1. NUMBER THEORY WEB (AUSTRALIAN SITE) Things of interest to number theorists collected by Keith Matthews http://www.maths.uq.edu.au/~krm/web.html

Number Theory Web (Australian Site) Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages in Brisbane The American mirror site is at University of Georgia, Athens, USA The Italian mirror site The British mirror site is at University of Cambridge, UK The Japanese mirror site is at University of Electro-Communication, Tokyo The Indian mirror site is at Harish-Chandra Research Institute, Allahabad Created and maintained by Keith Matthews , Dept of Mathematics, University of Queensland, Brisbane, Australia Suggestions for additions or improvements are welcome. Email: krm@maths.uq.edu.au Last modified 30th January 2003

2. Algebraic Number Theory Archives Access the preprint archives for papers in algebraic number theory and arithmetic geometry. Includes submission instructions. 375 January 5, 2003, padic Arakelov theory, by Amnon Besser. 20, 2002, Some congruences on prime factors of class number of algebraic extensions K/Q (update), by Roland Queme. http://www.math.uiuc.edu/Algebraic-Number-Theory

Algebraic Number Theory Archives Date: Wed, 8 Jan 2003 12:03:33 -0600 (CST) To: Algebraic-Number-Theory@listserv.uiuc.edu Subject: Algebraic-Number-Theory preprint archives I shall no longer be managing the Algebraic Number Theory preprint archives. The web site is now frozen and is not accepting new submissions and subscriptions. Michael Zieve has kindly agreed to assume control, with the help of Greg Kuperberg, and new submissions should be directed to the new URL for the archive, http://front.math.ucdavis.edu/ANT/ Your subscription will continue, unless you choose otherwise. I thank Dan Grayson for setting up the archives and his patient help with technical issues, and Michael and Greg for volunteering to take on this work. Nigel Boston http://www.math.wisc.edu/~boston/ Welcome to the preprint archives for papers in Algebraic Number Theory and Arithmetic Geometry. Use the Find facility of your browser on this page, or search: Our mirror site in the United Kingdom , set up by Richard Pinch. Our main site in the USA Instructions for authors Instructions for joining the mailing list . Members of the mailing list receive announcements of preprints when they are deposited in the archives. Some TeX fonts , stored in a tar image compressed with gzip, including the lams* and xy* fonts, which are needed for some of the preprints.

3. 11: Number Theory 11 number theory number theory is one of the oldest branches of pure mathematics, and one of the largest. Of course, it concerns questions about numbers, usually meaning whole numbers or rational numbers (fractions). Elementary number theory involves divisibility among integers the division "algorithm", the Euclidean algorithm (and http://www.math.niu.edu/~rusin/known-math/index/11-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11: Number theory Introduction Number theory is one of the oldest branches of pure mathematics, and one of the largest. Of course, it concerns questions about numbers, usually meaning whole numbers or rational numbers (fractions). Elementary number theory involves divisibility among integers the division "algorithm", the Euclidean algorithm (and thus the existence of greatest common divisors), elementary properties of primes (the unique factorization theorem, the infinitude of primes), congruences (and the structure of the sets Z /n Z as commutative rings), including Fermat's little theorem and Euler's theorem extending it. But the term "elementary" is usually used in this setting only to mean that no advanced tools from other areas are used not The remaining parts of number theory are more or less closely allied with other branches of mathematics, and typically use tools from those areas. For example, many questions in number theory may be posed as Diophantine equations equations to be solved in integers without much preparation. Catalan's conjecture are 8 and 9 the only consecutive powers? asks for the solution to

