81. London Number Theory Seminar Weekly meetings during term, rotating between University College, King's College and Imperial College.Category Science Math number theory Events......London number theory Seminar, The London number theory Seminar ishosted in rotation for one semester each by UCL, IC and KCL. A http://www.mth.kcl.ac.uk/events/numbtheo.html

London Number Theory Seminar The London Number Theory Seminar is hosted in rotation for one semester each by UCL IC and KCL A list of previous seminars held is available here This term it's being held in room 658 of the maths department (i.e. the Huxley building) of Imperial College (instructions on how to get there are here on Wednesdays at 4.15 pm . Tea is available in the common room beforehand. For more details, please contact the organiser, Dr Kevin Buzzard ( buzzard@ic.ac.uk Also on Wednesdays in Imperial this term: Alexei Skorobogatov will be giving an informal seminar series on rational points and related topics. This seminar also starts on 15th Jan. It's again in room 658, from 1200 to 1330 or so. There will be a study group on Drinfel'd Modules, also in room 658, from 1430 to 1530++ as usual. Contrary to earlier rumours however, this will start on the 22nd. It's organised by Manuel Breuning and we'll be looking at Rosen's book and/or `Basic Structures of Function Field Arithmetic' by Goss. Skorobogatov's abstract for his course: Among the things of general interest I propose to look at the paper "Unramified correspondences" by Bogomolov-Tschinkel. They prove that any hyperelliptic curve over an algebraically closed field has a finite etale cover that maps surjectively to the curve y

82. Dirichlet Proved that in any arithmetic progression with first term coprime to the difference there are infinitely many primes, units in algebraic number theory, ideals, proposed the modern definition of a function. http://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Dirichlet.html

Johann Peter Gustav Lejeune Dirichlet Born: Died: Click the picture above to see five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Lejeune Dirichlet Gymnasium in Bonn in 1817, at the age of 12, he had developed a passion for mathematics and spent his pocket-money on buying mathematics books. At the Gymnasium he was a model pupil being [1]:- ... an unusually attentive and well-behaved pupil who was particularly interested in history as well as mathematics. After two years at the Gymnasium in Bonn his parents decided that they would rather have him attend the Jesuit College in Cologne and there he had the good fortune to be taught by Ohm . By the age of 16 Dirichlet had completed his school qualifications and was ready to enter university. However, the standards in German universities were not high at this time so Dirichlet decided to study in Paris. It is interesting to note that some years later the standards in German universities would become the best in the world and Dirichlet himself would play a hand in the transformation. Dirichlet set off for France carrying with him Gauss 's Disquisitiones arithmeticae Biot Fourier Francoeur Hachette ... Legendre , and Poisson Dirichlet's first paper was to bring him instant fame since it concerned the famous Fermat's Last Theorem . The theorem claimed that for n x y z such that x n y n z n . The cases n = 3 and n = 4 had been proved by Euler and Fermat , and Dirichlet attacked the theorem for

83. SAL- Mathematics - Number Theory This section has several number theory software. Search SAL number theory (Commercial, Shareware, GPL) CLN a C++ class library for numbers. http://sal.kachinatech.com/A/4/index.shtml

This section has several Number Theory software. Search SAL: Number Theory Commercial, Shareware, GPL CLN a C++ class library for numbers. ECPP a software package for primality proving. KANT/KASH computational algebraic number theory. LiDIA C++ library for computational number theory. Number Theoretic bc a fast prototyping scripting language for use in number theoretic applications. NTL a library for doing number theory. Pari/GP formal computations on recursive types at high speed. SIMATH computer algebra system for number theoretic purposes. Also Check Out: Algae a high-level interpreted language for numerical analysis. ARIBAS an interactive interpreter for big integer and multi-precision floating point arithmetic. MAGMA a system for algebra, number theory, geometry and combinatorics. Other Resources on the Internet Things of interest to number theorists http://www.maths.uq.oz.au/~krm/listi.html Statistics Miscellaneous Software SAL Home Mathematics Herng-Jeng Jou Kachina Technologies, Inc.

