81. Home Page J. S. Milne. Includes preprints and course notes on Group Theory, Fields and Galois Theory, Algebraic Geometry, Algebraic number theory,Modular Functions and Modular Forms, Elliptic Curves, Abelian Varieties, Etale Cohomology, and Class Field Theory. http://www.jmilne.org/math/

82. Number Theory And Physics Archive This website is an attempt to document in detail the rapidly emerging connections between physics and number theory. number theory and physics archive. http://www.maths.ex.ac.uk/~mwatkins/zeta/physics.htm

number theory and physics archive introduction tutorial mystery new ... a message about the future of this website

83. 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 3x + 1 Fractal The Picture-Perfect Numbers ... 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. var PUpage="76001088"; var PUprop="geocities";

84. The USC Number Theory Home Page s in number theory....... I also have interests in the application of these results to gap problems in number theory. Graduate Course http://www.math.sc.edu/~filaseta/numthry.html

Research Interests: Research Interests: elementary number theory, analytic prime number theory, quadratic forms, class number formulae, forms of higher order, quadratic and higher power residues, comparative prime number theory, Gauss and Jacobi sums, computer results in number theory. (Retired but still collaborating in research) Research Interests: aspects of Computational and Elementary Number Theory, including work on cyclotomic polynomials, Euler's phi function, and problems related to digits in integer sequences. Research Interests: Analytic Number Theory and Approximation Theory with particular interests in the use of finite differences to determine information about lattice points close to a curve or surface. I also have interests in the application of these results to gap problems in Number Theory. Research Interests: Analytic and Elementary Number Theory with particular interests in the distribution of primes, Waring's problem, arithmetic properties of elliptic curves over the rationals, and applications of the theory of modular forms. Information: Sergei Konyagin of Moscow State University will be visiting for the month of January, 2004. He is world renowned for his work in Number Theory, Approximation Theory, and Harmonic Analysis. In particular, he was recognized for his work in Harmonic Analysis as a recipient of the Salem Prize in 1990.

85. Number Theory Website Home Page Welcome To number theory Web site. NextCard Internet Visa. http://numbertheory.freeservers.com/

Free Web site hosting - Freeservers.com Web Hosting - GlobalServers.com Choose an ISP NetZero High Speed Internet ... Dial up $14.95 or NetZero Internet Service $9.95 Welcome To Number Theory Web site Site owner: Li Ke Xiong Email: likexiong@126.com The Correction Of Part F Of "Primary Proof" For The FLT A New Interesting Way in Mathematics -"Relative congruence" From the basic facts: integer a,b,s. prime the solution always exists and unique (except ). We can use the fractions to express congruence value, directly that is to say the fractions have congruence meaning. 2. So we can make the definition: (2) Never can p be denomination divisor in any finite expression, otherwise meaningless. 3. Thus the basic operation can be used on the both sides of without any doubt, it is easy to be proved. 4. Furthermore, we extend the above concept to real number, based on and controlled by power expansion series, that is to say we have discovered the concept of Relative Congruence. 5. Thus we get the necessary condition mod p for , then we proved mod p never can be satisfied with the same p.

86. 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

87. Math 780 Material Math 780 Elementary number theory. A postcript version of the course description can be obtained below. Class notes (55 pages) can http://www.math.sc.edu/~filaseta/gradcourses/Math780.html

Math 780: Elementary Number Theory A postcript version of the course description can be obtained below. Class notes (55 pages) can also be obtained in postscript form below. These notes are from a course taught by Michael Filaseta in the Fall of 1997 and may not reflect the current semesters material. A graph, at the bottom of the page, compares Li(x), Pi(x), and x/log(x). Math 780 Course Description (postscript file) Math 780 Class Notes A Page For Our Undergraduate Elementary Number Theory Course Graduate Number Theory Courses At The University of South Carolina

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 General Networking LINUX Networking Related Titles Security Computer Security (Paperback) by Dieter Gollmann Internet Privacy For Dummies (Paperback) by John R. Levine, Ray Everett-Church, Greg Stebben, David Lawrence (Foreword by) Storage Security: Protecting SANs, NAS and DAS (Paperback) by John Chirillo, Scott Blaul Security+ Certification For Dummies (Paperback) by Lawrence H. Miller, Peter H. Gregory Security+ Prep Guide (Paperback) by Ronald L. Krutz, Russell Dean Vines Secrets of Computer Espionage: Tactics and Countermeasures (Paperback) by Joel McNamara Firewalls For Dummies, 2nd Edition (Paperback) by Brian Komar, Ronald Beekelaar, Joern Wettern Join a Computing Mailing List Security Primality and Cryptography Evangelos Kranakis ISBN: 0-471-90934-3 Hardcover 252 pages April 1987 US $260.00

