61. Elliptic Curves: Number Theory And Cryptography By Larry Washington (Chapman+Hall/CRC, 2003). Contents, errata. http://www.math.umd.edu/~lcw/ec.html

Elliptic Curves: Number Theory and Cryptography By Lawrence C. Washington The Table of Contents for the book can be viewed here Contact Information: Larry Washington Department of Mathematics University of Maryland College Park, MD 20742 lcw @math.umd.edu. Errata A list of corrections is being compiled and periodically updated here Please send comments and corrections to lcw @math.umd.edu.

62. IPAM - Workshop I: Number Theory And Cryptography - Open Problems Securing Cyberspace Applications and Foundations of Cryptography and Computer Security. http://www.ipam.ucla.edu/programs/scws1/

Securing Cyberspace: Applications and Foundations of Cryptography and Computer Security Workshop I: Number Theory and Cryptography - Open Problems October 9 - 13, 2006 Schedule and Presentations Program Poster PDF Hotel Accommodation and Air Travel Organizing Committee: Arjen Lenstra, Chair (‰cole Polytechnique F©d©rale de Lausanne (EPFL)) Don Blasius (UCLA) Kristin Lauter (Microsoft Research) Alice Silverberg (University of California, Irvine) Joseph Silverman (Brown University) Scientific Background Cryptography depends on a continuing stream of new insights and methods from number theory, arithmetic algebraic geometry, and other branches of algebra. In the past, there have been important developments in primality testing, factoring large integers, lattice-based cryptography, sieve methods, elliptic curve cryptography, ECPP, torus-based cryptosystems, discrete log problems, Weil pairing, cyclicity of elliptic curves and hyperelliptic cryptosystems. The content of this workshop will be based on emerging developments and discussion of open problems posed by applications. Invited Speakers Don Blasius (UCLA) Johannes Buchmann (Technishche Universtitat Darmstadt) Denis Charles (Microsoft Research) Jean-Marc Couveignes (Universit© de Toulouse II (Le Mirail)) Yvo Desmedt (University College London) Kirsten Eisentrager (University of Michigan)

63. Visible Structures In Number Theory By Peter Borwein and Loki Jörgenson. Recognising number patterns visually. http://www.cecm.sfu.ca/~loki/Papers/Numbers/

Next: Abstract Visible Structures in Number Theory Centre for Experimental Simon Fraser University, Burnaby, B.C. CANADA V5L 2T7 (236 kB) Color cover page Gzip'd PostScript (color) (306 kB) Alternat cover page Gzip'd PostScript (color) (232 kB) Color cover page with abstract Gzip'd PostScript (color) (148 kB) Color paper Gzip'd PostScript (color) (736 kB) Preprint: Submitted for publication ABSTRACT Number theorists have been interested in the characteristics of numerical constants like and for centuries. These numbers, real irrationals, are composed of an unending string of digits in a specific but seemingly random order. As statistical methods and traditional analysis have revealed very little, it has been proposed that the natural visual capacities of human perception be employed to search for complex correlations in the numerical distributions. Keywords irrationality, continued fractions, zero/one polynomi als, visualization Introduction In Pursuit of Patterns In Support of Proof The Structure of Numbers ... About this document ... loki@cecm.sfu.ca

64. REU In Computational Number Theory And Combinatorics Research Experiences for Undergraduates Computational number theory and Combinatorics Clemson University Clemson South Carolina http://www.math.clemson.edu/~kevja/REU/

Research Experiences for Undergraduates Computational Number Theory and Combinatorics Clemson University Clemson South Carolina 2008 REU Application Review has begun and will continue until all positions are filled. Program Description Special Colloquium Series Who may apply? Application Materials. ... Printable Announcement Please help us advertise this program by posting this announcment in your department. A List of Some Possible Problems. This list is meant to be representative of the types of problems on which we typically focus. It is not in any way complete and some of these problems have already recieved attention by previous REU participants. Thinking about graduate school? Getting started with LaTeX. The Clemson University department of Mathematical Sciences is very pleased to offer a National Science Foundation supported Research Experience for undergraduates. This program began in summer 2002 and is currently funded through summer 2010. For more information please contact Kevin James kevja@clemson.edu