84. James Wanless Elementary number theory and Geometry. http://www.bearnol.pwp.blueyonder.co.uk/

Math Art Bridge Chess Math Art Bridge Chess

85. History Of Mathematics: History Of Arithmetic And Number Theory A bibliography by D. Joyce.Category Science Math number theory History......History of Arithmetic and number theory. See also the history of numbers and counting.On the Web. Mathematics Archive's index to number theory on the web. http://aleph0.clarku.edu/~djoyce/mathhist/arithmetic.html

History of Arithmetic and Number Theory See also the history of numbers and counting. On the Web Mathematics Archive's index to number theory on the web Pages on arithmetic and number theory at the Mathematical MacTutor History of Mathematics archive Prime numbers Fermat's last theorem ... History of Fermat's Last Theorem by Andrew Granville (TeX) Bibliography Cunnington, Susan. The story of arithmetic, a short history of its origin and development. Swan Sonnenschein, London, 1904. Dickson, Leonard Eugene. History of the theory of numbers. Three volumes. Reprints: Carnegie Institute of Washington, Washington, 1932. Chelsea, New York, 1952, 1966. Fine, Henry Burchard (1858-1928). The number system of algebra treated theoretically and historically. Karpinski, Louis Charles (1878-1956). The history of arithmetic. Number theory and its history. McGraw-Hill, New York, 1948. Weil, Andre. Number theory: an approach through history. Birkhauser, Boston, 1984. Reviewed: Math. Rev. Regional mathematics Subjects Books and other resources Chronology ... Home

86. Jlpe's Number Recreations Page Features original number recreations by the author, such as generalized perfect numbers, digital diversions, diophantine equations, didactic numbers, and number theory. http://www.geocities.com/windmill96/numrecreations.html

jlpe's number recreations page The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures. Joseph Marie de Maistre I have hardly ever known a mathematician who was capable of reasoning. Plato On a Generalization of Perfect Numbers Ana's Golden Fractal The Picture-Perfect Numbers Fractal Dimension, Primes, and the Persistence of Memory ... The Justice of Numbers : The author will not be responsible for any frustration or sleepless nights suffered by the would-be solver. Number of Visits: J. L. Pe Last update: 16 February 2003.

87. Elementary Number Theory -- A Lightning Course Notes by Jeremy Teitelbaum.Category Science Math number theory Education......Elementary number theory A Lightning Course. number theory is themathematical study of the integers and their generalizations. http://raphael.math.uic.edu/~jeremy/crypt/math.html

UIC Honors Seminar in Cryptography Spring, 2002 Elementary Number Theory A Lightning Course Number theory is the mathematical study of the integers and their generalizations. The portion of number theory needed to understand the basic public key algorithms is elementary and dates back to the work of Pierre de Fermat and Leonhard Euler. Integers and rational numbers. An integer is a positive or negative whole number, or zero. A rational number is a positive or negative fraction, or zero. Prime numbers and composite numbers. A prime number is an integer n with no divisors other than 1 and n. A composite number is an integer which is not prime. The first few prime numbers are 2,3,5,7,11,13,.... There are infinitely many prime numbers. (This result is due to Euclid. Lists of prime numbers can be constructed by a process called the Sieve of Eratosthenes, described in a University of Utah Math 216 Problem Set. Factoring. Any positive integer can be written in only one way (up to order) as a product of powers of prime numbers. 12=(3)(2)(2) and 124=(2)(2)(31) This result was proved carefully by Gauss in his Disquisitiones Arithmeticae. Writing an integer as a product of primes is called

88. Wiley :: Primality And Cryptography Evangelos Kranakis. A comprehensive account of recent algorithms developed in computational number theory and primality testing. http://www.wiley.com/cda/product/0,,0471909343,00.html