89. By J. Orlin Grabbe The ability of digital cash systems to give some measure of security and privacy has more to do with number theory than banking regulations. http://www.aci.net/kalliste/cryptnum.htm

Cryptography and Number Theory for Digital Cash by J. Orlin Grabbe Note: In order to read the following text properly, your web browser must be able to handle subscripts and superscripts; i.e. the html commands “sub” and “sup”. These commands are used sparingly, but they are used. The ability to attack or misuse a digital cash system depends a lot on the cryptography and cryptographic protocols involved. A good cash system uses good cryptography. Good cryptography requires strong algorithms, keys of adequate length, and secure key management. Without these, there can be little privacy. A good cash system uses good protocols. The digital cash system of Stefan Brands, for example, is largely based on digital signaturesthe Schnorr signature scheme, in particular. The system, properly implemented, is thus only as secure as the underlying signature system. If there are flaws in the latter, the attractive features of anonymous digital cash disappear alsofeatures like untraceability, unlinkability, and security for all parties. If we are looking for privacy and security in banking, we can't ignore cryptography and we can't ignore mathematics. The ability of digital cash systems to give some measure of security and privacy has more to do with number theory than banking regulations.

90. VersionUS Conference in honour of Michel Raynaud. Orsay, 1822 June 2001. http://www.math.u-psud.fr/~mr2001/confraynaudus.htm

French version ALGEBRAIC GEOMETRY AND APPLICATIONS TO NUMBER THEORY A CONFERENCE IN HONOR OF MICHEL RAYNAUD ORSAY, JUNE 18-22, 2001 Invited speakers Ahmed Abbes, John Coates, Gerd Faltings, David Harbater, Yasutaka Ihara, Johan de Jong, Nicholas M. Katz, Barry Mazur, Vikram. B. Mehta, Laurent Moret-Bailly, Frans Oort, Michael Rapoport, Kenneth A. Ribet, Jean-Pierre Serre, Christopher Skinner, Tetsuji Shioda, Akio Tamagawa, John Tate. Program Organizing Committee Luc Illusie Jean-Marc Fontaine Yves Laszlo Information : mr2001@math.u-psud.fr You have also an hotel list available on the web. Mathematicians who plan to attend the conference are asked to fill the registration form

91. ANTS VI ANTS VI. Algorithmic number theory Symposium. University of Vermont. 13 18 June 2004. Since their inception in Cornell in 1994, the http://web.ew.usna.edu/~ants/

General Schedule Participants Proceedings ... Registration ANTS VI Algorithmic Number Theory Symposium University of Vermont 13 - 18 June 2004 NEW Information for Participants NEW Since their inception in Cornell in 1994, the biennial ANTS meetings have become the premier international forums for the presentation of new research in computational number theory. The sixth Algorithmic Number Theory Symposium (ANTS VI) will be held Sunday 13 June to Friday 18 June 2004 on the campus of the University of Vermont in Burlington, Vermont, USA. Important Dates 10 December 2003 - Deadline for papers (see Directions for Authors Saturday 12 June 2004 - Arrival day, reception in early evening Sunday 13 June 2004 - first day of talks for ANTS VI conference Wednesday afternoon - excursions Thursday evening - conference banquet Friday 18 June 2004 - last day of talks for ANTS VI conference 20-25 June 2004 - CNTA-8 (Canadian Number Theory Association meeting, Toronto, Canada) Paper Submission www.springeronline.com then on "Computer Science", then on "LNCS - print and online", and then on "For Authors" for details. Location ANTS VI will be held on the campus of the University of Vermont in Burlington, Vermont. Burlington, the largest city in Vermont, is located on the east coast of the United States, approximately 220 miles (355 kilometers) northwest of Boston, 285 miles (460 kilometers) north of New York City and 100 miles (160 kilometers) southeast of Montreal.

92. Five College Number Theory Seminar Five College number theory Seminar 20032004. Where and When, March 2. David Cox (Amherst College). Geometry and number theory on Clovers. March 9. http://www.math.umass.edu/~siman/seminar.html

Five College Number Theory Seminar Where and When Five College Number Theory Seminar talks are generally held at Amherst College in the Seeley Mudd building , which houses Amherst College's Department of Mathematics and Computer Science. Unless noted otherwise, all talks take place at 4:00 p.m. in room Seeley-Mudd 207 . Refreshments are served at 3:30 p.m. in Seeley-Mudd 208. Driving Direction to Amherst College Campus map of Amherst College Map of Lord Jeffrey Inn Parking Directions To find the parking lot in back of Seeley Mudd, drive east on College Street (Route 9) past the Amherst town common on your left. Two blocks after the common, turn right onto the College campus (just before you go under a railroad overpass). Take your second right and follow it until the road ends at the Seeley Mudd parking lot. From the parking lot, take the stairs in the Life Sciences building, just to the right of Seeley Mudd, up one flight, exit and turn left toward Seeley Mudd. Campus maps for Hampshire, Mt. Holyoke, Smith, and UMass

