21. The School Of Mathematics UEA: Number Theory research. http://www.uea.ac.uk/~h090/number_theory.html

Research in Number Theory at UEA Number theory is a broad, all-encompasing kind of subject that uses tools from many diverse areas. But it does not mean you need to be an egg-head to do original research. The way into many outstanding problems can often be at quite a low level. At UEA, the research centres around two different areas. (1) Diophantine Equations (2) Elliptic Curves. For (1), we look at special classes of equations where there are known to be infinitely many integer solutions. We look at special properties of these solutions and try to study their finer properties such as their location in `space' or their divisibilty by primes. For a good introduction, try Alan Baker's book "An Introduction to the Theory of Numbers". You could also have a look at some of the papers on my list of publications. Interest looks set to rise in (2) owing to Wiles' proof of Fermat' Theorem. Recently I have looking at inter-actions between the arithmetic of elliptic curves and dynamical systems. The approach is fairly down-to-earth although the language of algebraic geometry is becoming increasingly used. For an interesting explanation of the use of elliptic curves in number theory try Alf van der Poorten's book "Notes on Fermat's Last Theorem". You could also look at some of my recent papers on elliptic curves in my list of publications.

22. Brainflux: Axioms Of Number Theory Number theory is a theory about the integers, a set which we call where . The operations defined on this set are addition, multiplication, and the ordering http://www.brainflux.org/Math/Number_Theory/Axioms_of_Number_Theory/index.html

Overview Number theory is a theory about the integers, a set which we call where . The operations defined on this set are addition, multiplication, and the ordering relation "less than." What follows are the basic properties of the integers Axiom: Closure Property of Addition If then Axiom: Closure Property of Multiplication If then Axiom: Commutative Property of Addition If then Axiom: Commutative Property of Multiplication If then Axiom: Associative Property of Addition If then Axiom: Associative Property of Multiplication If then Axiom: Distributive Property of Multiplication over Addition If then Axiom: Additive Identity Property is a special number with the property: If then Axiom: Multiplicitive Identity Property is a special number with the property: If then Axiom: Additive Inverse Property If then where In other words, there is another integer in which we'll call When you add this other integer to the origional, you get back , the additive identity. We introduce the following familiar notation: If then is written as Axiom: Zero Property of Multiplication If then Axiom: Cancelation Property of Addition If and then Axiom: Cancelation Property of Multiplication If and then Axiom: Trichotomy Law If , then exactly one of the following statements is true: (i) (ii) (iii) Axiom: Properties of Inequality (i) If and , then (ii) If , and , then (iii) If , and , then Axiom: Well Ordering Property Every non-empty set of positive integers contains a least element. More rigorously: If

23. THINGS OF INTEREST TO NUMBER THEORISTS Jul 15, 2010 Computational Number Theory programs and number theory tables Number theory centres Number theory conferences, new and old http://www.numbertheory.org/ntw/number_theory.html

Things of interest to Number Theorists Computational Number Theory programs and number theory tables Number theory centres Number theory conferences, new and old Number theory research programs ... Publishers/Booksellers/Libraries Number theory books: 1993 or before Number theory listservers and archives Biographies of past number theorists and various items of historical interest The Number Theory Foundation Mathematical gateways to the World-Wide Web Return to Number Theory Web page Last modified 15th July 2010

24. Number Theory Tutorials, lessons, and resources to support number theory in mathematics. http://math.about.com/od/numbertheory/Number_Theory.htm

zWASL=1 zGL='0';zGR='ca-about-radlink'; zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') zDO=0 Home Education Mathematics Mathematics Search Mathematics Worksheets Subjects Filed In: Math Help and Tutorials Tutorials, lessons, and resources to support number theory in mathematics. Basics of Computation Number Theory A good introductory site. Includes interactive tutorials and samples. Brun's Constant In 1919 Brun showed that the sum of the reciprocals of the twin primes converges to a sum. Find out more... zSB(3,3) Fibonacci Numbers (University) It began with Fibonacci's Rabbits and how fast they could breed! Here you will find over 200 resources to support Fibonacci Numbers and the Golden Section. Glaisher-Kinkelin Constant Stirling's formula provides a well-known estimate for large factorials for this number theory constant. Largest Known Primes Introduction to the Primes, a list of the Primes and Euclid's Proof of the Infinitude of Primes. Number Theory Help This site features a collection of calculators, tables and articles about number theory. It also includes an applet that is able to factor big numbers and a quadratic diophantine equation solver, among other things. Number Theory Top Picks from your guide for texts and resources for self study in Number Theory. Items for the beginner to the graduate level math student.

