61. Number Theory At UC Irvine Karl Rubin photo, Karl Rubin Thorp Professor of Mathematics krubin@math.uci.edu, Elliptic curves, Iwasawa theory, special values of Lfunctions, http://www.math.uci.edu/~krubin/ntg/number_theory.html

UC Irvine Number Theory group Faculty Karl Rubin Thorp Professor of Mathematics krubin@math.uci.edu Elliptic curves, Iwasawa theory, special values of L-functions, cryptography Alice Silverberg Professor of Mathematics and Computer Science asilverb at uci.edu Number theory, cryptography, arithmetic algebraic geometry Daqing Wan Professor of Mathematics dwan@math.uci.edu Number theory, arithmetic geometry and applications Samuel Kadziela Visiting Assistant Professor kadziela@math.uci.edu Rigid analytic spaces, Mumford curves, p -adic uniformization ... Barry Smith Visiting Assistant Professor barryrsmith@gmail.com Special values of L -functions, Stark's conjectures ... Nick Alexander ncalexan AT math DOT uci DOT edu Sunil Chetty schetty@math.uci.edu Timothy Choi tchoi@math.uci.edu Phong Le ... chwong@math.uci.edu Southern California Number Theory Day at UCSD, May 2006 Events Southern California Number Theory Day at Caltech, 3/8/2008 There is an e-mail list used for announcements of events of interest to number theorists at UCI and southern California generally. Feel free to subscribe UCI Number Theory Seminar schedule Past events Southern California Number Theory Day at UCI, 10/27/2007

62. UM Mathematics: Number Theory Graduate Program in Number Theory. Staff, research interests, courses, seminars. http://www.math.lsa.umich.edu/research/number_theory/

Home People Graduate Program Undergraduate Program ... Links Search Mathematics Search WWW Graduate Program in Number Theory at the University of Michigan The department has long maintained a vigorous graduate program in number theory. Faculty Permanent: B. Conrad Algebraic number theory; arithmetic geometry. K. Soundararajan Analytic number theory, distribution of prime numbers H.L. Montgomery Analytic number theory, distribution of prime numbers, Fourier analysis, analytic inequalities, probability. C. Skinner Algebraic number theory;arithmetic of L-values. T. Wooley Analytic number theory, diophantine equations. Faculty in related areas include: I. Dolgachev (algebraic geometry), W. Fulton (algebraic geometry), R. Lazarsfeld (algebraic geometry), S. DeBacker (representation theory), G. Prasad (arithmetic of algebraic groups).

63. University Of Bristol - Department Of Mathematics - Research - Pure Mathematics Sub navigation. Analysis and Partial Differential Equations Ergodic Theory and Dynamical Systems Geometric Group Theory Number Theory http://www.maths.bris.ac.uk/research/pure/themes/number_theory/

Access sey s: Skip to content Access Key n: Skip to Main navigation Access sey m: Skip to Sub navigation University of Bristol Department of Mathematics Main navigation Home Study Research People ... Events Search form Search Sub navigation Analysis and Partial Differential Equations Ergodic Theory and Dynamical Systems Geometric Group Theory Number Theory ... Representation Theory Related topics Apply for Graduate Study Contacts Tim Browning Room: 4.16 Tel: +44 (0)117 331-5242 Extension: 15242 Email: t.d.browning Fax: +44 (0)117 928-7999 Breadcrumb Research Pure Mathematics Research Themes Number Theory Number theory Commonly referred to as the queen of mathematics, number theory is an ancient branch of pure mathematics that deals with properties of the integers. Bringing together tools from analysis, geometry and algebra, the work that takes place in Bristol centres largely upon Diophantine equations and prime numbers. Despite its blue-sky nature, number theory research has fundamental application in modern life and the group collaborates closely with other disciplines, such as quantum physics and computational science. As an example of this, the subject of algorithmic number theory is closely linked to cryptography, the basis of secure e-commerce and internet communications. The number theory group shares a seminar programme with the Heilbronn institute (named after the famous number theorist Hans Heilbronn who was a professor at Bristol), and organises a number of advanced lecture courses throughout the year. See the

64. Public Key Cryptography: Number Theory Public Key Cryptography Number Theory. Algebraic Number Theory Archives www.mersenne.org; Primes. Prime Number (Definition from mathworld) http://www.adastral.ucl.ac.uk/~helger/crypto/link/number_theory/