93. Number Theory At The University Of Georgia number theory and Arithmetic Geometry Group. Members, seminars. http://www.math.uga.edu/~lorenz/Number_Theory_Group.html

Number Theory and Arithmetic Geometry Group Permanent faculty and their fields of interests. William Alford Associate Professor, Ph.D. Tulane, 1963. Factoring and other number theory problems by computer. Matthew Baker Assistant Professor, Ph.D. U.C. Berkeley, 1999. Galois actions on torsion points. Modular curves and their Jacobians. Discreteness problems for arithmetic heights. Linear series and vector bundles in characteristic p. Arithmetic of curves and their Jacobians. Sybilla Beckmann Associate Professor, Ph.D. U. Penn., 1986. Galois theory. The inverse galois problem, that is, to determine whether every finite group is the galois group of some extension of the rational numbers. Arithmetic information on branched coverings, such as fields of definition. Tilings of the plane. Mathematics education. Andrew Granville Barrow Professor, Ph.D. Queens,1987. Distribution of primes. Sieving intervals. Distribution of `smooth' numbers. Properties of binomial coefficients. Cyclotomic fields. Carmichael numbers. Exponential sums. Integer solutions to Diophantine equations. Binary quadratic forms and the elementary theory of elliptic curves. Questions related to factoring and primality testing. Symbolic computation and `computing by homomorphisms'. Computational complexity, particularly lower bounds. Power series and the combinatorics of coefficients. Counting lattice points. Dan Lieman Associate Professor, Ph.D. Brown, 1992.

94. The Math Forum - Math Library - Number Theory mathematics. This page contains sites relating to number theory. Browse and Search the Library Home Math Topics number theory. http://mathforum.org/library/topics/number_theory/

Browse and Search the Library Home Math Topics : Number Theory Library Home Search Full Table of Contents Suggest a Link ... Library Help Subcategories (see also All Sites in this category Algebraic Number Theory Analytic Number Theory Sequences and Sets Fibonacci Sequence Selected Sites (see also All Sites in this category Continued Fractions: an Introduction - Adam Van Tuyl A brief introduction to the field of continued fractions, including some basic theory about the subject; the history of continued fractions, tracing some of the major developments in the field in the past 2500 years; some interactive applications that demonstrate the uses of continued fractions and let you calculate them; and the resources used in creating this site, including a bibliography and links to other sites on the Web. more>> Fermat's Last Theorem - MacTutor Math History Archives Essay describing Fermat's theorem with links to mathematicians such as Sophie Germain, Legendre, Dirichlet, Shimura and Taniyama, etc., from its inception through Andrew Wiles' proof, with another web site and 17 references (books/articles). more>> Number Theory - Dave Rusin; The Mathematical Atlas

95. Home Page Of Robert B. Ash University of Illinois. Downloadable texts in Abstract Algebra, Algebraic number theory, Commutative Algebra (PDF). http://www.math.uiuc.edu/~r-ash/

Robert B. Ash Professor Emeritus, Mathematics Dept. of Mathematics University of Illinois 1409 W Green St. Urbana, IL 61801 e-mail r-ash@math.uiuc.edu Books etc. On Line Abstract Algebra: The Basic Graduate Year A Course In Algebraic Number Theory A Course In Commutative Algebra A Pari/GP Tutorial Click below to read/download chapters in pdf format. PDF files can be viewed with the free program Adobe Acrobat Reader Comments and suggestions for improvement are welcome. Abstract Algebra: The Basic Graduate Year (Revised 11/02) This is a student-oriented text covering the standard first year graduate course in algebra. Solutions to all problems are included and some of the reasoning is informal. Front Preface and Table of Contents (110 K) Chapter 0 Prerequisites (194 K) Chapter 1 Group Fundamentals (150 K) Chapter 2 Ring Fundamentals (222 K) Chapter 3 Field Fundamentals (135 K) Chapter 4 Module Fundamentals (357 K) Enrichment Chapters 1-4 (288 K) Chapter 5 Some Basic Techniques of Group Theory (405 K) Chapter 6 Galois Theory (480 K) Chapter 7 Introducing Algebraic Number Theory (410 K) Chapter 8 Introducing Algebraic Geometry(448 K) Chapter 9 Introducing Noncommutative Algebra (350 K) Chapter 10 Introducing Homological Algebra(437 K) Supplement (315 K) Solutions Chapters 1-5 (461 K) Solutions Chapters 6-10 (449 K) End Bibliography, List of Symbols and Index (233 K)