25. Number Theory - MathWiki Nov 5, 2006 Number theory Problems 1,3,5,7. 315,,715115 -. Retrieved from http//web. gnowledge.org/wiki/index.php/number_theory http://web.gnowledge.org/wiki/index.php/Number_theory

Number theory From MathWiki edit Number theory Problems edit Question 1 Exhibit 3 integers that are relatively prime but not relatively prime in pairs. edit Answer 1 Retrieved from " http://web.gnowledge.org/wiki/index.php/Number_theory Views Article Discussion Edit History Personal tools Create an account or log in Navigation Main Page Algebra Geometry Trigonometry ... Help Search Toolbox What links here Related changes Special pages This page was last modified 23:16, 5 Nov 2006. This page has been accessed 4056 times. About MathWiki A project of Homi Bhabha Centre for Science Education , TIFR

26. Number Theory - Includipedia, The Inclusionist Encyclopaedia Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that http://www.includipedia.com/wiki/Number_theory

Number theory From Includipedia, the inclusionist encyclopedia Jump to: navigation search Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. ( See the list of number theory topics The term " arithmetic " is also used to refer to number theory. This is a somewhat older term, which is no longer as popular as it once was. Number theory used to be called the higher arithmetic , but this too is dropping out of use. Nevertheless, it still shows up in the names of mathematical fields ( arithmetic functions arithmetic of elliptic curves fundamental theorem of arithmetic ). This sense of the term arithmetic should not be confused either with elementary arithmetic , or with the branch of logic which studies Peano arithmetic as a formal system Mathematicians working in the field of number theory are called number theorists Image:Ulam 1.png

27. Number Theory Fibonacci Numbers in Nature Dr. Math FAQ Pascal s Triangle Pascal s Triangle Tower of Hanoi Online. MORE ODDITIES OF NUMBER THEORY http://lindalobue.com/number_theory.htm

Prime Time Ultimate Celebrity Number ... Think you know all there is to know about 0, 1, 2, 3...,? Prime Numbers Playing the Factor Game (vs. the Computer) FAQ: Dr. Math on Primes The Prime Pages Amby's Primes Tutorial GoMath Mini-Lesson on Primes Sieve of Eratosthenes and more! Prime Histor y Divisibility Tests Math League: List of Tests Mrs. Glosser's Math Goodies does Divisibility Tests Programming Art's Basic Facts Kids Numbers ... Everyday Math Guide to Algorithms Prime Factorization Amby's Prime Factorization Math Steps: What is It? PurpleMath: Factoring Numbers Math Spoken Here Order of Operations Ask Dr. Math FAQ: Order of Operations The Language of Algebra: Order of Operations (4 Levels) eMath Lab: Order of Operations The Purple Page: Order of Operations Mrs. Glosser's Math Goodies... Lesson on Order of Operations Lesson on O of O including Exponents Exponents from math.com Square Roots from math.com ... Mrs. Glosser's Math Goodies: Exponents Multiple (LCM) 4 Steps to GCF and 4 Steps to LCM Algebra.Helps Teaches GCF, including Variables AAA Math does LCM and AAA Math does GCF Amby does LCM (with lots of practice!)

28. History Of Number Theory - Mathematics Department - Welcome www.math.rutgers.edu/~mjraman/number_theory.pdf SimilarNumber Theory IndexNumber systems in ancient civilisations, Other number theory. Arabic number systems http//www-history.mcs.st-andrews.ac.uk/Indexes/number_theory.html. http://www.math.rutgers.edu/~mjraman/number_theory.pdf

29. Department Of Mathematics At The University Of Georgia Mar 22, 2010 Number Theory and Arithmetic Geometry Group Our number theory group is complemented by a large group in algebraic geometry, http://www.math.uga.edu/research/number_theory.html

Number Theory and Arithmetic Geometry Group Permanent faculty and their fields of interests. Pete L. Clark Assistant Professor, Ph.D. Harvard 2003. Arithmetic of abelian varieties; torsion points, endomorphism algebras, Weil-Chatelet groups. Modular curves and Shimura curves. Period-index problems. Pointless varieties and the (anti-) Hasse principle. Geometric approaches to the inverse Galois problem. Jonathan Hanke Assistant Professor, Ph. D. Princeton, 1999 . Arithmetic of Quadratic forms and their connections to Automorphic Forms, with an emphasis on computation. Topics include Local-Global principles, Local Densities, Mass Formulas, Class Numbers, Explicit Finiteness Theorems, and Computing all integers represented by a given Quadratic Form. Daniel Krashen Assistant Professor, Ph.D University of Texas 2001 , Finite dimensional division algebras, quadratic forms, and their interplay with algebraic groups and homogeneous varieties. Algebraic cycles and motives. Moduli and configuration spaces.