Vacancies at UCL MSc in information security at UCL Public Key Cryptography: Number Theory Algebraic Number Theory Archives www.mersenne.org Primes Prime Number (Definition from mathworld) The Prime Page (First known illegal prime) Sloane's On-Line Encyclopedia of Integer Sequences (Neil Sloane) Books Reciprocity Laws Suitable books (not only) for high-schoolers (?) Number Theory and its History (Oystein Ore (Dover)) The Higher Arithmetic (Harold Davenport) A Friendly Introduction to Number Theory (Joe Silverman) Elementary Number Theory and Its Applications ( Kenneth Rosen) Journal of Number Theory Factoring Primality tests Finding solutions to polynomials Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities ( Don Coppersmith, JoC 1997) Finite fields Introductions ABSTRACT ALGEBRA ON LINE: finite fields Introduction to Finite Fields (Bill Cherowitzo) Course 373 (% Finite Fields) Algorithms (Kazumaro Aoki, Kazuo Ohta, SAC 97) Algorithms for exponentiation in finite fields (Gao, von zur Gathen, Shoup, Panario, 1999) Software GNU GMP Pari GP GMP (GNU Multiprecision) MAGMA Magma for Cryptographic Applications (Scott Contini) LiDIA FFTW KANT/KASH Lecture Notes and Courses Introduction to Analytic Number Theory (Noam Elkies, 1998)

65. Number Theory — The World Almanac For Kids Number Theory. Nature of Integers · Primes. Branch of mathematics that deals with the properties and relationships of numbers . http://www.worldalmanacforkids.com/WAKI-ViewArticle.aspx?pin=x-nu069000a&article

66. Number Theory – Technical Forex Analysis Number theory such as the Fibonacci sequence and Gann numbers can help in technical forex analysis for currency deals with EasyForex Australia. http://forex.easy-forex.com.au/learn_fx_trading/technical_analysis/approaches/nu

FOREX Making Foreign Exchange Easy Australia Information Centre Learn FX Trading Currency Trading Overview Forex Deals Components of a Forex deal ... Forex Glossary Now it's FREE - The New 2006 Forex eBook! Years of experience in Forex trading have gone into this book. Download it NOW. Australian Financial Services (AFS) Licence 246566 Home Learn FX Trading Technical Analysis Approaches - Number theory -Technical Forex Analysis Number theory – Technical Forex Analysis Fibonacci numbers Gann numbers W.D. Gann was a stock and a commodity trader working in the '50s, who reputedly made over $50 million in the markets. He made his fortune using methods that he developed for trading instruments based on relationships between price movement and time, known as time/price equivalents. There is no easy explanation for Gann's methods, but in essence he used angles in charts to determine support and resistance areas, and to predict the times of future trend changes. He also used lines in charts to predict support and resistance areas. Need personal assistance and free training?

67. Open Site - Science: Mathematics: Number Theory: Prime Numbers Prime numbers have mystified humans since the dawn of time. Much progress has been made on deciphering their unique properties and behaviours. http://open-site.org/Science/Mathematics/Number_Theory/Prime_Numbers

Enter your search terms Submit search form Web open-site.org home log in apply to edit help ... Number Theory : Prime Numbers Prime numbers have mystified humans since the dawn of time. Much progress has been made on deciphering their unique properties and behaviours. Prime Numbers Prime numbers are positive integers that can only be divided by 1 and themselves. The first few prime numbers are 2,3,5,7,11,13,17,19 and 23. Non-prime numbers are called composite numbers, except for 1, which is neither prime nor composite, and is called the unit. How many primes are there? There are an infinite number of primes. There are several proofs of this fact, the first was by Euclid. Euclid asked us to suppose that there are only a finite number of primes, say p to p n . However the product of these primes plus 1 must be divisible by some prime, yet is not divisible by any of the primes listed, assumed to be a complete set, therefore the assumption that there are only a finite number of primes is wrong, and hence there are an infinite umber of primes. Mersenne Primes Mersenne primes are named after Marin Mersenne. They are prime numbers of the form 2

68. PrimeForm For Windows If you are already a member of eGroups, you may find the PrimeForm community under Science/Math/number_theory/Prime_Numbers/Primality_Proving. http://pages.prodigy.net/chris_nash/primeform.html

