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         Number Theory:     more books (100)
  1. Number Theory and Its History (Dover Classics of Science and Mathematics) by Oystein Ore, 1988-04-01
  2. Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications) by Lawrence C. Washington, 2003-05-28
  3. Problems in Algebraic Number Theory (Graduate Texts in Mathematics) by M. Ram Murty, Jody Esmonde, 2004-10-25
  4. The Theory of Algebraic Numbers by Harry Pollard, Harold G. Diamond, 1998-01-12
  5. Introduction to Number Theory (Discrete Mathematics and Its Applications) by Martin Erickson, Anthony Vazzana, 2007-10-30
  6. A Primer of Analytic Number Theory: From Pythagoras to Riemann by Jeffrey Stopple, 2003-06-23
  7. Additive Number Theory The Classical Bases (Graduate Texts in Mathematics) by Melvyn B. Nathanson, 1996-06-25
  8. Elementary Number Theory (A Series of Books in the Mathematical Sciences) by Underwood Dudley, 1978-09-15
  9. Elements of Number Theory (Dover Phoenix Editions) by Ivan Matveevich Vinogradov, 2003-02-20
  10. A Course in Number Theory and Cryptography (Graduate Texts in Mathematics) by Neal Koblitz, 1994-09-02
  11. Computational Algebraic Number Theory (Oberwolfach Seminars) by M.E. Pohst, 2004-02-04
  12. An Introduction to Number Theory by Harold M. Stark, 1978-05-30
  13. Learning and Teaching Number Theory: Research in Cognition and Instruction (Mathematics, Learning, and Cognition)
  14. Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity (Springer Series in Information Sciences) by M.R. Schroeder, 2005-12-19

41. Combinatorics/Number Theory RESEARCH DIRECTORY
Graph theory, combinatorial number theory.
Combinatorics/Number Theory Directory
The main subareas of interest and the faculty connected with them are listed below. Some of these faculty have additional research interests
Graph Theory
Arthur Hobbs
Analytic Number Theory
Doug Hensley
Combinatoric Number Theory
Itshak Borosh
Combinatorial Topology
Laura Anderson
Toric Varieties
J. Maurice Rojas
Hal Schenck
Research Directory

42. Number Theory Foundation
Private philanthropic US organization for research in number theory.
Number Theory Foundation
The NTF pages have been moved to the University of Illinois. Please change your link to "": The new Number Theory Foundation web page.

43. Number Theory Foundation
number theory Foundation. Please change your link to http// The new number theory Foundation web page.
Number Theory Foundation
The NTF pages have been moved to the University of Illinois. Please change your link to "": The new Number Theory Foundation web page.

44. Math Resources
Contains links to software, professional organizations, research institutes, teaching aids, algebra, number theory, geometry, calculus, differential equations.
Math Resourses This page contains links to web sites with mathematically related information organized as follows: General Resource sites Home pages for professional organizations and research institutes:

45. NT Number Theory
Very large number theory section of the mathematics eprint arXiv.
Fri 4 Jun 2004 Search Submit Retrieve Subscribe ... iFAQ
NT Number Theory
Conferences Calendar Search
Authors: All AB CDE FGH ... U-Z
New articles (last 12)
4 Jun math.NT/0406065 Exponents of inhomogeneous Diophantine Approximation. Yann Bugeaud , Michel Laurent . 18 pages. NT
4 Jun math.NT/0406064 Exponents of Diophantine Approximation and Sturmian Continued Fractions. Yann Bugeaud , Michel Laurent . 25 pages. NT
3 Jun math.NT/0406048 Zeros of polynomials over Cayley-Dickson algebras. S. V. Ludkovsky . 9 pages. NT GR
3 Jun math.NT/0406033 Primitive root producing quadratics. Pieter Moree . 17 pages. NT
3 Jun math.NT/0406025 Divisibility tests and recurring decimals in Euclidean domains. Apoorva Khare . 21 pages. NT
2 Jun math.NT/0406018 An uncertainty principle for arithmetic sequences. Andrew Granville , K. Soundararajan . 39 pages. NT CA
2 Jun math.NT/0406012 Vanishing of L-functions of elliptic curves over number fields. Chantal David , Jack Fearnley , Hershy Kisilevsky . AIM 2004-10. NT MP
1 Jun math.NT/0405581 Restriction theory of the Selberg sieve, with applications. Ben Green , Terence Tao . 29 pages. NT CA
1 Jun math.CO/0405573