Shopping Cart My Account Help Contact Us By Keyword By Title By Author By ISBN By ISSN Wiley Computing Computer Science Networking ... Security Primality and Cryptography Related Subjects UNIX Networking LINUX Networking General Networking Related Titles Security Computer Security (Paperback) Dieter Gollmann Stephen A. Thomas Computer Security Handbook, 4th Edition (Paperback) Seymour Bosworth (Editor), M. E. Kabay (Editor) Cryptography and E-Commerce: A Wiley Tech Brief (Paperback) Jon C. Graff The CISSP Prep Guide: Mastering the Ten Domains of Computer Security (Hardcover) Ronald L. Krutz, Russell Dean Vines Join a Computing Mailing List Security Primality and Cryptography Evangelos Kranakis ISBN: 0-471-90934-3 Hardcover 252 Pages April 1986 US $260.00 Add to Cart If you are an instructor, you may request an evaluation copy for this title. Description Table of Contents A comprehensive account of recent algorithms developed in computational number theory and primality testing. Provides a general framework for the theoretical study of public key cryptography and pseudorandom generators. Unique in its approach, the book will be a valuable addition to computer literature.

89. Computational Projects Interesting problems, usually requiring extensive verifications or enumerations, to occupy the idle Category Science Math number theory Computational...... future. List of available software packages related to number theory.Fast implementation of the segmented sieve of Eratosthenes. http://www.ieeta.pt/~tos/hobbies.html

Computational projects (computo, ergo sum) Introduction Projects Software Contact ... [Up] (The Latin locution in the title of this page was copied from the home page of David Bailey Introduction WinZip , and then view them with a text editor. As far as I am aware, some of the results reported in these pages are records of computation. List of available computational project descriptions The 3x+1 conjecture Some generalizations of the 3x+1 conjecture Determination of the minimum width of admissible prime constellations Verification of the Goldbach conjecture ; you can help extend the range of this massive computation Statistics about prime gaps (a by-product of the Goldbach conjecture verification) Tables with values of the prime counting functions pi(x) and pi2(x) Statistics about least primitive roots of prime numbers (Artin's conjecture) Statistics about very large solutions of Pell's equation Enumeration of polyominoes and other animals (not yet finished) Some of the results presented or made available in the pages described above have not yet been double-checked. They are thus potentially inaccurate. Simple screening tests were used to identify and reject wrong results. However, these screening tests are not perfect, and thus wrong results may have been accepted. So far, all double checking computations have not uncovered any wrong results, but that is no guarantee that this will not happen in the future. List of available software packages related to number theory Fast implementation of the segmented sieve of Eratosthenes All software is released under the version 2 of the

90. Algebra And Number Theory Algebra and number theory the KANT group. Members, software (KANT/KASH), publications.Category Science Math number theory Research Groups......Algebra and number theory. The KANT Group. KANT stands for Computational Algebraicnumber theory with a slight hint to its German origin (Immanuel Kant). http://www.math.tu-berlin.de/algebra/

Algebra and Number Theory The KANT Group The KANT Group: [members] [publications] [links] [Math ... [ftp] People Prof. Dr. M. E. Pohst (pohst@math.tu-berlin.de) Members of the KANT Group KASH / KANT - computer algebra system Immanuel Kant The KANT functions are accessible through a user-friendly shell named KASH (KAnt SHell) which is freely available. You can pick up the current release of KASH using ftp Publications You can download the publications of members of the KANT Group. Last modified: 2001-06-14

91. Discovering Number Theory A textbook by John Jones and Jeff Holt.Category Science Math number theory Publications Books......Discovering number theory is a textbook by John Jones and Jeff Holtpublished by WH Freeman and Company. Requests for examination http://math.la.asu.edu/~jj/dnt/

Discovering Number Theory is a textbook by John Jones and Jeff Holt published by W. H. Freeman and Company Requests for examination copies of the materials should go directly to the publisher. Visit this W.H. Freeman page and you should find a link which you can use to request a copy of the book. W.H. Freeman is starting a web page with materials for the book . It is in the process of being updated. Development of these course materials was supported by the NSF under grant Revitalizing Undergraduate Number Theory Chart showing chapter dependencies Course Basics The basic operation of the course is as follows. (This is also explained in the first day handout below.) Each chapter starts with the pre-lab sheet. It contains background, exercises to be worked by hand, and may mention the larger questions which will be taken up in the computer lab. Each student turns in their individual answers to pre-lab questions the following class, which is . . . The next 2-3 classes are held in the lab. Students work through the lab notebooks in teams of two. Each notebook contains "Research questions" and "Exercises". Exercises are intended to be straightforward while research questions are not. Typically, the research questions will require experimentation, forming of conjectures, and proofs. We expect students to make varying degrees of progress on these questions.