30. CAT Math - Sample Question - Number Theory : Ascent Education - Best MBA Prepara The given question is a question on factors/divisors of a number in the topic number theory. A concept that gets tested frequently in tests such as the CAT, http://questions.ascenteducation.com/iim_cat_mba_free_sample_questions_math_quan

Number theory, factors, divisors of an integer - IIM CAT preparation, XAT, PGSEM, TANCET practice problems LATEST NEWS CAT '10 batch @ Chennai Enrol for CAT 10 Mock CATs Ascent Success Stories TANCET Classes @ Chennai ... Contact us Ascent's Courses CAT Classroom Chennai TANCET 2010 Classes XAT Classes CAT Correspondence India ... Ascent Success Stories Contact Us info@ascenteducation.com Postal Address You are here: Home CAT Questions Number Theory Factors and divisors Factors/divisors - Quant/Math - CAT 2010 The given question is a question on factors/divisors of a number in the topic number theory. A concept that gets tested frequently in tests such as the CAT, XAT and sometimes in TANCET. Question If both 11 and 3 are factors of the number a * 4 , then what is the smallest possible value of a? Correct choice . Correct Answer - Explanatory Answers is a factor of the given number. The number does not have a power or multiple of 11 as its factor. Hence, "a" should include 11 is a factor of the given number. 6 is a part of the number. 6

31. Factoring Xn 1 Cyclotomic And Aurifeuillian Polynomials File Format PDF/Adobe Acrobat Quick View http://www.math.umn.edu/~garrett/m/number_theory/aurifeuillian.pdf

32. Number Theory File Format PDF/Adobe Acrobat Quick View http://www.cs.uiuc.edu/class/fa10/cs173/Lectures/number_theory.pdf

33. Number Theory Group | School Of Mathematical Sciences Its five permanent members are working in various parts of number theory, which use structures, methods and tools from algebra, geometry and analysis. http://www.maths.nott.ac.uk/research/pure_mathematics/number_theory/

Home Staff Directory Contact the School Admissions Admissions Undergraduate Postgraduate Taught Postgraduate Research ... Schools and Colleges Research Research Applied Mathematics Pure Mathematics Statistics ... Conferences Current Undergraduates Current Undergraduates News and events Careers Undergraduate Student Handbook ... School Office Hours and Locations Current Postgraduates Current Postgraduates News and Events Careers Research Student Handbook [PDF] ... School Office Hours and Locations For Staff For Staff Staff Handbook Information for Contract Staff Staff Forms ... Division of Pure Mathematics Number Theory Group Pages in this Section: People Areas of Research PhD Projects Welcome to the Nottingham number theory group, one of the largest number theory groups in the UK. Its five permanent members are working in various parts of number theory, which use structures, methods and tools from algebra, geometry and analysis. These include arithmetic geometry, analytic number theory, computational number theory, and interaction of number theory with algebraic K-theory, functional analysis, noncommutative analysis, model theory, group theory, mathematical physics. The number theory group includes several research visitors, both junior and senior, see

34. Lesson 1 NUMBER THEORY - WikiEducator File Format PDF/Adobe Acrobat http://wikieducator.org/images/7/7f/Lesson_1-number_theory.pdf

35. Discrete Mathematics/Number Theory - Wikiversity Jun 14, 2010 There you can find information, media and quotations to develop Discrete mathematics/Number theory as an educational resource. http://en.wikiversity.org/wiki/Discrete_mathematics/Number_theory

Discrete mathematics/Number theory From Wikiversity Jump to: navigation search Please help develop this page This page was created, but so far has little content . Please help expand it. See the editing tutorial and the MediaWiki syntax reference for guidance. To help you get started, there references below to other Wikimedia projects. There you can find information media and quotations to develop "Discrete mathematics/Number theory" as an educational resource. Please do not simply copy-and-paste large sections from other projects. Links in the blue box will help you classify this page by subject, educational level, and resource type. Search for Discrete mathematics/Number theory on Wikipedia Search Wikimedia Commons for images, sounds and other media related to: Discrete mathematics/Number theory Search for Discrete mathematics/Number theory on the following projects: Wikisource Wikinews Wikiquote Wiktionary ... Lost on Wikiversity? Please help by choosing project boxes to classify this resource by: subject educational level resource type Considered by many as the most beautiful branch of mathematics, Number Theory is the study of the properties of numbers, especially integers and natural numbers. edit See also Topic:Number Theory Introduction to Math for Computer Programming Introductory Discrete Mathematics for Computer Science Topic:Discrete Mathematics for Computer Science Discrete mathematics/Number theory Topic:Discrete mathematics Topic:Discrete Maths for Olympiads Computer science program Topic:Discrete Mathematics for Computer Science ... School:Mathematics Retrieved from "

36. Wapedia - Wiki: Number Theory Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. (See the list of number theory http://wapedia.mobi/en/Number_theory

