1. 11: Number Theory Selected topics here 11 number theory. Introduction. number theory is one of the oldest branches of pure mathematics, and one of the largest. Elementary number theory involves divisibility among integers the division "algorithm", the Euclidean a course in "elementary" number theory usually includes classic and elegant 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

2. Algebraic Number Theory Archives Electronic preprint archives for mathematics research papers in algebraic number theory and arithmetic geometry. Algebraic number theory Archives. From Nigel Boston boston@math.uiuc.edu gt. Date Wed, 8 Jan 2003 120333 0600 (CST) To Algebraic-Number-Theory@listserv.uiuc. edu 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. Archives Of NMBRTHRY@LISTSERV.NODAK.EDU Archives of NMBRTHRY@LISTSERV.NODAK.EDU. number theory List. Search the archives 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) June 2004 May 2004 April 2004 March 2004 ... September 1987 Back to the LISTSERV home page at LISTSERV.NODAK.EDU.

4. MathPages: Number Theory number theory. Symmetric Pseudoprimes. Is e Normal http://www.mathpages.com/home/inumber.htm

Number Theory Symmetric Pseudoprimes Is e Normal? Identities for Linear Recurring Sequences The Half-Totient Tree ... Math Pages Main Menu

5. NUMBER THEORY WEB (AUSTRALIAN SITE) number theory Web. (Australian Site). http://www.math.uga.edu/~ntheory/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 The American mirror site at University of Georgia, Athens, USA has been discontinued as of 21st April 2003; please adjusts your bookmarks The main site is in Vancouver, as of 31st May 2003 The Australian mirror site is at University of Queensland, Brisbane, Australia 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 19th April 2004

6. NUMBER THEORY WEB Things of interest to number theorists collected by Keith Matthews. http://www.numbertheory.org/ntw/

Number Theory Web Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages The American mirror site at University of Georgia, Athens, USA has been discontinued as of 21st April 2003; please adjust your bookmarks The main site is now in Vancouver, as of 31st May 2003 The Australian mirror site is at University of Queensland, Brisbane, Australia 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 7th July 2003

7. Number Theory Files For David Eppstein NumberTheoretic Hacks. I have implemented a number of simple number-theoretic algorithms. for my own amusement, and provide them here on the net. Source code is available for producing similar 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. This version is an update to my code by Achim Flammenkamp, to make it run under less archaic versions of C++ and allow numbers with more bits than machine precision; the original code is here C++ fast algorithm for computing 2-adic inverse.

8. Mathematics Archives - Topics In Mathematics - Number Theory Aesthetics of the Prime Sequence. Algorithmic number theory Bibliography. AMS - Fermat's Last Theorem KEYWORDS number theory, Fermat's Last Theorem, History, Reports, Articles 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

9. An Introduction To The Theory Of Numbers - Number Theory Text By Leo Moser - The An Introduction to the Theory of Numbers by Leo Moser is a textbook covering following topics Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial number theory; and Geometry of Numbers. The textbook can be downloaded in several formats in pdf. Licensing terms for various uses are described on the web page. http://www.trillia.com/moser-number.html

An Introduction to the Theory of Numbers by Leo Moser Description: This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate student on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text. Audience: This book is appropriate for a second undergraduate course in Number Theory, or as an introduction to the subject for beginning graduate students. Publishing Information: An Introduction to the Theory of Numbers , by Leo Moser, ISBN 1-931705-01-1, published by The Trillia Group, 2004. 87+vi pages, 231 problems, 6 figures, hypertextual cross-references. Download size: 463 to 478 KB, depending on format. Excerpts from the Text: The Terms and Conditions and the Preface Reviews: Review this book at The Assayer Terms and Conditions: All uses of this text are subject to the Terms and Conditions contained in this text. As part of these terms, we offer this text

10. 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 The University of Sydney number theory seminar 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 The University of Toronto Number Theory/Representation Theory Seminar 2003/2004 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: Montpellier Paris Paris VI/VII:

11. BIOGRAPHIES OF PAST NUMBER THEORISTS And VARIOUS ITEMS OF HISTORICAL INTEREST Return to Menu page. Return to number theory Web page. Some biographies of past contributors to number theory. Some of the major sources http://www.numbertheory.org/ntw/N14.html

Biographies of past number theorists and various items of historical interest 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) Collected Works Collected papers of Peter Roquette , editors: Anthony V. Geramita and Paulo Ribenboim, Queens University Ouvres J.-P. Serre I-III , Springer 2003 Biographies The Man Who Knew Infinity (A life of the genius Ramanujan), R. Kanigel, Washington Square Press 1992 The Apprenticeship of a Mathematician Prizes Serre receives Abel prize , Notices of the AMS, Volume 50, Number 6, 2003 Serre awarded Abel Prize Interview with Jean-Pierre Serre , NAMS February 2004 Henryk Iwaniec, Peter Sarnak and Richard Taylor receive the 7th Ostrowski Prize

12. 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) Representations of Finite Groups (based on a 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

13. 11P: Additive Number Theory; Partitions Parent field 11 number theory. Nathanson, Melvyn B. Additive number theory; The classical bases , Graduate Texts in Mathematics, 164. http://www.math.niu.edu/~rusin/known-math/index/11PXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11P: Additive number theory; partitions Introduction History Applications and related fields Note that some of the principal questions about partitions can be answered with Bell numbers and Stirling numbers; these are discussed in 11B among other Sets and Sequences . More general set-partitioning problems are treated in Combinatorics Subfields Waring's problem and variants Lattice points in specified regions Goldbach-type theorems; other additive questions involving primes Applications of the Hardy-Littlewood method, See also 11D85 Inverse problems of additive number theory [new in 2000] Elementary theory of partitions, See also 05A17 Analytic theory of partitions Partitions; congruences and congruential restrictions None of the above but in this section Parent field: 11: Number Theory Browse all (old) classifications for this area at the AMS. Textbooks, reference works, and tutorials Nathanson, Melvyn B.: "Additive number theory; The classical bases", Graduate Texts in Mathematics, 164. Springer-Verlag, New York, 1996. 342 pp. ISBN 0-387-94656-X

14. 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.

15. 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.

16. Journal Of Number Theory The Journal of number theory was founded at The Ohio State University in 1969 by Professors R.P http://www.math.ohio-state.edu/Groups/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, including a list of editorial board members and author instructions, please see Elsevier 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

17. Millennial Conference On Number Theory - Final Announcement Millennial Conference on number theory. May 21 26, 2000. An additional 11 number theorists registered for the conference, but could not attend in person. 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.

18. Mathematik.com Individual pages on different topics in Mathematics. Examples group theory, dynamical systems theory, geometry or number theory. http://www.mathematik.com/

Mathematik.com Gradus Suavitatis Turing Billiard Bifurcation ... Feedback

19. Number Theory number theory This math site contains seven interactive lessons and a solutions page dealing with number theory. Included are lessons on factors and the greatest common factor; multiples and the http://rdre1.inktomi.com/click?u=http://www.mathgoodies.com/lessons/toc_vol3.sht

20. ScienceDirect - Journal Of Number Theory - List Of Issues Publisher's site. http://www.sciencedirect.com/science/journal/0022314X

This Feature requires JavaScript Register or Login: Password: Athens Login Journal of Number Theory Bookmark this page as: http://www.sciencedirect.com/science/journal/0022314X Articles in Press Volume 107 Volume 107, Issue 1 , Pages 1-206 (July 2004) Volume 106 Volume 105 Volume 104 Volume 103 ... Volume 43 Alert me when new Journal Issues are available Add this journal to My Favorite Journals Sample Issue Online More Publication Info Information for Authors Feedback ... Elsevier B.V.

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