92. Number Theory Group, Oxford number theory Group. Members, publications, meetings. http://www.maths.ox.ac.uk/ntg/

The Number Theory Group Mathematical Institute Oxford University The interests of the group are diverse, covering analytic number theory, arithmetic geometry, computational number theory, elliptic curves and zeta functions. See individual homepages for further information on particular members' interests. Research Members of the research group Junior number theory seminars Number theory seminars Graduate lectures ... (EPSRC grant no. GR/R93155/01) Papers Preprints by members of the research group Papers relating to Rational Points on Algebraic Varieties (EPSRC grant no. GR/R93155/01) Links AMS Mathematics Subject Classification Arithmetic Geometry Network London Mathematical Society MathSciNet Search ... NoMaDS (North of England algebraic number theory group) Number Theory Web SECANTS (South of England Computational and Algorithmic Number Theory Seminars) Other information Vacancies within the Department Location of the Department visitors since 17th February, 2003 This page last modified by Tim Browning Thursday, 06-Mar-2003 09:46:31 GMT

93. Numbers And Number Theory Mathematical Association of America (MAA) recently published book list. Each title is described and Category Science Math number theory Publications......Numbers and number theory. Invitation to number theoryOystein Ore;Irrational NumbersIvan Niven; Lore of Large Numbers, ThePJ Davis; http://www.maa.org/pubs/books/numbers.html

Numbers and Number Theory Conjecture and Proof Miklos Laczkovich Cryptology Albrecht Beutlespacher Cryptological Mathematics Robert Lewand Diophantus and Diophantine Equations I.G. Bashmakova Euler: The Master of Us All William Dunham From Zero to Infinity Constance Reid The Geometry of Numbers C.D. Olds, Anneli Lax and Giuliana Davidoff Invitation to Number Theory Oystein Ore Irrational Numbers Ivan Niven Lore of Large Numbers, The P.J. Davis Lure of the Integers Joe Roberts Numbers; Rational and Irrational Ivan Niven Power Play Edward J. Barbeau A Primer of Abstract Mathematics Robert Ash

94. C R A N T S A regional seminar for the greater Capital District of New York (the area of Albany, Saratoga Springs, Schenectady, and Troy) devoted to number theory, algebra, and related topics in mathematics. http://math.albany.edu:8000/math/Current/Crants/

C R A N T S CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR Spring Semester, 2003 William Hammond, Univ. at Albany, February 12 at Univ. at Albany Alex Tchernev, Univ. at Albany, February 26 at Skidmore College Alex Tchernev, Univ. at Albany, March 19 at Univ. at Albany Fall Semester, 2002 Alex Tchernev, Univ. at Albany, October 9 at Univ. at Albany Hara Charalambous, Univ. at Albany, October 23 at Univ. at Albany Alex Tchernev, Univ. at Albany, November 13 at Skidmore College Alex Tchernev, Univ. at Albany, December 4 at Univ. at Albany Previous CRANTS talks General Information CRANTS is a regional seminar for the greater Capital District of New York (the area of Albany, Saratoga Springs, Schenectady, and Troy) devoted to number theory, algebra, and related topics in mathematics. The Seminar meets biweekly during the academic year, generally on Wednesday afternoons at 4:30 p.m. It relies on its members to provide locations for its meetings. From the beginning it was established that a meeting should not be hosted at the institution, if any, where the speaker is in residence. Although there have been exceptions to this rule, there is a continuing determination to uphold it. At various times in the past the seminar has met at: Siena College , Latham, NY Skidmore College , Saratoga Springs, NY Union College , Schenectady, NY University at Albany (SUNY), Albany, NY

