Geometry Algebra Number Theory And Their Information Technology Applications
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| Author | : Amir Akbary |
| Publisher | : Springer |
| Total Pages | : 523 |
| Release | : 2018-09-18 |
| Genre | : Mathematics |
| ISBN | : 3319973797 |
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 | : Miles Reid |
| Publisher | : Cambridge University Press |
| Total Pages | : 312 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9780521545181 |
This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.
| Author | : Michal Křížek |
| Publisher | : Springer Nature |
| Total Pages | : 342 |
| Release | : 2021-09-21 |
| Genre | : Mathematics |
| ISBN | : 3030838994 |
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 | : Elisabeth Bouscaren |
| Publisher | : Springer |
| Total Pages | : 223 |
| Release | : 2009-03-14 |
| Genre | : Mathematics |
| ISBN | : 3540685219 |
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
| Author | : Michal Krizek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 0387218505 |
The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.
| Author | : Bob F. Caviness |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 455 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3709194598 |
George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. This volume is a state-of-the-art collection of important papers on CAD and QE and on the related area of algorithmic aspects of real geometry. It contains papers from a symposium held in Linz in 1993, reprints of seminal papers from the area including Tarski’s landmark paper as well as a survey outlining the developments in CAD based QE that have taken place in the last twenty years.
| Author | : Moshe Jarden |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 200 |
| Release | : 2021-05-03 |
| Genre | : Education |
| ISBN | : 1470452073 |
This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.
| Author | : Richard A. Mollin |
| Publisher | : CRC Press |
| Total Pages | : 440 |
| Release | : 2009-08-26 |
| Genre | : Computers |
| ISBN | : 1420083295 |
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 mo
| Author | : Vijaya Kumar Murty |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 142 |
| Release | : 2010 |
| Genre | : Computers |
| ISBN | : 0821843117 |
Focusing on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields the topics covered in this volume include Schoof's $\ell$-adic point counting algorithm, the $p$-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on the Jacobians of $C_{ab}$ curves and zeta functions.
| Author | : David Eisenbud |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 784 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461253500 |
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