4. NUMBER THEORY WEB (AMERICAN SITE) number theory Web. (American Site). http://www.math.uga.edu/~ntheory/web.html

Number Theory Web (American Site) Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages in Athens, Georgia This site is a mirror of the Australian site at University of Queensland, Brisbane, Australia The Italian mirror site The British mirror site is at University of Cambridge The Japanese mirror site is at University of Electro-Communication, Tokyo The Indian mirror site is at the Harish-Chandra Research Institute, Allahabad (courtesy of Shripad Garge Created and maintained by Keith Matthews , Dept of Math, University of Queensland, Brisbane, Australia Suggestions for additions or improvements are welcome Email: krm@maths.uq.edu.au Last modified 19th December 2002

5. Mathematics Archives - Topics In Mathematics - Number Theory Aesthetics of the Prime Sequence. Algorithmic number theory Bibliography. AMS - Fermat's Last Theorem http://archives.math.utk.edu/topics/numberTheory.html

Topics in Mathematics Number Theory Absolute Primes ADD. KEYWORDS: Article, Repunits SOURCE: Arkadii Slinko, University of Auckland and Mathematics Olympiad Learning Centre TECHNOLOGY: Adobe Acrobat Reader Aesthetics of the Prime Sequence Algorithmic Number Theory - Bibliography AMS - Fermat's Last Theorem ADD. KEYWORDS: Number theory, Fermat's Last Theorem, History, Reports, Articles AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases Arithmetic properties of Binomial Coefficients ADD. KEYWORDS: Elementary Number Theory, Lucas' Theorem, Pascal's triangle via cellular automata, Bernoulli numbers and polynomials, Theorems of Morley and Emma Lehmer and their generalizations, Some useful p-adic numbers Bernoulli (Beta) and Integer Part Sequences ADD. KEYWORDS: Article SOURCE: Rod Nillsen, Keith Tognetti and Graham Winley, University of Wollongong TECHNOLOGY: Adobe PDF, Postscript and DVI readers

6. NUMBER THEORY WEB (UK SITE) number theory Web. (UK Site) http://www.dpmms.cam.ac.uk/Number-Theory-Web

Number Theory Web (UK Site) Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages in Cambridge, UK This site is a mirror of the Australian site at Brisbane, Australia The American mirror site is at University of Georgia, Athens, USA, courtesy of Andrew Granville The Italian mirror site Francesco Pappalardi The Japanese mirror site is at the University of Electro-Communication, Tokyo (courtesy of Masanari Kida The Indian mirror site is at the Harish-Chandra Research Institute, Allahabad (courtesy of Shripad Garge Maintained by Keith Matthews , Dept of Math, University of Queensland, Brisbane, Australia Suggestions for additions or improvements are welcome. Contact me by email at krm@maths.uq.edu.au This page last modified 12th December 2001

7. Number Theory Files For David Eppstein I have implemented a number of simple numbertheoretic algorithms for my own amusement, and provide them here on the net. Source code is available for producing similar figures. Other number theory on the web http://www.ics.uci.edu/~eppstein/numth

Number-Theoretic Hacks I have implemented a number of simple number-theoretic algorithms for my own amusement, and provide them here on the net. Egyptian Fractions algorithms and references. This notebook for Mathematica 2.2/Macintosh (also available in HTML format) describes and implements a number of different algorithms for representing rational numbers as sums of distinct unit fractions. C++ implementation of J.H.Conway's "nimber" arithmetic. Conway's nimbers (used in combinatorial game theory ) form an infinite field of characteristic two, with a natural binary representation in which truncation to a fixed number of bits produces finite subfields GF[2^2^k]. The algorithms in this file implement nimber multiplication, square root, and other functions, using O(k 3^k) bit operations. This bound is somewhat worse than what one can achieve for the more standard irreducible polynomial representation of GF[2^2^k] but is simpler and more uniform. C++ fast algorithm for computing 2-adic inverse. The p-adic numbers, much beloved of a certain net.crackpot, can be thought of as describing arithmetic modulo powers of p^k, in the limit as k becomes large. The 2-adic inverse of some odd integer x is then another integer y such that xy=1 mod 2^k. (Actually y is only well-defined mod 2^k rather than as an integer itself.) The algorithm in this file defines a fast method for finding such inverses (mod 2^32) found by analogy to a standard method for floating point inversion. C program for rational approximation of real numbers.