95. Basic Library List-Number Theory Compiled by the Mathematical Association of America (MAA). This site subdivides number theory into Category Science Math number theory Publications......number theory. Back to Table of Contents. number theory Introductory Texts. * Andrews,George E. number theory. Dover Publications, 1998. ISBN 0486682528 http://www.maa.org/BLL/numtheory.htm

Number Theory Back to Table of Contents Number Theory: Introductory Texts * Andrews, George E. Number Theory. Dover Publications, 1998. ISBN 0486682528 ** Baker, Alan. A Concise Introduction to the Theory of Numbers New York, NY: Cambridge University Press, 1985. ISBN 0521286549. Burn, R.P. A Pathway Into Number Theory New York, NY: Cambridge University Press, 1996. ISBN 0521575400 Burton, David M. Elementary Number Theory, New York, McGraw-Hill Companies, 1997. Second Edition. ISBN 0070094667 * Davenport, Harold. The Higher Arithmetic: An Introduction to the Theory of Numbers, New York, NY: Cambridge University Press, 1998. ISBN 0521634466. Elements of the Theory of Numbers. San Diego, Academic Press, 1999. ISBN 0122091302 Dudley, Underwood. Elementary Number Theory, New York, NY: W.H. Freeman, 1978. ISBN 071670076X. Flath, Daniel E. Introduction to Number Theory * * * Hardy, Godfrey H. and Wright, E. M. Introduction to the Theory of Numbers. Oxford University Press, 1980. ISBN 0198531702 (Out of Print) Hua, Loo-Keng.

96. Thabit Gives information on background and contributions to noneuclidean geometry, spherical trigonometry, number theory and the field of statics. Was an important translator of Greek materials, including Euclid's Elements, during the Middle Ages. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Thabit.html

Al-Sabi Thabit ibn Qurra al-Harrani Born: 826 in Harran, Mesopotamia (now Turkey) Died: 18 Feb 901 in Baghdad, (now in Iraq) Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Thabit ibn Qurra was a native of Harran and a member of the Sabian sect. The Sabian religious sect were star worshippers from Harran often confused with the Mandaeans (as they are in [1]). Of course being worshipers of the stars meant that there was strong motivation for the study of astronomy and the sect produced many quality astronomers and mathematicians. The sect, with strong Greek connections, had in earlier times adopted Greek culture, and it was common for members to speak Greek although after the conquest of the Sabians by Islam, they became Arabic speakers. There was another language spoken in southeastern Turkey, namely Syriac, which was based on the East Aramaic dialect of Edessa. This language was Thabit ibn Qurra's native language, but he was fluent in both Greek and Arabic. Some accounts say that Thabit was a money changer as a young man. This is quite possible but some historians do not agree. Certainly he inherited a large family fortune and must have come from a family of high standing in the community.

97. Tools On Number Theory Tools on number theory Web. About TNT; Tools on number theory WebLinks; TNT Mailing List; TNT ftp site; archive of TNT Mailing List; http://tnt.math.metro-u.ac.jp/

Japanese Department of Mathematics Tokyo Metropolitan University Tools on Number Theory Web About TNT Tools on Number Theory Web Links TNT Mailing List TNT ftp site archive of TNT Mailing List Symposium on Algebra and Computation Workshop on Algorithmic Number Theory Maintained by Ogino Junya, NAKAMULA Ken , Dept of Math, Tokyo Metropolitan University , Suggestions for additions or improvements are welcome. Contact me by email at webmaster@tnt.math.metro-u.ac.jp Please report problems with this web to webmaster@tnt.math.metro-u.ac.jp $Id: index.html,v 1.1.1.1 2003/01/10 02:07:28 root Exp $

98. Home Page Of Jeffrey O. Shallit Algorithmic number theory (primality testing, and factoring), formal languages and automata theory (especially connections with number theory), history of mathematics and computer science, ethical use of computers. http://www.math.uwaterloo.ca/~shallit/