96. Pi à La Mode: Science News Online, Sept. 1, 2001 An article describing a potential link between two disparate mathematical fieldsnumber theory and chaotic dynamics-that could lead to a proof that every digit of pi occurs with the same frequency. http://www.sciencenews.org/20010901/bob9.asp

Math Trek Mozart's Melody Machine Food for Thought Germ-Fighting Germs Science Safari Reading Faces TimeLine 70 Years Ago in Science News Week of Sept. 1, 2001; Vol. 160, No. 9 , p. 136 Pi à la Mode Mathematicians tackle the seeming randomness of pi's digits Ivars Peterson Memorizing the digits of pi—the ratio of a circle's circumference to its diameter—presents a hefty challenge to anyone undertaking that quixotic exercise. Starting with 3.14159265, the decimal digits of pi run on forever, and there is no discernible pattern to ease the task. This irregular landscape represents the form that emerges when a computer plots the first 1 million decimal digits of pi as a random walk. D.V. Chudnovsky and G.V. Chudnovsky The apparent randomness of pi's digits has long intrigued mathematician David H. Bailey of the Lawrence Berkeley (Calif.) National Laboratory. In the 1970s, when Bailey was a graduate student at Stanford University, he memorized the value of pi to more than 300 decimal places. It served "as a diversion during classroom lectures," Bailey confesses. In 1986, after joining NASA's Ames Research Center in Mountain View, Calif., he tested a new supercomputer by having it compute pi to nearly 30 million digits (SN: 2/8/86, p. 91). Any errors would reflect problems in the computer. "The program actually did disclose hardware bugs," Bailey says.

97. Courses Introduction to number theory ps file (495K); Introduction to number theory - pdf file (242K) This is a first course in number theory. http://www.maths.nott.ac.uk/personal/ibf/courses.html

Lecture Notes of Courses (.ps and .pdf files) Introduction to number theory - ps file (495K) Introduction to number theory - pdf file (242K) This is a first course in number theory. It includes p-adic numbers. Commutative algebra - ps file (381K) Commutative algebra - pdf file (202K) This course is an introduction to categories, modules over rings, Noetherian modules, unique factorization domains and polynomial rings over them, modules over principal ideal domains, localization. Introduction to algebraic number theory - ps file (432K) Introduction to algebraic number theory - pdf file (193K) This course (36 hours) is a relatively elementary course which requires minimal prerequisites from Commutative Algebra (see above) for its understanding. Integrality over rings, algebraic extensions of fields, field isomorphisms, norms and traces are discussed in the second part. Dedekind rings, factorization in Dedekind rings, norms of ideals, splitting of prime ideals in field extensions, finiteness of the ideal class group and Dirichlet's theorem on units are treated in the second part. Homological algebra - ps file (479K) Homological algebra - pdf file (228K) This is a very short introduction to homological algebra This course (25 hours) presents categories, functors, chain complexes, homologies, free, projective and injective obejcts in the category of modules over a ring, projective and injective resolutions, derived functors, Tor and Ext, cohomologies of modules over a finite group, restriction and corestriction.

98. 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.

99. G13NUM: NUMBER THEORY G13NUM number theory. Module aims To provide an an introduction to number theory, including elementary theory and some advanced topics and applications. http://www.maths.nott.ac.uk/personal/jec/courses/G13NUM/

G13NUM: NUMBER THEORY Autumn Semester 2003/2004 NEWS Solutions to the numerical parts of exam questions for 00/01, 01/02, 02/03 are now available here NEWS NEWS Confirmed examination time: 9 am on Thursday 15 January 2004 in Coates C13 NEWS Information Lecture log Handouts Coursework ... Links Module information for 2003/2004 Credits Duration : 33 lectures, three lectures a week in Autumn Semester, starting Monday 29/9/2003 Lecturer : Prof J. E. Cremona Lecture times Office hours : Monday 11-12, Tuesday 9-10, Wednesday 9-10 (C100). Brief content description: This is a first module in number theory, the study of problems concerning integers, including such topics as solutions of equations in integers, functions of an integer variable, and the distribution of special types of integers. The module includes topics such as unique factorization , linear congruences , quadratic congruences, the quadratic reciprocity law Gaussian integers Diophantine equations p -adic integers. Prerequisites: Module aims: To provide an an introduction to number theory, including elementary theory and some advanced topics and applications. Module objectives: By the end of the module, students should:

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)

Page 5     81-100 of 178    Back | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | Next 20