65. A Friendly Introduction To Number Theory JH Silverman. Contents, preface, errata, further material. http://www.math.brown.edu/~jhs/frint.html

A Friendly Introduction to Number Theory Joseph H. Silverman A Friendly Introduction to Number Theory is an introductory undergraduate text designed to entice non-math majors into learning some mathematics, while at the same time teaching them how to think mathematically. The exposition is informal, with a wealth of numerical examples that are analyzed for patterns and used to make conjectures. Only then are theorems proved, with the emphasis on methods of proof rather than on specific results. Starting with nothing more than basic high school algebra, the reader is gradually led to the point of producing their own conjectures and proofs, as well as getting some glimpses at the frontiers of current mathematical research. Instructors : To receive an evaluation copy of A Friendly Introduction to Number Theory , send an email request to: Tim Galligan, Marketing Manager, Prentice-Hall. Please include your title and full mailing address. Click on the links for the following material. Table of Contents, Preface, and Introduction (PDF 60K) Two Sample Chapters (PDF 115K) Some Numerical and Computer Exercises Exercise 18.4

66. Algorithmic Number Theory Eric Bach and Jeffrey Shallit. Errata, bibliography in BibTeX format. http://www.cs.uwaterloo.ca/~shallit/ant.html

Algorithmic Number Theory Eric Bach and Jeffrey Shallit Algorithmic Number Theory, Volume I: Efficient Algorithms Published by MIT Press , August 1996 xvi + 512 pages US $55.00 ISBN 0-262-02405-5 (v.1) Library of Congress Call Number QA 241.B1085 1996 Description and Table of Contents What Some Readers and Reviewers Have Said Bibliography Errata and Addenda ... When will Volume 2 be published? E-mail:

67. Number Theory - Wolfram Mathematica number theory. Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on http://reference.wolfram.com/mathematica/guide/NumberTheory.html

baselang='NumberTheory.en'; PreloadImages('/common/images2003/link_products_on.gif','/common/images2003/link_purchasing_on.gif','/common/images2003/link_forusers_on.gif','/common/images2003/link_aboutus_on.gif','/common/images2003/link_oursites_on.gif'); DOCUMENTATION CENTER SEARCH Mathematica Mathematics and Algorithms Number Theory Mathematica draws on almost every major result in number theory. A key tool for two decades in the advance of the field, Mathematica 's symbolic architecture and web of highly efficient algorithms make it a unique platform for number theoretic experiment, discovery and proof. FactorInteger find the factors of an integer PrimeQ test whether an integer is prime Prime NextPrime PrimePi EulerPhi ... PowerMod modular powers, roots and inverses PrimitiveRoot MultiplicativeOrder ChineseRemainder Reduce find general solutions to Diophantine equations FindInstance search for particular solutions to Diophantine equations Element test field, ring, etc. memberships Integers Rationals Reals Algebraics ... Root represent an algebraic number RootReduce reduce algebraic numbers to canonical form GaussianIntegers allow factorization over Gaussian integers MinimalPolynomial RootApproximant ContinuedFraction FromContinuedFraction ... Rationalize find rational approximations LatticeReduce find short bases in integer lattices IntegerDigits RealDigits FromDigits DigitCount ... IntegerPartitions find restricted and unrestricted partitions of integers PartitionsP PartitionsQ FrobeniusNumber SquaresR ... PowersRepresentations find representations of integers as sums of powers

68. Department Of Mathematics - University Of Georgia Our number theory group is complemented by a large group in algebraic Three recent theses in number theory win UGA award for best thesis of the year. http://www.math.uga.edu/research/number_theory.html

Number Theory and Arithmetic Geometry Group Permanent faculty and their fields of interests. Pete L. Clark Assistant Professor, Ph.D. Harvard 2003. Arithmetic of abelian varieties; torsion points, endomorphism algebras, Weil-Chatelet groups. Modular curves and Shimura curves. Period-index problems. Pointless varieties and the (anti-) Hasse principle. Geometric approaches to the inverse Galois problem. Jonathan Hanke Assistant Professor, Ph. D. Princeton, 1999 . Arithmetic of Quadratic forms and their connections to Automorphic Forms, with an emphasis on computation. Topics include Local-Global principles, Local Densities, Mass Formulas, Class Numbers, Explicit Finiteness Theorems, and Computing all integers represented by a given Quadratic Form. Dino Lorenzini Professor, Ph.D. U.C. Berkeley, 1988 Neil Lyall Assistant Professor Ph.D., University of Wisconsin, 2004