46. Paul Garrett: Crypto And Number Theory
Crypto and number theory. my homepage Introduction to cryptology, numbertheory, algebra, and algorithms. Protocols.
Crypto and Number Theory
my homepage updated 14:50, 17 May 04] [this page is] (No, I will not be teaching Crypto in 2004-05.) Some overheads from Fall '03 class:

47. Algebraic Number Theory Archive
Eprint archive for research in algebraic number theory and arithmetic geometry. Algebraic number theory Archive. Welcome to the
Algebraic Number Theory Archive
Welcome to the (new) Algebraic Number Theory Archive, founded by Nigel Boston and Dan Grayson and currently maintained by Michael Zieve . This archive is for research in algebraic number theory and arithmetic geometry. It is being converted to an overlay for the mathematics arXiv
  • Instructions for authors: Please contribute new submissions to the NT (Number Theory) category of the math arXiv following these submission instructions . Submissions in algebraic number theory will automatically appear here within a few days. Please send email if your arXiv article has been overlooked.
  • Members of the mailing list receive announcements of new e-prints. To subscribe (or unsubscribe), please write to the Michael Zieve
  • Some TeX fonts in compressed tar format, including the lams* and xy* fonts, which are needed for some of the e-prints.
    math.AG/0405529 : 27 May 2004, Cyclic p-groups and semi-stable reduction of curves in equal characteristic p>0 , by Mohamed Saidi.
    math.NT/0405505 : 26 May 2004
  • 48. Basics Of Computational Number Theory
    Basics of Computational number theory. Robert Campbell. Contents. 1. Introduction. This document is a gentle introduction to computational number theory.
    Basics of Computational Number Theory
    Robert Campbell
  • Introduction Modular Arithmetic Appendices
  • Programming Notes References Glossary
  • Introduction
    This document is a gentle introduction to computational number theory. The plan of the paper is to first give a quick overview of arithmetic in the modular integers. Throughout, we will emphasize computation and practical results rather than delving into the why. Simple programs, generally in JavaScript, are available for all of the algorithms mentioned. At the end of the paper we will introduce a the Gaussian Integers and Galois Fields and compare them to the modular integers. Companion papers will examine number theory from a more advanced perspective.
    Modular Arithmetic
    Modular arithmetic is arithmetic using integers modulo some fixed integer N . Thus, some examples of operations modulo 12 are:
    • 7 + 7 = 14 = 2 (mod 12) 5 * 7 = 35 = 11 (mod 12)
    Further examples can be generated and checked out with the following short programs. Note that, as JavaScript cannot compute with integers larger than 20 digits, the largest modulus allowed is 10 digits. (mod
    Among the basic operations we have missed the division operator. If we were working in the integers we would almost never be able to define a quotient (unless the answer is itself an integer). In the modular integers we can often, but not always, define a quotient:

    49. Magma Documentation -- Moved!
    WEB DI TEORIA DEI NUMERI (SITO ITALIANO) Translate this page Things of Interest to Number Theorists). Ricerca nel Web di Teoria dei Numeri di Roma (Search the number theory Web Pages in Rome).
    The Magma documentation has moved
    Please go to the new Magma front page You should update any bookmarks or links.

    s of areas/courses in number theory, lecture notes. Return to Menu page. Return to number theory Web page. Last modified 3rd April 2004.......
    Descriptions of areas/courses in number theory, lecture notes
  • The ABC Conjecture
  • Arithmetical Geometry
  • 51. Tools On Number Theory Web
    Tools on Number Theory Web

    52. LiDIA - A Library For Computational Number Theory
    Based at the Darmstadt University of Technology, Germany. LiDIA is a C++ library for computational number theory which provides a collection of highly optimized implementations of various multiprecision data types and timeintensive algorithms.

