41. Combinatorics/Number Theory RESEARCH DIRECTORY Graph theory, combinatorial number theory. http://www.math.tamu.edu/research/research_areas/cnt.html

Combinatorics/Number Theory Directory The main subareas of interest and the faculty connected with them are listed below. Some of these faculty have additional research interests Graph Theory Arthur Hobbs Analytic Number Theory Doug Hensley Combinatoric Number Theory Itshak Borosh Combinatorial Topology Laura Anderson Toric Varieties J. Maurice Rojas Hal Schenck Algebra Applied Mathematics ... Research Directory

42. Number Theory Foundation Private philanthropic US organization for research in number theory. http://www.cerias.purdue.edu/homes/ssw/ntf/index.html

Number Theory Foundation The NTF pages have been moved to the University of Illinois. Please change your link to "http://www.math.uiuc.edu/ntf/": The new Number Theory Foundation web page.

43. Number Theory Foundation number theory Foundation. Please change your link to http//www.math.uiuc.edu/ntf/ The new number theory Foundation web page. http://www.cerias.purdue.edu/homes/ssw/ntf/

Number Theory Foundation The NTF pages have been moved to the University of Illinois. Please change your link to "http://www.math.uiuc.edu/ntf/": The new Number Theory Foundation web page.

44. Math Resources Contains links to software, professional organizations, research institutes, teaching aids, algebra, number theory, geometry, calculus, differential equations. http://comers.citadel.edu/www/math.htm

Math Resourses This page contains links to web sites with mathematically related information organized as follows: General Resource sites Professional Organizations and Research Institutes Math Teaching Resources Algebra ( including Lattice Theory), Discrete Math and Number Theory ... Other General Resource sites The MathSci Net (On-campus access) The list of Mathematics Information Servers maintained by Penn State University The Mathematics Archives WWW Server at the University of Tennessee The World-Wide Web Virtual Library: Mathematics Mathematical Resources on the Web , from Univ Florida E-Tutor Connected Learning for K-12 Centre for the Popularisation of Mathematics Interactive Math , Miscellany and puzzles Spreadsheets in Education and Mathematics (Erich Neuwirth) Spreadsheet User , a journal devoted to novel spreadsheet applications Mega Math from Los Alamos Nat. Lab MatLab in Education and MatLab Connections listing third-party tools MathSkills Newsletters from the British Dept of Education and Employment and MathSkills home page Mathematical PREprint Server System by the European Math Soc Math Placement and Gateway Exams from Michagan State University Organics Math Workshop Conference proceedings Home pages for professional organizations and research institutes: AMS , the MAA the Eisenhower National Clearinghouse and EXTEND an Internet forum on math education.

45. NT Number Theory Very large number theory section of the mathematics eprint arXiv. http://front.math.ucdavis.edu/math.NT

Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ NT Number Theory Conferences Calendar Search Authors: All AB CDE FGH ... U-Z New articles (last 12) 4 Jun math.NT/0406065 Exponents of inhomogeneous Diophantine Approximation. Yann Bugeaud , Michel Laurent . 18 pages. NT 4 Jun math.NT/0406064 Exponents of Diophantine Approximation and Sturmian Continued Fractions. Yann Bugeaud , Michel Laurent . 25 pages. NT 3 Jun math.NT/0406048 Zeros of polynomials over Cayley-Dickson algebras. S. V. Ludkovsky . 9 pages. NT GR 3 Jun math.NT/0406033 Primitive root producing quadratics. Pieter Moree . 17 pages. NT 3 Jun math.NT/0406025 Divisibility tests and recurring decimals in Euclidean domains. Apoorva Khare . 21 pages. NT 2 Jun math.NT/0406018 An uncertainty principle for arithmetic sequences. Andrew Granville , K. Soundararajan . 39 pages. NT CA 2 Jun math.NT/0406012 Vanishing of L-functions of elliptic curves over number fields. Chantal David , Jack Fearnley , Hershy Kisilevsky . AIM 2004-10. NT MP 1 Jun math.NT/0405581 Restriction theory of the Selberg sieve, with applications. Ben Green , Terence Tao . 29 pages. NT CA Cross-listings 1 Jun math.CO/0405573