69. QVNTS Every second Thursday, either in Montréal, in Burlington, or in Québec city. Seminar schedules from 1995. http://www.mathstat.concordia.ca/faculty/cdavid/qvnts.html

Québec-Vermont Number Theory Seminars The Québec-Vermont number theory seminars are held every second Thursday in Montréal, and occasionally in Burlington, or in Québec city. Schedule of the seminar in Past years: Fall 2005 Winter 2006

70. Mathematicians Unlock Major Number Theory Puzzle PhysOrg news Mathematicians unlock major number theory puzzle. http://www.physorg.com/news91813611.html

PhysOrg Account: Sign In Sign Up Home Nanotechnology ... All subcategories Published: 15:46 EST, February 27, 2007 Toolbox Rating: 4.2 Bookmark Save as PDF Print Email Blog It Digg It del.icio.us Slashdot It! Stumble It! Mathematicians unlock major number theory puzzle By Paroma Basu Mathematicians have finally laid to rest the legendary mystery surrounding an elusive group of numerical expressions known as the "mock theta functions." Number theorists have struggled to understand the functions ever since the great Indian mathematician Srinivasa Ramanujan first alluded to them in a letter written on his deathbed, in 1920. Now, using mathematical techniques that emerged well after Ramanujan's death, two number theorists at the University of Wisconsin-Madison have pieced together an explanatory framework that for the first time illustrates what mock theta functions are, and exactly how to derive them. Their new theory is proving invaluable in the resolution of long-standing open questions in number theory. In addition, the UW-Madison advance will for the first time enable researchers to apply mock theta functions to problems in a variety of fields, including physics, chemistry and several branches of mathematics. The findings appear in a series of three papers, the third appearing today in the Proceedings of the National Academy of Sciences "It's extremely gratifying to be able to say we solved the 'final problem' of Ramanujan," says co-author Ken Ono, UW-Madison Manasse Professor of Letters and Science, who is widely noted for contributions to number theory. "We simply got really lucky."

71. Arithmetic Geometry And Number Theory - Main Page Conference to honour Nicholas M. Katz on his 60th birthday. Princeton, NJ, USA; 1114 December 2003. http://www.math.princeton.edu/katzconf/

Main Page Conference Schedule Conference Participants Arithmetic Geometry and Number Theory Conference to Honor Nicholas M. Katz on his 60th birthday. December 11 - 14, 2003 Princeton University Mathematics Department Speakers Include: Jean-Benoit Bost Aise Johan deJong Pierre Deligne Helene Esnault Gerd Faltings Benedict H. Gross Christopher Hooley Mark Kisin Neal Koblitz Barry Mazur Philippe Michel John Tate Organizing Committee: Brian Conrey Gerard Laumon Peter Sarnak Andrew Wiles Funding Sources: National Science Foundation American Institute of Mathematics Princeton University Mathematics Department1 For more information about the conference please e-mail dona@princeton.edu

72. SFU Number Theory Group number theory is one of the oldest, deepest and most vibrant branches of modern mathematics. It centrally incorporates some of the most sophisticated and http://www.math.sfu.ca/numthry/

Department About Us Contact Info Surrey ... Employers Text Size: SFU Math Home Number Theory Group Current Events Coming talks Members Past events ... Reports and Theses Number Theory Group Current events Members Past events Reports and Theses Number theory is one of the oldest, deepest and most vibrant branches of modern mathematics. It centrally incorporates some of the most sophisticated and profound mathematical ideas that have been developed (witness the recent proof of Fermat's Last Theorem) and yet remains broadly useful in many areas of pure and applied mathematics. It is remarkable how often number theory comes to bear both in other areas of mathematics and in applications. A notable recent example is internet security whose protocols are based on number theoretic problems. Number theory has historically been motivated by the study of properties of integers and solutions to equations in integers, but now includes many other aspects, each with its own flavour and viewpoints. Broadly speaking, these can be divided into Analytic, Algebraic, Diophantine, and Geometric aspects of Number Theory. Research in Number Theory today often involves knowledge and expertise from areas such as Algebra, Algebraic Geometry, Analysis, Combinatorics, Probability Theory, Representation Theory, Topology. Connections to applicable fields include Coding Theory and Cryptography. At Simon Fraser University, we have a strong group in Number Theory which covers the spectrum of Number Theory. Together with the