    A C++ Library For Computational Number Theory
    Main Page
    May 2004
    LiDIA 2.1.1 released
    LiDIA 2.1.1 is available for download The LiDIA 2.1 release of yesterday contained a bug that broke LiDIA on some platforms. We also encountered a defect in the standard library shipping with g++ 2.95.2 that caused builds with this compiler to fail. LiDIA 2.1 is withdrawn. LiDIA 2.1.1 brings a long list of bugfixes that accumulated since LiDIA 2.1pre7. Other changes include:
    • Unless you explicitly configure LiDIA with `enable-shared', only static LiDIA libraries are built. If you build LiDIA with g++, then the compiler's command line option `-fno-implicit-templates' is no longer used. LiDIA can be built atop the current cln release (1.1.6) again. Jochen Hechler contributed a new primality proofer (in the GEC package).
    Please refer to the release notes for an exhaustive list of changes and the known problems in LiDIA 2.1.
    Older News
    More news and facts about LiDIA can be found on LiDIA's NEWS page
    LiDIA is a C++ library for computational number theory which provides a collection of highly optimized implementations of various multiprecision data types and time-intensive algorithms. LiDIA is developed by the LiDIA Group at the Darmstadt University of Technology.

    number theory ftp sites/calculator programs/archives. Algebraic number theory Archives; finite rings. number theory Tables. Iwasawa invariants
    Number theory ftp sites/calculator programs/archives

    54. Number Theory Index
    History Topics Numbers and number theory Index. Number systems in ancient civilisations, Other number theory. Arabic number systems. Babylonian number systems.
    History Topics: Numbers and Number Theory Index
    Number systems in ancient civilisations Other number theory
  • Arabic number systems
  • Babylonian number systems
  • Egyptian number systems
  • Greek number systems ... Search Form JOC/EFR January 2004 The URL of this page is:
  • 55. Math 259: Introduction To Analytic Number Theory (Spring 1998)
    Lecture notes for Math 259 Introduction to Analytic number theory (Spring 1998) If you find a mistake, omission, etc., please let me know by email.
    Lecture notes for Math 259: Introduction to Analytic Number Theory (Spring 1998) If you find a mistake, omission, etc., please let me know by e-mail. The orange ball marks our current location in the course. For an explanation of the background pattern, skip ahead to the end of the page. and : administrivia and philosophy/examples : Elementary methods I: variations on Euclid : Elementary methods II: The Euler product for s>1 and consequences : Dirichlet characters and L-series; Dirichlet's theorem modulo the non-vanishing of L-series at s=1 click here For Erdos' simplification of Cebysev's proof of the "Bertrand Postulate": there exists a prime between x and 2x for all x>1. Adapted from Hardy and Wright, pages 343-344. : Functions of finite order: Hadamard's product formula and its logarithmic derivative : Conclusion of the proof of the Prime Number Theorem with error bound; some consequences and equivalents of the Riemann Hypothesis. Here's a bibliography

    56. The School Of Mathematics UEA:
    number theory research.
    Research in Number Theory at UEA
    Number theory is a broad, all-encompasing kind of subject that uses tools from many diverse areas. But it does not mean you need to be an egg-head to do original research. The way into many outstanding problems can often be at quite a low level. At UEA, the research centres around two different areas. (1) Diophantine Equations (2) Elliptic Curves. For (1), we look at special classes of equations where there are known to be infinitely many integer solutions. We look at special properties of these solutions and try to study their finer properties such as their location in `space' or their divisibilty by primes. For a good introduction, try Alan Baker's book "An Introduction to the Theory of Numbers". You could also have a look at some of the papers on my list of publications. Interest looks set to rise in (2) owing to Wiles' proof of Fermat' Theorem. Recently I have looking at inter-actions between the arithmetic of elliptic curves and dynamical systems. The approach is fairly down-to-earth although the language of algebraic geometry is becoming increasingly used. For an interesting explanation of the use of elliptic curves in number theory try Alf van der Poorten's book "Notes on Fermat's Last Theorem". You could also look at some of my recent papers on elliptic curves in my list of publications.