8. Lessons On Number Theory From Math Goodies Math Goodies offers 7 interactive lessons on topics number theory including factors, multiples, primes, composites, divisibility, and exponents. additional problems that challenge students' understanding of number theory. Problems are drawn from reallife http://www.mathgoodies.com/lessons/toc_vol3.shtm

interactive click here fun Lessons CD-ROM Forums Homework ... Newsletter numbers Advertise Recommend Puzzles About Us ... Contact Us Our interactive math lessons are comprehensive learning modules that includes examples, diagrams, summaries and exercises. Lessons are organized into Volumes, each of which includes a related group of lessons, Practice Exercises, Challenge Exercises, and a Solutions Page. Read our Terms and Conditions under which these lessons are provided to you. If you are using our lessons for the first time, you also need to read this important technical information Lesson Learning Objectives Factors and Greatest Common Factors To define factor and greatest common factor (GCF). To learn the procedure for finding all factors of a whole number. To learn the procedure for finding the GCF of two or more whole numbers. Multiples and Least Common Multiples To define multiple and least common multiple (LCM). To learn the procedure for finding the multiples of a whole number. To learn the procedure for finding the LCM of two or more whole numbers. Available on CD-ROM only Prime and Composite Numbers To define prime and composite numbers. To determine if a number is prime or composte by examining its factors.

9. Archives Of NMBRTHRY@LISTSERV.NODAK.EDU Archives of postings to the number theory mailing list (NMBRTHRY).Category Science Math number theory......Archives of NMBRTHRY@LISTSERV.NODAK.EDU. number theory List. Search thearchives; Post to the list; Join or leave the list (or change settings); http://listserv.nodak.edu/archives/nmbrthry.html

Archives of NMBRTHRY@LISTSERV.NODAK.EDU Number Theory List Search the archives Post to the list Join or leave the list (or change settings) Manage the list (list owners only) March 2003 February 2003 January 2003 December 2002 ... September 1987 Back to the LISTSERV home page at LISTSERV.NODAK.EDU.

10. A. Baker: Lecture Notes Andrew Baker, University of Glasgow. http://www.maths.gla.ac.uk/~ajb/course-notes.html

Andrew Baker: Lecture notes The pdf files below contain versions of course notes that I have written over the past decade or so. I am making them available for the benefit of anyone who wishes to make use of them. Please let me know if you find them useful or otherwise and let me know of any errors (mathematical, typesetting,...) that you find. All files are formatted for A4 sized paper. If you experience problems printing these files please contact me. I can also supply dvi and ps versions. An Introduction to p -adic Numbers and p ... -adic Analysis (University of Manchester final year Honours course) Finite Groups and their Representations (University of Glasgow level BSc Honours degree course) Algebra and Number Theory (University of Glasgow level 3 non-Honours degree course) Galois Theory (University of Glasgow level 4 Honours degree course Mathematics 4H: Galois theory Groups, symmetry and fractals (University of Glasgow level 2 course Mathematics 2Q: Groups, symmetry and fractals An Introduction to Matrix Groups and their Applications (University of Bern course, Spring 2000). The notes for this course have now appeared as a book, Matrix Groups: An Introduction to Lie Group Theory , published by Springer-Verlag.