Wiki: Number theory Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. ( See the list of number theory topics The terms " arithmetic " or "the higher arithmetic" as nouns are also used to refer to elementary number theory. These are somewhat older terms, which are no longer as popular as they once were. However the word "arithmetic" is popularly used as an adjective rather than the more cumbersome phrase "number-theoretic", and also "arithmetic of" rather than "number theory of", e.g. arithmetic geometry arithmetic functions arithmetic of elliptic curves In this graphic the natural numbers are arranged as in the Ulam spiral and a disk of size proportional to the number of divisors is drawn for each number: this yields an intriguing, yet not fully understood pattern. Contents: 1. Fields

37. Number Theory/partition - Mathematics Wiki Oct 30, 2007 This article incorporates material from Partition (number theory) on Wikipedia, which is licensed under the GFDL. http://www.mathematics.thetangentbundle.net/wiki/Number_theory/partition

partition From Mathematics wiki Number theory Jump to: navigation search The partition of a positive integer is a way of writing as a sum of positive integers Contents Partition function Generating function Number of partitions of length N Rerefences Partition function The partition function is the number of partitions of Generating function Number of partitions of length N We would like to determine the number of ways of partitioning into exactly integers. Consider the infinite product When distributed , the number of ways can appear is given by the coefficient of . Since is just a bookkeeping device , we may assume that , and use the geometric series result to find that Then Rerefences This article incorporates material from Partition (number theory) on Wikipedia, which is licensed under the GFDL Partition (number theory) , from Wikipedia , The free encyclopedia ; Retrieved August 7, 2007. Thermal Physics (2nd Edition) ISBN 978-0716710882 Retrieved from " http://www.mathematics.thetangentbundle.net/wiki/Number_theory/partition Category Wikipedia sourced articles Views Page Discussion View source History Personal tools Log in / create account Navigation Main Page TheTangentBundle Community portal Editing guidelines ... Support this project Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 04:29, 30 October 2007.

38. Number Theory Q What topic within number theory do you find most interesting and intriguing? From complex numbers to knot theory to the search for large perfect numbers, what do You http://www.kosmix.com/topic/number_theory

Kosmix One sec... we're building your guide for Number Theory document.k_start_apptier = "Oct 30 23:33:47.273496"; kapp.assignCol($('ads_banner_top'), 'topnav_container'); Number theory Overview Shopping Images Video ... Reference kapp.nav_menu_container = $('refine_nav').down(".navs_container"); kapp.assignCol($('refine_nav'), 'topnav_container'); kapp.assignCol($('uc_kosmixarticles_shadow'), 'right_container'); Articles for Number theory The Kosmix Community Number theory is pure mathematics. This branch of math studies numbers and integers which are the positive and negative numbers including all fractions and decimals. There are a number of fields and methods used to study questions raised in this field. In elementary number theory numbers are studied in regard to questions such as divisibility and greatest common divisor. Important discoveries in this area are Euler's theorem and the Chinese remainder theorem; also, study and applications of Fibonacci numbers. Another branch is the analytic number theory. In this area of study ... see more Number theory is pure mathematics. This branch of math studies numbers and integers which are the positive and negative numbers including all fractions and decimals. There are a number of fields and methods used to study questions raised in this field.

39. Elementary Number Theory File Format PDF/Adobe Acrobat Quick View http://modular.math.washington.edu/edu/fall05/168/refs/stein-number_theory.pdf

40. Definition:Congruence (Number Theory) - ProofWiki Jul 5, 2010 DefinitionCongruence (Number Theory) Retrieved from http//www.proofwiki. org/wiki/DefinitionCongruence_(number_theory) http://www.proofwiki.org/wiki/Definition:Congruence_(Number_Theory)

Definition:Congruence (Number Theory) From ProofWiki Jump to: navigation search Contents General Definition Definition by Equivalence Relation Definition by Modulo Operation Definition by Integral Multiple ... edit General Definition Let edit Definition by Equivalence Relation We define a relation on the set of all This relation is called congruence modulo , and the real number is called the modulus If , we write: and say " is congruent to modulo Similarly, if , we write: and say " is not congruent (or incongruent to modulo We have that congruence modulo is an equivalence relation edit Definition by Modulo Operation Let be defined as the modulo operation Then: edit Definition by Integral Multiple Equivalently, is congruent to modulo iff their difference is an integral multiple of edit Definition for Integers The concept of congruence is usually considered in the integer domain. Let Then we define congruence modulo as the relation on the set of all The other definitions also apply under the same restriction. Thus we see that is congruent to modulo if their difference is a multiple of This gives us an alternative method of defining congruence modulo an integer edit Equivalence of Definitions The definitions as given here are equivalent edit Residue A residue of modulo is another word meaning remainder , and means any number congruent to modulo edit Sources Allan Clark Elements of Abstract Algebra T.S. Blyth

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