Jeffrey O. Shallit Professor School of Computer Science University of Waterloo Waterloo Ontario ... Canada Office: Davis Centre 3134 Telephone: (519) 888-4804 Fax: (519) 885-1208 E-mail: Areas of interest: Algorithmic number theory (primality testing, factoring, etc.), formal languages and automata theory (especially connections with number theory), history of mathematics and computer science, ethical use of computers. See my rating at ratemyprofessors.com. Professional Activities Algorithmic Number Theory published by MIT Press, August 1996. Automatic Sequences: Theory, Applications, Generalizations to be published by Cambridge University Press. Editor-in-chief, Journal of Integer Sequences Center for Applied Cryptographic Research Courses taught by JOS Curriculum vitae of JOS Selected papers of JOS Recent talks by JOS Book reviews by JOS Published and unpublished essays by JOS Graduate students supervised by JOS Library catalogues Links to other CS and math-related sites This week's Math/CS talks at Waterloo Vice-President, Electronic Frontier Canada Unprofessional Activities Friends Quotations Letters to the editor by JOS Community Editorial Board JOS's favorite animal (Also visit here My Elvis number Travel Photographs Other interesting web pages Urban Legends Debunked Today's weather in southern Ontario Today's weather in Kitchener-Waterloo : Nothing on this page should be taken to represent the official views of the University of Waterloo.

99. Number Theory http://www.ma.utexas.edu/users/voloch/numberthy.html

Number Theory at the Mathematics Dept. of the University of Texas Permanent faculty in Number Theory, and their fields of interest. Frank Gerth gerth@math.utexas.edu ): Algebraic number theory, including class numbers, class groups, discriminants, class field theory, density theorems, Iwasawa theory. John Tate tate@math.utexas.edu ): Algebraic Number Theory (local and global fields), Class Field Theory, Galois cohomology, Galois representations, L-functions and their special values, modular forms, elliptic curves and abelian varieties. Jeffrey Vaaler vaaler@math.utexas.edu ): Analytic number theory, Diophantine approximation and the geometry of numbers in local and global fields, Diophantine inequalities, polynomials, effective measures of irrationality and transcendence, applications of Fourier analysis in number theory, inequalities and extremal problems. villegas@math.utexas.edu ): Special values of L-functions (Birch-Swinnerton-Dyer and Bloch-Beilinson conjectures), arithmetic of elliptic curves, modular forms, Mahler measure of polynomials. Felipe Voloch voloch@math.utexas.edu

100. Rsabook S.C. Coutinho. An introduction to number theory and its applications to cryptography. A revised and updated translation from original in Portuguese. http://www.dcc.ufrj.br/~collier/rsabook.htm

S. C. Coutinho The Mathematics of Ciphers: Number theory and RSA cryptography About the book Table of contents Download the errata (ps file) Hints for classroom use Portuguese edition About the book This is an introduction to number theory and its applications to cryptography. The aim of the book is to explain in detail how the public key cryptosystem known as RSA works. The system was invented in 1977 by Rivest, Shamir and Adlemanhence RSAand it is one of the most successful of the public key cryptosystem now in use in commercial applications. Althouth this is the aim of the book, we do not follow a straight path to this end. Instead we stroll about the landscape, never forgetting our aim, but stopping to explore whatever reachs are available on the way. Thus the book includes a chapter on group theory, and it is pepered with historical notes that range from biographical facts on famous mathematicians to little anecdotes. The mathematics behind most of the books subject is, naturally enough, number theory. Most of the traditional topics of a beginners course on number theory are to be found here. Thus there are chapters on the Euclidean algorithm, factorization of integers, primes, modular arithmetic, Fermat's little theorem, the Chinese remainder theorem and Mersenne and fermat numbers. However we follow na algorithmic approach, so that the proofs the theorems are, whenever possible, of a constructive nature. Back to the top Table of contents 1. Fundamental algorithms (division and Euclidean algorithms)

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