11. LiDIA - Main Page C++ Library For Computational number theory.Category Science Math number theory Software......A C++ Library For Computational number theory Main Page. 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) N EWS Patch 2 for LiDIA 2.1pre7 released Per Christoffersen reported a bug in LiDIA's gec package that is fixed by patch 2. As ususal, the file LiDIA-2.1pre7.patch2.gz is available on our ftp server . Installation instructions are given in the announcement to the mailing list. Patch 1 for LiDIA 2.1pre7 released We provide a patch to LiDIA 2.1pere7 on our FTP server that fixes two bugs in the NF package. Details can be found in the announcement to the mailing list. LiDIA 2.1pre7 released LiDIA 2.1pre7 is available for download ! This is a bugfix release that hopefully resolves all major problems. If it turns out to be sufficiently stable, the next release will be LiDIA 2.1. The most important bugfixes included in LiDIA 2.1pre7 are: All necessary template instantiations are generated again, even if compiled with gcc 2.95.2. Added missing object identifiers in Now it's also possible to build LiDIA with STLport 's implementation of the C++ Standard Library.

12. HISTORICAL THINGS IN NUMBER THEORY Historical things in number theory. Return to Menu page. Return to NumberTheory Web page. Some biographies of past contributors to number theory. http://www.math.uga.edu/~ntheory/N14.html

Historical things in Number Theory History of Number Theory (Franz Lemmermeyer) Some biographies of past contributors to number theory Cornell Digital Library Math Collection : Old Mathematics books listed by Title - including Hensel, Sommer Mathematicians of the Seventeenth and Eighteenth Centuries , Hasse's work on the Riemann hypothesis for curves over finite fields - An historical perspective by Professor Peter Roquette (plus notes on class-field theory, Artin L-functions, Erich Hecke) Two Hundred Years of Number Theory after Carl-Friedrich Gauss's Disquisitiones Arithmeticae , A list of lectures at an Oberwolfach conference, June 17-23, 2001 Aus der Geschichte der Zahlentheorie (Wolfgang Schwarz - pdf) Biographies The Man Who Knew Infinity (A life of the genius Ramanujan), R. Kanigel, Washington Square Press 1992 The Apprenticeship of a Mathematician Prizes Henryk Iwaniec, Peter Sarnak and Richard Taylor receive the 7th Ostrowski Prize Kevin Buzzard wins 2002 LMS Whitehead Prize Susan Howson wins 2002 Cambridge University Adams Prize Henryk Iwaniec receives 2002 AMS Cole Prize ... Don Zagier receives Von Staudt Prize , Notices of the AMS, September 2001 Henri Cohen receives the F.L. Bauer Prize

13. NUMBER THEORY CENTRES Listed in the number theory Web. http://www.maths.uq.edu.au/~krm/N2.html

Number theory centres A B C E ... U Australia CeNTRe for Number Theory Research, Macquarie University Austria Number theory at the University of Vienna Number Theory Group, University For Natural Resources, Vienna Kommutative Algebra und Zahlentheorie Belarus Department of Number Theory , Institute of Mathematics of the National Academy of Sciences of Belarus Belgium Number Theory and Algebraic Geometry Seminar, KUL-RUG UCL Crypto Group Brazil Canada The Canadian Number Theory Association The Number Theory Research Group at the University of British Columbia Algebra, Number Theory and Cryptography research group, University of Calgary Centre for Information Security and Cryptography (CISaC), University of Calgary Number Theory Research Group at CICMA Algebra and Number Theory Group at Queens University, Kingston, Ontario, Canada Number Theory Research Group at McGill Algebra/Number Theory Seminar , McMaster University Pacific Institute for the Mathematical Sciences (PIMS) Centre for Applied Cryptographic Research , University of Waterloo China Number Theory in Shandong University Croatia Seminar on Number Theory and Algebra , University of Zagreb European Community Arithmetical Algebraic Geometry Galois Theory and Explicit Methods in Arithmetic (GTEM) Finland Number Theory Group , Oulu Number Theory Group , University of Turku France Bordeaux Caen: SDAD Clermont-Ferrand : Grenoble: Members Lille: Limoges: Luminy: Lyon: Nancy: Paris Paris VI/VII: Paris-Sud: Paris XIII: Rennes: Strasbourg: , IRMA Toulouse: Germany Aachen: Augsburg: Berlin: Algebra and Number Theory , The Kant Group