46. Paul Garrett: Crypto And Number Theory Crypto and number theory. garrett@math.umn.edu my homepage Introduction to cryptology, numbertheory, algebra, and algorithms. Protocols. http://www.math.umn.edu/~garrett/crypto/

Crypto and Number Theory my homepage updated 14:50, 17 May 04] [this page is http://www.math.umn.edu/~garrett/crypto/] (No, I will not be teaching Crypto in 2004-05.) Some overheads from Fall '03 class: general info updated 14:55, 17 May 04] 08 Sept 2003 updated 10:44, 10 Sep 03] 10 Sept 2003 updated 18:15, 10 Sep 03] 15 Sept 2003 updated 14:43, 15 Sep 03] 17 Sept 2003 updated 15:10, 17 Sep 03] 22 Sept 2003 updated 18:22, 22 Sep 03] 24 Sept 2003 updated 13:14, 24 Sep 03] 29 Sept 2003 updated 15:20, 07 Oct 03] 01 Oct 2003, Vigenere updated 12:36, 01 Oct 03] 01 and 06 Oct 2003, Intro RSA, Diffie-Hellman, public-key issues updated 18:12, 06 Oct 03] 13 Oct 2003 updated 11:12, 15 Oct 03] 15-20 Oct 2003 updated 17:56, 21 Oct 03] 20 Oct 2003 updated 17:09, 20 Oct 03] 22 Oct 2003 updated 15:13, 22 Oct 03] 27 Oct 2003 updated 13:50, 28 Oct 03] 29 Oct 2003 updated 16:17, 18 Nov 03] 03 Nov 2003 updated 17:38, 04 Nov 03] comments on projects updated 14:04, 08 Nov 03] 10 Nov 2003 updated 18:58, 10 Nov 03] 17 Nov 2003 updated 12:09, 22 Nov 03]

47. Algebraic Number Theory Archive Eprint archive for research in algebraic number theory and arithmetic geometry. Algebraic number theory Archive. Welcome to the http://front.math.ucdavis.edu/ANT/

Algebraic Number Theory Archive Welcome to the (new) Algebraic Number Theory Archive, founded by Nigel Boston and Dan Grayson and currently maintained by Michael Zieve . This archive is for research in algebraic number theory and arithmetic geometry. It is being converted to an overlay for the mathematics arXiv Instructions for authors: Please contribute new submissions to the NT (Number Theory) category of the math arXiv following these submission instructions . Submissions in algebraic number theory will automatically appear here within a few days. Please send email if your arXiv article has been overlooked. Members of the mailing list receive announcements of new e-prints. To subscribe (or unsubscribe), please write to the Michael Zieve Some TeX fonts in compressed tar format, including the lams* and xy* fonts, which are needed for some of the e-prints. Papers math.AG/0405529 : 27 May 2004, Cyclic p-groups and semi-stable reduction of curves in equal characteristic p>0 , by Mohamed Saidi. math.NT/0405505 : 26 May 2004

48. Basics Of Computational Number Theory Basics of Computational number theory. Robert Campbell. Contents. 1. Introduction. This document is a gentle introduction to computational number theory. http://www.math.umbc.edu/~campbell/NumbThy/Class/BasicNumbThy.html

Basics of Computational Number Theory Robert Campbell Contents Introduction Modular Arithmetic GCD - The Euclidean Algorithm Exponentiation - The Russian Peasant Algorithm ... Galois Fields Appendices Programming Notes References Glossary Introduction This document is a gentle introduction to computational number theory. The plan of the paper is to first give a quick overview of arithmetic in the modular integers. Throughout, we will emphasize computation and practical results rather than delving into the why. Simple programs, generally in JavaScript, are available for all of the algorithms mentioned. At the end of the paper we will introduce a the Gaussian Integers and Galois Fields and compare them to the modular integers. Companion papers will examine number theory from a more advanced perspective. Modular Arithmetic Modular arithmetic is arithmetic using integers modulo some fixed integer N . Thus, some examples of operations modulo 12 are: 7 + 7 = 14 = 2 (mod 12) 5 * 7 = 35 = 11 (mod 12) Further examples can be generated and checked out with the following short programs. Note that, as JavaScript cannot compute with integers larger than 20 digits, the largest modulus allowed is 10 digits. (mod (mod Among the basic operations we have missed the division operator. If we were working in the integers we would almost never be able to define a quotient (unless the answer is itself an integer). In the modular integers we can often, but not always, define a quotient:

49. Magma Documentation -- Moved! WEB DI TEORIA DEI NUMERI (SITO ITALIANO) Translate this page Things of Interest to Number Theorists). Ricerca nel Web di Teoria dei Numeri di Roma (Search the number theory Web Pages in Rome). http://www.maths.usyd.edu.au:8000/comp/magma/Overview.html

The Magma documentation has moved Please go to the new Magma front page You should update any bookmarks or links.

50. DESCRIPTIONS OF AREAS/COURSES IN NUMBER THEORY, LECTURE NOTES s of areas/courses in number theory, lecture notes. Return to Menu page. Return to number theory Web page. Last modified 3rd April 2004....... http://www.maths.uq.edu.au/~krm/N4.html

Descriptions of areas/courses in number theory, lecture notes Mathematics Subject Classification, 11-XX Eric Weisstein's World of Mathematics (Number Theory section) ABC conjecture Aliquot Sequences, Perfect, Amicable Numbers Algebraic Number theory Analytic Number Theory ... Recreations in Number Theory The ABC Conjecture It's As Easy As abc , Andrew Granville and Thomas J. Tucker, AMS Notices, November 2002, The ABC Conjecture Home Page (Abderrahmane Nitaj) Arithmetical Geometry Topics in Arithmetical Geometry (Outline of a course by Shou-Wu Zhang - pdf) Grothendieck's SGA Differential algebraic geometry, a scheme theoretic approach (lecture notes by Henri Gillet, 1998) Lecture notes on the local Langlands correspondence (Michael Harris) Modular Mahler Measures , slides by Fernando Villegas Course notes on Heights , (pdf 720K) (Nils-Peter Skoruppa) Diophantine geometry in characteristic p: a survey , (Felipe Voloch) Draft of PCMI Lecture Notes on Open Questions in Arithmetic Algebraic Geometry (Alice Silverberg) (ps file 803K) Lecture Notes from H.L. Lenstra's Algebraic Curves Math 274, 1995

51. Tools On Number Theory Web 整数論関連のコンピュータツールのアーカイブとリンク集。「代数学と計算」研究集会の惠報もある。 http://tnt.math.metro-u.ac.jp/index.j.html

English Tools on Number Theory Web <%8(B <%899?7MzNr(B TNT$B$K$D$$$F(B TNT Mailing List archive TNT FTP <0%_%i! <%5%$%H0lMw(B ... $BG[I[J*(B ] [TNT$B$K$D$$$F(B] $Date: 2004/06/03 05:48:30 $+ 9:00:00 (JST)

52. LiDIA - A Library For Computational Number Theory Based at the Darmstadt University of Technology, Germany. LiDIA is a C++ library for computational number theory which provides a collection of highly optimized implementations of various multiprecision data types and timeintensive algorithms. http://www.informatik.tu-darmstadt.de/TI/LiDIA/

A C++ Library For Computational Number Theory Main Page News Introduction Online Documentation System Requirements ... Activate LiDIA's Remote Control (JavaScript) News May 2004 LiDIA 2.1.1 released LiDIA 2.1.1 is available for download The LiDIA 2.1 release of yesterday contained a bug that broke LiDIA on some platforms. We also encountered a defect in the standard library shipping with g++ 2.95.2 that caused builds with this compiler to fail. LiDIA 2.1 is withdrawn. LiDIA 2.1.1 brings a long list of bugfixes that accumulated since LiDIA 2.1pre7. Other changes include: Unless you explicitly configure LiDIA with `enable-shared', only static LiDIA libraries are built. If you build LiDIA with g++, then the compiler's command line option `-fno-implicit-templates' is no longer used. LiDIA can be built atop the current cln release (1.1.6) again. Jochen Hechler contributed a new primality proofer (in the GEC package). Please refer to the release notes for an exhaustive list of changes and the known problems in LiDIA 2.1. Older News More news and facts about LiDIA can be found on LiDIA's NEWS page Introduction LiDIA is a C++ library for computational number theory which provides a collection of highly optimized implementations of various multiprecision data types and time-intensive algorithms. LiDIA is developed by the LiDIA Group at the Darmstadt University of Technology.

