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Algorithmics@NUS notes:number_theory Trace: Number Theory Algorithmics@NUS Online Judge Login ... Sidebar Teaching Teaching Resources Training Getting Started Training Resources ICPC Workshop 2007 IOI Workshop 2007 ... i-Whiz Workshop 2006 Articles Programming FAQ Selection Contest FAQ Competition strategies Organising a contest ... Server Setup Picture Galleries NOI 2007 Kanpur 2006 Manila 2006 Mexico 2006 ... Aizu 2003 Notes Dynamic Programming Number Theory People Melvin Internal pages SINGRC CS1102 Labs CS3230 Projects Selection Contests ... Programming Exercises Table of Contents Number Theory Notes Online Books Number Theory Alexander has kindly helped to conduct a few sessions on some topics in Mathematics that are relevant to programming contests during our last ICPC workshop. He has also prepared a set of notes based on the materials covered in these sessions. Notes Modular arithmetic by Alexander Number theory by Naki Sato for IOM training Online Books A Computational Introduction to Number Theory and Algebra Elementary Number Theory An Introduction to the Theory of Numbers

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Seeding the pseudo random number generator Marc van Woerkom Wed Jun 9 10:46:11 CEST 2004 Previous message: Seeding the pseudo random number generator Next message: ErlCee++ Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Have a look to the Primes numbers generator from Joe's example at http://www.erlang.org/examples/examples-2.0.html The seed function is: H1 = H * X rem 32767, M1 = M * X rem 32767, S1 = S * X rem 32767, This function generates different numbers each time when it's called. The ICFP contest featured such a modular arithmetic based pseudo random number generator as well. See the part number theory in the task description. http://www.cis.upenn.edu/proj/plclub/contest/task.php Previous message: Seeding the pseudo random number generator Next message: ErlCee++ Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the erlang-questions mailing list

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55. Number Theory - Encyclopedia Article - Citizendium From Hammurapi to Legendre. Birkhäuser, Boston, MA, 1984. External links. Retrieved from http//en.citizendium.org/wiki/number_theory http://en.citizendium.org/wiki/Number_theory

We are creating the world's most trusted encyclopedia and knowledge base. The general public and experts collaborate, using their real names. Number theory From Citizendium, the Citizens' Compendium Jump to: navigation search Main Article Talk Related Articles Bibliography External Links This is a draft article , under development. These unapproved articles are subject to edit intro Number theory is a branch of mathematics devoted primarily to the study of the integers. Any attempt to conduct such a study naturally leads to an examination of the properties of that which integers are made of (namely, prime numbers) as well as the properties of objects made out of integers (such as rational numbers) or defined as generalisations of the integers (such as, for example, algebraic integers). Integers can be considered either as such or as solutions to equations ( diophantine geometry ). Some of the main questions are those of distribution: questions, say, on patterns or their absence (in the primes or other sequences) or, more generally, questions on size, number and growth. Such matters are often best understood through the study of analytical objects (e.g., the Riemann zeta function ) that encode them in some fashion ( analytical number theory ). One may also study real numbers in relation to rational numbers, e.g., as approximated by the latter (

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skip to main skip to sidebar Ebook-Powerz Enter your search terms Submit search form Web e-powerz.blogspot.com Tuesday, February 5, 2008 A Computational Introduction To Number Theory And Algebra - Victor Shoups A course in computational algebraic number theory - Cohen A Course in Homological Algebra - P. Hilton, U. Stammbach A Course In Universal Algebra - S. Burris and H.P. Sankappanavar A First Course In Linear Algebra - Robert A. Beezer A First Course in Noncommutative Rings - T. Lam A Primer of Algebraic D-modules - S. Coutinho Abel's Theorem in Problems and Solutions - V.B. Alekseev Abstract Algebra - the Basic Graduate Year - R. Ash Advanced Modern Algebra - Joseph J. Rotman Algebra Abstract - Robert B. Ash Algebra Demystified - Rhonda Huettenmueller Algebra I Basic Notions Of Algebra - Kostrikin A I , Shafarevich I R Algebra Sucsess In 20 Minutes a Day - LearningExpress Algebraic D-modules - A. Borel et. al Algebraic Groups and Discontinuous Subgroups - A. Borel, G. Mostow Algebraic Surfaces and Holomorphic Vector Bundles - R. Friedman Algorithmic Algebra - B. Mishra

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Home About Us NPCDS/PNSDC Mathematics Education ... Search THEMATIC PROGRAMS March 30, 2008 Fall 2006 Thematic Program in Cryptography Workshop on Computational challenges arising in algorithmic number theory and Cryptography October 30- November 3, 2006 Organizers: Renate Scheidler, Andreas Stein, Edlyn Teske Audio of talks Confirmed Participants Visitor Information Schedule ... back to Thematic Program page Despite intense research over many decades and sometimes even centuries, there are numerous number theoretic problems for which efficient solutions continue to elude us. Moreover, such solutions are generally not even known to exist. For example, it is unkown whether it is possible to find solutions to Pell equations and other norm equations quickly. Furthermore, to date, no efficient algorithm for factoring a large randomly chosen number into its prime factors is known, and the true complexity of the integer factorization problem is not even clear. Nevertheless, the popular RSA cryptosystem is based on the assumed difficulty of this problem. In general, the security of most public-key cryptographic systems relies on the believed difficulty of a certain number theoretic problem. In exploring such problems, researchers face mathematical as well as computational and algorithmic difficulties. This workshop is intended to address the manifold computational challenges arising in number theoretic algorithms and cryptographic applications. Questions to be explored may include, but are by no means limited to:

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