PrimeForm - Probable Prime and Classical Primality Testing for 32-bit Windows This page is dedicated to hosting PrimeForm, a primality-testing program for general mathematical expressions based on the wonderful mathematical libraries of Yves Gallot, used with his express permission under license. The PrimeForm program is available for all 32-bit Windows operating systems and has been tested under Windows 95, 98, NT3.51, NT4.0, and Windows 2000. Pentium processors and higher (or equivalent) are recommended, although PrimeForm should run quite happily (but slowly!) on a 486. Other operating systems or processor versions are not available at this time. What Is PrimeForm? Download A worked example Features ... Related Pages What Is PrimeForm? PrimeForm is a program that performs the "Fermat little theorem" in order to test whether a number is a probable prime. While probable primality does not in itself prove primality, it is a valuable tool and a very quick test to establish if a number is composite. If probable primality is established, it may be possible to prove primality by further testing. In particular, PrimeForm can apply the classical "N-1" and "N+1" tests in the cases where N-1 or N+1 has many small factors. This allows PrimeForm to be used in the proof and discovery of a wide variety of forms. PrimeForm is under constant development, and more features will be added over the coming months. User feedback is an important part of this process, so if you use PrimeForm, check out the

69. HR - Automatic Theory Formation In Pure Mathematics 11. HR WORKING IN NUMBER THEORY. Subsections Encyclopedia Reinvented Sequences New Sequences Refactorables CRCM. There are many ways to break an integer http://www.dai.ed.ac.uk/homes/simonco/research/hr/number_theory.html

11. HR WORKING IN NUMBER THEORY Subsections: Encyclopedia Re-invented Sequences New Sequences Refactorables ... CRCM There are many ways to break an integer into a finite set. HR can work in number theory by using a finite decomposition of integers into one or more of the following: Triples (a,b,c) for which a=bxc . Eg. (10,5,2) Triples (a,b,c) for which a=b+c . Eg. (10,4,6) Pairs (a,b) for which b is a digit in the base 10 representation of a . Eg. (12,1), (12,2) In practice, the decomposition of the integers up to 50 are given to HR by the user. HR then uses exactly the same production rules that were developed in group theory to produce number theory concepts. The Encyclopedia of Integer Sequences HR works closely with its own copy of the encyclopedia of integer sequences, the home page for which is here: Sloane's On-Line Encyclopedia of Integer Sequences The encyclopedia contains over 47,000 integer sequences, all of which detail a different number theory concept. Each sequence has a unique "A-number", for example the sequence of prime numbers has number A000040. HR can turn its number theory concepts into integer sequences by either: Writing down the integers of a particular type, eg. 2,3,5,7,11,... (primes)

70. University Of The Witwatersrand, Johannesburg, Faculty Of Science Student Home; Student Services Alumni Alumni Home Convocation President of Convocation The University Statute Complete EXCO Members http://web.wits.ac.za/Academic/Science/

@import "/WITS_CMS_WEB/Stylesheets/WitsStaticWWW.css"; @import "/WITS_CMS_WEB/Stylesheets/CustomStyles/Acedemic.css"; @import "/WITS_CMS_WEB/Stylesheets/CustomStyles/FacultyScience/FacultyScience.css"; @import "/WITS_CMS_Web/Stylesheets/submodal.css"; @import "/WITS_CMS_WEB/Stylesheets/WitsStaticWWW.css"; @import "/WITS_CMS_WEB/Stylesheets/CustomStyles/Acedemic.css"; @import "/WITS_CMS_WEB/Stylesheets/CustomStyles/FacultyScience/FacultyScience.css"; @import "/WITS_CMS_Web/Stylesheets/submodal.css"; @import "/WITS_CMS_Web/Stylesheets/PrintPage.css"; document.domain="wits.ac.za" Wits Home Prospective Students Undergraduate SEnC Home ... Search Quick links Make a selection Index Term Dates 2008 Alumni Apply to Wits Curriculum Planning Exam Results Exam Timetables Tuition Fees IntraWits (Internal Web) Libraries Sport at Wits Wits Enterprise Wits Foundation Student Home Faculty of Science Faculty Staff Contact Schools within the Faculty ... Forms for Students University of the Witwatersrand, Johannesburg, Faculty of Science Wits Home Academic Science Faculty of Science Print this page Faculty of Science Acting Dean: Professor Rob Veale The Wits Faculty of Science is one of the leading Science Faculties in the country and has an excellent track record in both teaching and research. Staff are highly competent scientists and educators who are committed to providing quality learning environments. Our courses and qualifications are on par with the best in the world as evidenced by their recognition by prestigious major institutions abroad.

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