Publisher : Birkhäuser
Page : 232 pages
File Size : 41,9 Mb
Release : 2017-05-07
Category : Mathematics
ISBN : 9783319477794

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Algebraic Geometry and Number Theory by Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin Pdf

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Number Theory and Its Applications

Cem Y. Yildrim,Serguei A. Stepanov
Number Theory and Its Applications Book PDF

Author : Cem Y. Yildrim,Serguei A. Stepanov
Publisher : CRC Press
Page : 364 pages
File Size : 54,9 Mb
Release : 2020-03-06
Category : Mathematics
ISBN : 9781000657418

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Number Theory and Its Applications by Cem Y. Yildrim,Serguei A. Stepanov Pdf

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.

Number Theory for Computing

Song Y. Yan
Number Theory for Computing Book PDF

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 41,7 Mb
Release : 2002-04-24
Category : Computers
ISBN : 3540430725

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Number Theory for Computing by Song Y. Yan Pdf

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.

Basic Modern Algebra with Applications

Mahima Ranjan Adhikari,Avishek Adhikari
Basic Modern Algebra with Applications Book PDF

Author : Mahima Ranjan Adhikari,Avishek Adhikari
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 46,6 Mb
Release : 2013-12-08
Category : Mathematics
ISBN : 9788132215998

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Basic Modern Algebra with Applications by Mahima Ranjan Adhikari,Avishek Adhikari Pdf

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

Glimpses of Algebra and Geometry

Gabor Toth
Glimpses of Algebra and Geometry Book PDF

Author : Gabor Toth
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 40,6 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387224558

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Glimpses of Algebra and Geometry by Gabor Toth Pdf

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

Contributions in Analytic and Algebraic Number Theory

Valentin Blomer,Preda Mihăilescu
Contributions in Analytic and Algebraic Number Theory Book PDF

Author : Valentin Blomer,Preda Mihăilescu
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 50,7 Mb
Release : 2011-11-19
Category : Mathematics
ISBN : 9781461412199

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Contributions in Analytic and Algebraic Number Theory by Valentin Blomer,Preda Mihăilescu Pdf

The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson", held at the University Göttingen, July 27-29 2009. Many of the included chapters have been contributed by invited participants. This volume presents and investigates the most recent developments in various key topics in analytic number theory and several related areas of mathematics. The volume is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.

Number Theory

Canadian Number Theory Association. Conference
Number Theory Book PDF

Author : Canadian Number Theory Association. Conference
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 49,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821833315

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Number Theory by Canadian Number Theory Association. Conference Pdf

This volume contains a collection of articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. The book represents a cross section of current research and new results in number theory. Topics covered include algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation. The volume contains both research and expository papers suitable for graduate students and researchers interested in number theory.

Advanced Number Theory with Applications

Richard A. Mollin
Advanced Number Theory with Applications Book PDF

Author : Richard A. Mollin
Publisher : Unknown
Page : 0 pages
File Size : 41,7 Mb
Release : 2010
Category : Number theory
ISBN : OCLC:1341830851

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Advanced Number Theory with Applications by Richard A. Mollin Pdf

"Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data. With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat's Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue-Siegel-Roth theorem, Hall's conjecture, the Erdos-Mollin--Walsh conjecture, and the Granville-Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes', Selberg's, Linnik's, and Bombieri's sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring. By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level." -- Publisher.

Noncommutative Geometry

Igor V. Nikolaev
Noncommutative Geometry Book PDF

Author : Igor V. Nikolaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 276 pages
File Size : 40,7 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783110545258

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Noncommutative Geometry by Igor V. Nikolaev Pdf

This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field. Contents Part I: Basics Model examples Categories and functors C∗-algebras Part II: Noncommutative invariants Topology Algebraic geometry Number theory Part III: Brief survey of NCG Finite geometries Continuous geometries Connes geometries Index theory Jones polynomials Quantum groups Noncommutative algebraic geometry Trends in noncommutative geometry