73. Tools On Number Theory Department of Mathematics Tokyo Metropolitan University. Tools on number theory Web Workshop on Algorithmic number theory http://tnt.math.metro-u.ac.jp/

Japanese Department of Mathematics Tokyo Metropolitan University Tools on Number Theory Web About TNT Operations of TNT TNT Mailing List archive TNT FTP Site Official Mirror Site Symposium on Algebra and Computation ... Links $Date: 2004/08/19 08:43:56 $+ 9:00:00 (JST)

74. DIMACS Workshop On Combinatorial Number Theory DIMACS, Rutgers University, Piscataway, NJ, USA; 59 February 1996. http://dimacs.rutgers.edu/Workshops/CombNumber/index.html

DIMACS Workshop on Combinatorial Number Theory February 5-9, 1996 DIMACS Center - Rutgers University Piscataway, New Jersey Workshop Announcement Call for Participation Program How to Register ... Information on Travel Arrangements Proceedings were not published for this workshop. Workshop Index DIMACS Homepage Contacting the Center Document last modified on July 8, 1998.

75. Arithmetic, Numeration, Number Theory - Numericana Dr. Gerard P. Michon gives Final Answers to selected questions about elementary number theory, systems of numeration, divisibility, perfect numbers, http://home.att.net/~numericana/answer/numbers.htm

home index units counting ... physics Final Answers , Ph.D. Number Theory God created the integers, all else is the work of man Leopold Kronecker (1823-1891) The number 1 is not prime , as definitions are chosen to make theorems simple. Composite numbers are not prime, but the converse need not be true... Two prime numbers whose sum is equal to their product. Gaussian integers : Factoring into primes on a two-dimensional grid. The least common multiple may be obtained without factoring into primes. Standard Factorizations : n + 4 is never prime for n because Euclid's algorithm gives the greatest common divisor and : The GCD of p and q is of the form u p + v q. Greatest Common Divisor (GCD) defined for all commensurable numbers. Linear equation in integers can be solved using Pythagorean Triples : Right triangles whose sides are coprime integers. The number of divisors of an integer Perfect numbers and Mersenne primes Fast exponentiation by repeated squaring. Partition function . How many collections of positive integers add up to 15? A Lucas sequence whose oscillations never carry it back to -1.

76. INI Programme RMA Research session at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; 26 January 16 July 2004. http://www.newton.cam.ac.uk/programmes/RMA/

@import url("/css/prog-non_n4.css"); Institute Home Page Programmes Web-Seminars Programme Home Seminars Workshops Participants Long Stay Short Stay Additional Links Contacts Background Final Scientific Report Isaac Newton Institute for Mathematical Sciences Random Matrix Approaches in Number Theory 26 Jan - 16 Jul 2004 Organisers : Professor B Conrey ( Palo Alto ), Professor P Diaconis ( Stanford ), Dr F Mezzadri ( Bristol ), Professor P Sarnak ( Princeton ), Dr NC Snaith ( Bristol Programme theme The programme will mainly focus on how random matrix theory can further contribute to unanswered questions in number theory and on how to put the connection between random matrices and number theory on a rigorous footing. However, both random matrix theory and number theory individually play significant roles in theoretical physics and probability: random matrix statistics appear in the spectra of quantum systems whose classical limit is chaotic; the problem of quantum unique ergodicity has connections with the theory of modular surfaces and algebraic number theory; many of the main results on the statistics of ensembles of random matrices have been the work of probabilists; the Riemann zeta function even shows up in the theory Brownian motion - and this is just to name a few. These themes will also be developed through focused workshops. The main goal of this programme is to draw on the expertise of these diverse groups to produce new ideas on how random matrix theory can tackle important problems in number theory.

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