14. Millennial Conference On Number Theory - Final Announcement Millennial Conference on number theory. May 21 26, 2000. Universityof Illinois at Urbana-Champaign. Conference Wrap-Up. Group Photo http://www.math.uiuc.edu/nt2000/millennial/

Millennial Conference on Number Theory May 21 - 26, 2000 University of Illinois at Urbana-Champaign Conference Wrap-Up Group Photo (jpeg file [1,270k]) List of Participants (ps file [87k]) Titles of Talks (ps file [99k]) Abstracts (ps file [324k]) ... First announcement Conference statistics A total of 276 participants have registered for and attended the conference. An additional 11 number theorists registered for the conference, but could not attend in person. The participants represented 30 countries, ranging from the U.S. and Canada to European countries and to far-away places such as Fiji, Japan, Taiwan, China, and Australia. The conference featured 157 talks , of which 19 were one-hour plenary talks, 73 half-hour invited talks given in 4 parallel sessions, and 65 contributed talks given in 5 parallel sessions. In addition to these scientific talks, the conference included three 40 minute talks of historical and reminiscing flavor, and several after dinner speeches honoring Professor Emeritus Paul Bateman on his 80th birthday. Conference Proceedings The Conference Proceedings will be published by A K Peters in a projected set of two volumes totaling approximately 1000 pages. In addition to these traditional style proceedings, A K Peters will publish an economically priced paperback volume containing selected survey lectures given at the conference. The Proceedings are scheduled to appear in mid 2001.

15. Mathematics Centre, Wits University, Johannesburg, South-Africa Members, research interests, preprints, meetings. http://www.wits.ac.za/science/number_theory/centre.htm

The John Knopfmacher Centre for Applicable Analysis and Number Theory John Knopfmacher, founder and Director of the Centre until his retirement in 1997, died unexpectedly of a heart attack on 29th May 1999. A fuller description of his life and mathematical career is given on his home page The aim of the Centre, which was established as a research unit at the University of the Witwatersrand in 1992 by Professor John Knopfmacher , is to stimulate and pursue research within areas covered by its title - particularly within the areas of number theory, approximation theory, differential equations, combinatorics and functional analysis. The Centre was renamed in John Knopfmacher's honour after his untimely death.The Centre is distinct from, but closely allied to the Department of Mathematics at the University of the Witwatersrand , Johannesburg, South Africa. The Centre currently consists of an Director, Professor Helmut Prodinger , a Deputy Director,Professor Arnold Knopfmacher , around 5 associate members and 2 honorary members. Postgraduate students of members are also affiliated with the Centre. A small number of visiting research positions are available each year.

16. NUMBER THEORY FTP SITES/CALCULATOR PROGRAMS/ARCHIVES number theory ftp sites/calculator programs/archives. Algebraic NumberTheory Archives; finite rings. number theory Tables. Database of 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) Gatekeeper Site: look for bc-1.03.tar.gz MIT site: look for bc-1.03.tar.gz 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) CLINT (Hugh Montgomery's Computational Laboratories in Number Theory Computations on curves of genus2 and their jacobians (Paul Van Wamelen) Congruence Zeta Function Calculator (Hiroyuki Ogawa) Critical Strip Explorer 0.6

17. Algebraic Areas Of Mathematics Topics include number theory, groups and sets, commutative rings, algebraic geometry, and linear algebra. http://www.math.niu.edu/~rusin/known-math/index/tour_alg.html