53. NUMBER THEORY FTP SITES/CALCULATOR PROGRAMS/ARCHIVES number theory ftp sites/calculator programs/archives. Algebraic number theory Archives; finite rings. number theory Tables. Iwasawa invariants http://www.maths.uq.edu.au/~krm/N1.html

Number theory ftp sites/calculator programs/archives Algebraic Number Theory Archives apfloat : A C++ High Performance Arbitrary Precision Arithmetic Package by Mikko Tommila Ian Connell's elliptic curve calculator APECS ARIBAS . This is an interactive interpreter for big integer arithmetic and multi-precision floating point arithmetic with a Pascal/Modula like syntax. ARIBAS is used for the examples of number theoretic algorithms in the book Algorithmische Zahlentheorie , Otto Forster, Vieweg 1996 BC (the exact arithmetic Unix calculator program) BC bc number theory programs (Keith Matthews) BCMath/PHP number theory programs (Keith Matthews) The CAGE project CALC (Keith Matthews' number theory calculator) Number theory programs for Casio Graphic Calculators (Roy MacLean) Class polynomials of CM fields (Annegret Weng) CPG , a class polynomial generator (Marcel Martin) Computations on curves of genus2 and their jacobians (Paul Van Wamelen) Critical Strip Explorer 0.6 (Matthew Watkins and Raymond Manzoni) A Java applet which allows users to 'manually' explore the behaviour of the Riemann zeta function in and around the critical strip Curves of Genus 2 ftp site (Victor Flynn) CYCLOPROV , a LiDIA based C++ package for primality-proving using cyclotomy (DEC Alpha only) (Preda Mihailescu) A Database for Number Fields Discriminant Exponent Calculator (John Jones) ECPP The ECMNET Project : Find a factor of 50 digits or more by ECM EIS , computing Fourier coefficients of Eisenstein series attached to lattices, (M. Kuss and J. Bruinier)

54. Number Theory Index History Topics Numbers and number theory Index. Number systems in ancient civilisations, Other number theory. Arabic number systems. Babylonian number systems. http://www-gap.dcs.st-and.ac.uk/~history/Indexes/Number_Theory.html

History Topics: Numbers and Number Theory Index Number systems in ancient civilisations Other number theory Arabic number systems Babylonian number systems Egyptian number systems Greek number systems ... Search Form JOC/EFR January 2004 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Number_Theory.html

55. Math 259: Introduction To Analytic Number Theory (Spring 1998) Lecture notes for Math 259 Introduction to Analytic number theory (Spring 1998) If you find a mistake, omission, etc., please let me know by email. http://www.math.harvard.edu/~elkies/M259.98/

Lecture notes for Math 259: Introduction to Analytic Number Theory (Spring 1998) If you find a mistake, omission, etc., please let me know by e-mail. The orange ball marks our current location in the course. For an explanation of the background pattern, skip ahead to the end of the page. plan.ps and intro.ps : administrivia and philosophy/examples elem.ps : Elementary methods I: variations on Euclid euler.ps : Elementary methods II: The Euler product for s>1 and consequences dirichlet.ps : Dirichlet characters and L-series; Dirichlet's theorem modulo the non-vanishing of L-series at s=1 chebi.ps click here For Erdos' simplification of Cebysev's proof of the "Bertrand Postulate": there exists a prime between x and 2x for all x>1. Adapted from Hardy and Wright, pages 343-344. psi.ps zeta1.ps gamma.ps prod.ps : Functions of finite order: Hadamard's product formula and its logarithmic derivative zeta2.ps free.ps pnt.ps : Conclusion of the proof of the Prime Number Theorem with error bound; some consequences and equivalents of the Riemann Hypothesis. Here's a bibliography lsx.ps

56. The School Of Mathematics UEA: number theory research. http://www.mth.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.

