ÿþ<?xml version="1.0" encoding="utf-16"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title> Edgar R. Chavez .. Mathematics .. Number theory </title> <link rel="stylesheet" href="../erc01.css" type="text/css" /> </head> <body> <div id="top"> <img class="quill" src="../Images/myquill5.png" alt="myQuill"></img> <h2> Edgar R. Ch&aacute;vez</h2> <h3> Mathematics - Number theory </h3> </div> <div class="NavigationLinks"> <hr class="myLine" /> <ul> <li><a href="../home.html"> Home </a></li> <li><a href="./mathematics.html"> Mathematics </a></li> </ul> <hr class="myLine" /> <ul> <li><a href="#numbertheory"> Number Theory </a></li> </ul> <ul class="NavMargin1"> <li><a href="#onlinebooks"> Online books </a></li> <li><a href="#software"> Software </a></li> </ul> <ul class="NavMargin2"> <li><a href="./misc.html#software"> Software - Mathematics </a></li> </ul> <hr class="myLine" /> </div> <div class="InfoArea"> <div id="numbertheory"><span class="Subhead2"> Number theory </span> <div class="Tab5"> <p><a href="http://www.americanscientist.org/issues/id.7300,y.0,no.,content.true,page.1,css.print/issue.aspx"> The Higher Arithmetic </a> &nbsp; How to count to a zillion without falling off the end of the number line. Brian Hayes, American Scientist magazine. Describes level-index arithmetic. In the level-index system a number is represented by an expression of the form e&uarr;e&uarr; ... &uarr;e&uarr;m. Includes an illustrative example and excellent scholarly references. </p> <p><a href="http://secamlocal.ex.ac.uk/~mwatkins/zeta/tutorial.htm"> Introductory prime number theory resources </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; The distribution of prime numbers, Riemann's zeta function, the Riemann Hypothesis, and more. </p> <p><a href="http://en.wikipedia.org/wiki/Normal_number"> Normal number </a> &nbsp; In mathematics, a normal number is a real number whose digits in every base follow a uniform distribution: all digits being equally likely, all pairs of digits equally likely, all triplets of digits equally likely, etc. </p> <p><a href="http://archives.math.utk.edu/topics/numberTheory.html"> Number Theory </a> &nbsp; From the <a href="http://archives.math.utk.edu/"> Math Archives </a></p> <p><a href="http://numbers.computation.free.fr/Constants/constants.html"> Numbers, constants and computation </a> &nbsp; Mathematical, historical, and algorithmic aspects of classical mathematical constants and prime numbers. Also, fast and easey programs can be downloaded. </p> <p><a href="http://www.research.att.com/~njas/sequences/Seis.html"> Online Encyclopedia of Integer Sequences </a><br /> <a class="Tab3" href="http://oeis.org/"> Look up page </a></p> <p><a href="http://www.muppetlabs.com/~breadbox/txt/rsa.html"> Prime Number Hide-and-Seek: How the RSA Cipher Works </a></p> <p><a href="http://secamlocal.ex.ac.uk/~mwatkins/zeta/surprising.htm "> Surprising connections between number theory and physics </a></p> <p><a href="http://www.utm.edu/research/primes/"> The Prime Pages </a> &nbsp; Prime number research, records, and resources. </p> <p><a href="http://www.numbertheory.org/"> Number Theory Web </a></p> </div></div> <div id="onlinebooks"><span class="Subhead2"> Online books </span> <div class="Tab5"> <p><a href="http://www.shoup.net/ntb/"> A Computational Introduction to Number Theory and Algebra </a> &nbsp; By Victor Shoup. A book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background. Published by Cambridge University Press and now in its second edition, the book will continue to be freely available under a <a href="http://creativecommons.org/"> Creative Commons License</a>. Both editions are available in PDF format.</p> <p><a href="http://www.trillia.com/moser-number.html"> An Introduction to the Theory of Numbers </a> &nbsp; By Leo Moser. Aimed at graduate students. </p> <p><a href="http://www.math.umbc.edu/~campbell/NumbThy/Class/BasicNumbThy.html"> Basis of Computational Number Theory </a> &nbsp; by Robert Campbell, University of Maryland, Baltimore County. </p> <p><a href="http://www.google.com/url?sa=t&amp;rct=j&amp;q=theory%20of%20numbers&amp;source=web&amp;cd=13&amp;ved=0CE8QFjACOAo&amp;url=http%3A%2F%2Fwstein.org%2Fent%2Fent.pdf&amp;ei=Y-XWTvjMKKP10gHP1eCDDg&amp;usg=AFQjCNEFzblQIqhHeuOQD7cfNTCxKOMSsA&amp;cad=rja"> Elementary Number Theory: Primes, Congruences, and Secrets </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; By William Stein. Examples use Sage. </p> <p><a href="http://books.google.com/books?vid=OCLC25785851&amp;id=PywPAAAAIAAJ&amp;pg=RA1-PA95&amp;lpg=RA1-PA95&amp;dq=%22theory+of+numbers%22&amp;num=20&amp;as_brr=1#PRA1-PA9,M1"> Essays on the Theory of Numbers </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; By Richard Dedekind, Chicago: The Open Court Publishing Company, 1909. Full text. </p> <p><a href="http://www.math.swt.edu/~haz/prob_sets/notes/notes.html"> Introduction to Number Theory </a> &nbsp; X.-D. Jia, Soutwest Texas State University </p> <p><a href="http://marauder.millersville.edu/~bikenaga/numth/numnote.html"> Notes on Elementary Number Theory </a> &nbsp; By Bruce Ikenaga, Millersville Univeristy </p> <p><a href="http://www.numbertheory.org/ntw/lecture_notes.html"> Online Number Theory lecture notes </a></p> <p><a href="http://www.spd.dcu.ie/johnbcos/Courses_2nd_year.htm"> Number Theory notes </a> &nbsp; By John Cosgrave, St. Patrick's College, Dublin. </p> <p><a href="http://math.berkeley.edu/~ribet/Math115/other_books.html"> Textobooks recommended at Berkeley </a></p> <p><a href="http://www.gutenberg.org/ebooks/13693"> The Theory of Numbers </a> &nbsp; By R. D. Carmichael </p> </div></div> <div id="software"><span class="Subhead2"> Software </span> <div class="Tab5"> <p><a href="http://gmplib.org/"> GNU GMP </a> &nbsp; GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. GMP is carefully designed to be as fast as possible, both for small operands and for huge operands. </p> <p><a href="http://orion.math.iastate.edu/cbergman/crypto/bignums.html"> Large Integer Arithmetic </a> &nbsp; References to various implementations.</p> </div></div> <div class="Quote1"> <hr class="myLine" /> God created the integers, all else is the work of man. <br />-- Leopold Kronecker <hr class="myLine" /> </div> </div> <div class="MyCopyright"> <hr class="myLine" /> Copyright &copy; 2003-2012 by Edgar R. Ch&aacute;vez. All rights reserved. <hr class="myLine" /> </div> </body> </html>