Search Subject Index MathMap Tour ... Help! Algebraic Areas of Mathematics Return to start of tour Up to The Divisions of Mathematics The algebraic areas of mathematics developed from abstracting key observations about our counting, arithmetic, algebraic manipulations, and symmetry. Typically these fields define their objects of study by just a few axioms, then consider examples, structure, and application of these objects. We have included here the combinatorial topics and number theory ; each is arguably a distinctive area of mathematics but (as the MathMap suggests) these parts of mathematics, shown in shades of red, share definite affinities. The list on this page includes a rather large number of fields in the MSC scheme. It is also common to interpret the phrase "abstract algebra" in a more narrow sense - to view it as the fields obtained by adding successive axioms to describe the objects of study. Arguably then, abstract algebra is limited to sections 20 and 22 (Group Theory), 13, 16, and 17 (Ring Theory), 12 (Field Theory), and 15 (Linear Algebra), taken in this way as a succession from fewest to most restrictive sets of axioms. The use of algebra is pervasive in mathematics. This particularly true of group theory - symmetry groups arise very naturally in almost every area of mathematics. For example, Klein's vision of geometry was essentially to reduce it to a study of the underlying group of invariants; Lie groups first arose from Lie's investigations of differential equations. It is also true of linear algebra - a field which, properly construed, includes huge portions of Numerical Analysis and Functional Analysis, for example hence that field's central position in the MathMap.

18. Pell Worked on algebra and number theory, gave a table of factors of all integers up to 100000 in 1668. Pell's equation is y^2 = ax^2 + 1, where a is a nonsquare integer. http://history.math.csusb.edu/Mathematicians/Pell.html

John Pell Born: 1 March 1611 in Southwick, Sussex, England Died: 12 Dec 1685 in London, England Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index After attending Steyning School in Sussex, John Pell entered Trinity College, Cambridge in 1624. He received his B.A. in 1628 and his M.A. in 1630. After leaving Cambridge, Pell became a schoolmaster. He worked first in Horsham, then in Chichester. He spent five years from 1638 teaching mathematics in London. He then went abroad becoming Professor of Mathematics at a College in Amsterdam from 1643 until he took up a similar post the University of Breda in 1646. Pell returned to England in 1652 and was appointed by Oliver Cromwell to a post teaching mathematics in London. He spent the years 1654 to 1658 holding a government post in Zurich. On his return to England became a vicar and remained in this position in the church for the last 20 years of his life. Pell worked on algebra and number theory . He gave a table of factors of all integers up to 100000 in 1668. Pell's equation y ax + 1, where a is a non-square integer, was first studied by

19. Journal Of Number Theory The Journal of number theory was founded at The Ohio State University in 1969by Professors RP Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus. http://www.math.ohio-state.edu/JNT/

The Journal of Number Theory was founded at The Ohio State University in 1969 by Professors R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus. Editor-in-Chief: David Goss Managing Editor: Ranko Bojanic For more information see the Academic Press information page where you will find for instance Editorial Board Information for Authors Office Susan Hunter Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, Ohio 43210-1174 Phone: (614) 292-7670 Email: jnt@math.ohio-state.edu

20. Jordan Ellenberg Assistant Professor of Mathematics, Department of Mathematics, Princeton University. Subjects arithmetic algebraic geometry, number theory. http://www.math.princeton.edu/~ellenber

Jordan S. Ellenberg Assistant Professor of Mathematics 808 Fine Hall Department of Mathematics Washington Road Princeton, NJ 08544 e-mail: ellenber@math.princeton.edu I've been teaching at Princeton since the fall of 1998. My field is arithmetic algebraic geometry: my specific interests include Hilbert-Blumenthal abelian varieties, Q -curves, arithmetic of curves of low genus, the fundamental group of the thrice-punctured line, Serre's conjecture, the ABC conjecture, and Diophantine problems related to all of the above. In Fall 2002, I am teaching Math 214, "Numbers, Equations, and Proofs." This course, being given for the second time this term, uses classical number theory as a vehicle for teaching the concepts and techniques of higher mathematics. Papers and Preprints My CV ( .dvi version or .pdf version Personal Page Teaching Barry Mazur's Mathematical Genealogy ... Send me e-mail Jordan Ellenberg * ellenber@math.princeton.edu * revised 28 Aug 2001

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