57. Algorithmic Number Theory: Tables And Links Algorithmic (aka Computational) number theory Tables, Links, etc. Algorithmic number theory? What s that? Back to general math page http://www.math.harvard.edu/~elkies/compnt.html

Algorithmic (a.k.a. Computational) Number Theory : Tables, Links, etc. Tables of solutions and other information concerning Diophantine equations [equations where the variables are constrained to be integers or rational numbers]: Trinomials with unusual Galois groups ( x x x x x x x x +567, etc.) (Supporting computational data for Nils Bruin's theorem here Elliptic curves of large rank and small conductor arXiv preprint; joint work with Mark Watkins; to appear in the proceedings of ANTS-VI (2004)): Elliptic curves over Q of given rank r up to 11 of minimal conductor or discriminant known; these are new records for each r in [6,11]. We describe the search method tabulate the top 5 (bottom 5?) such curves we found for r in [5,11] for low conductor, and for r in [5,10] for low discriminant. Data and results concerning the elliptic curves ny =x -x arising in the ``congruent number'' problem: Transparencies for ANTS-V lecture, in PS and PDF added 7/2002 All for which the curve has analytic rank at least 3, listed and used; , under an additional conjecture;

58. Course 311 - Abstract Algebra Lecture notes by David Wilkins, Trinity College, Dublin. Topics in number theory; Group Theory; Galois Theory. http://www.maths.tcd.ie/~dwilkins/Courses/311/

Course 311 - Abstract Algebra The lecture notes for course 311 ( Abstract algebra ), taught at Trinity College, Dublin, in the academic year 2001-02, are available here. The course consists of three parts:- Part I: Topics in Number Theory DVI PDF PostScript Part II: Topics in Group Theory DVI PDF PostScript Part III: Introduction to Galois Theory DVI PDF PostScript The following handouts were also distributed in the academic year 2001-02: A collection of problems DVI PDF PostScript The resolvent cubic of a quartic polynomial DVI PDF PostScript dwilkins@maths.tcd.ie ... Trinity College , Dublin 2, Ireland dwilkins@maths.tcd.ie

59. Elementary And Analytic Number Theory Elementary and Analytic number theory. by WWL Chen. This set of notes has been renamed and moved. For access, please click here. http://www.maths.mq.edu.au/~wchen/lneantfolder/lneant.html

Elementary and Analytic Number Theory by WWL Chen This set of notes has been renamed and moved. For access, please click here

60. Mathematical Induction - Math Induction Problems And Puzzles A page of uncommon problems, most closely connected with number theory. http://www.geocities.com/jespinos57/induction.htm

SEE NEW SECTION AT THE END OF PROBLEM 30 MATHEMATICAL INDUCTION MATHEMATICAL INDUCTION Math Links PDF format Naoki Sato's Solutions PDF Spanish Version connected with Number Theory.Some properties may be proved in different ways.For more exercises, problems, puzzles, games, math riddles, brain teasers, etc. to see Math Links (not only of math induction). PROBLEM 1 Let : p-1 k=1 k n(p-1)+1 p-1 k=1 ((k )/2) - p(p-1)(n(p-1)+1)/2 Prove by induction that F(n) is divisible by p , for all integers n Hint PROBLEM 2 Use mathematical induction to prove the following: FIB(n) (FIB(n+2)=FIB(n+1)+FIB(n); FIB(1)=1,FIB(2)=1. Fibonacci sequence) Hint PROBLEM 3 Prove the following in more ways than one : n+1 FIB(n) (FIB(n+2)=FIB(n+1)+FIB(n); FIB(1)=1,FIB(2)=1. Fibonacci sequence ) Hint PROBLEM 4 M i=1 a i M i=1 a i kbc are divisible by b c i are relatively prime with respect to b and c). Let : M i=1 a i 1+(b-1)(c-1)n Prove by induction that : F(n) is divisible by b c ,for all integers n Solution PROBLEM 5 Let a, b, c be three positive integers where c= a + b . Let p be an odd factor of a +b +c (a +b +c ) is divisible by p.

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