    57. Algorithmic Number Theory: Tables And Links
    Algorithmic (aka Computational) number theory Tables, Links, etc. Algorithmic number theory? What s that? Back to general math page
    Algorithmic (a.k.a. Computational) Number Theory : Tables, Links, etc.
    Tables of solutions and other information concerning Diophantine equations [equations where the variables are constrained to be integers or rational numbers]:
    • Trinomials with unusual Galois groups ( x x x x x x x x +567, etc.)
      • (Supporting computational data for Nils Bruin's theorem here
    • Elliptic curves of large rank and small conductor arXiv preprint; joint work with Mark Watkins; to appear in the proceedings of ANTS-VI (2004)): Elliptic curves over Q of given rank r up to 11 of minimal conductor or discriminant known; these are new records for each r in [6,11]. We describe the search method tabulate the top 5 (bottom 5?) such curves we found for r in [5,11] for low conductor, and for r in [5,10] for low discriminant.
    • Data and results concerning the elliptic curves ny =x -x arising in the ``congruent number'' problem:
      • Transparencies for ANTS-V lecture, in PS and PDF added 7/2002
      • All for which the curve has analytic rank at least 3, listed and used;
      • , under an additional conjecture;

    58. Course 311 - Abstract Algebra
    Lecture notes by David Wilkins, Trinity College, Dublin. Topics in number theory; Group Theory; Galois Theory.
    Course 311 - Abstract Algebra
    The lecture notes for course 311 ( Abstract algebra ), taught at Trinity College, Dublin, in the academic year 2001-02, are available here. The course consists of three parts:-
    Part I: Topics in Number Theory
    DVI PDF PostScript
    Part II: Topics in Group Theory
    DVI PDF PostScript
    Part III: Introduction to Galois Theory
    DVI PDF PostScript
    The following handouts were also distributed in the academic year 2001-02:
    A collection of problems
    DVI PDF PostScript
    The resolvent cubic of a quartic polynomial
    DVI PDF PostScript ... Trinity College , Dublin 2, Ireland

    59. Elementary And Analytic Number Theory
    Elementary and Analytic number theory. by WWL Chen. This set of notes has been renamed and moved. For access, please click here.
    Elementary and Analytic Number Theory by WWL Chen This set of notes has been renamed and moved. For access, please click here

    60. Mathematical Induction - Math Induction Problems And Puzzles
    A page of uncommon problems, most closely connected with number theory.
    Math Links
    PDF format Naoki Sato's Solutions PDF Spanish Version
    connected with Number Theory.Some properties may be proved in different ways.For more exercises, problems, puzzles, games, math riddles, brain teasers, etc. to see Math Links (not only of math induction). PROBLEM 1 Let : p-1 k=1 k n(p-1)+1 p-1 k=1 ((k )/2) - p(p-1)(n(p-1)+1)/2 Prove by induction that F(n) is divisible by p , for all integers n Hint
    PROBLEM 2 Use mathematical induction to prove the following: FIB(n) (FIB(n+2)=FIB(n+1)+FIB(n); FIB(1)=1,FIB(2)=1.
    Fibonacci sequence) Hint
    PROBLEM 3 Prove the following in more ways than one : n+1 FIB(n) (FIB(n+2)=FIB(n+1)+FIB(n); FIB(1)=1,FIB(2)=1.
    Fibonacci sequence ) Hint
    PROBLEM 4 M i=1 a i M i=1 a i kbc are divisible by b c i are relatively prime with respect to b and c). Let : M i=1 a i 1+(b-1)(c-1)n Prove by induction that : F(n) is divisible by b c ,for all integers n Solution
    PROBLEM 5 Let a, b, c be three positive integers where c= a + b . Let p be an odd factor of a +b +c
  • (a +b +c ) is divisible by p.
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