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 .. Algebra </title> <link rel="stylesheet" href="../erc01.css" type="text/css" /> </head> <body> <div id="top"> <img class="quill" src="../Images/myqull5.png" alt="myQuill"></img> <h2> Edgar R. Ch&aacute;vez</h2> <h3> Mathematics </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="#algebra"> Algebra </a></li> </ul> <ul class="NavMargin1"> <li><a href="#articles"> Articles </a></li> <li><a href="#grouptheory"> Group Theory </a></li> <li><a href="#misc"> Miscellaneous </a></li> <li><a href="#software"> Software </a></li> <li><a href="#textbooks"> Textbooks </a></li> </ul> <hr class="myLine" /> </div> <div class="InfoArea"> <div id="algebra"><span class="Subhead2"> Algebra </span> <div class="Tab5"> <p><a href="http://www.math.umn.edu/~garrett/m/algebra/"> Abstract Algebra </a> &nbsp; Paul Garrett, University of Minnesota </p> <p><a href="http://www.math.niu.edu/~beachy/aaol/"> Abstract Algebra online </a> &nbsp; By John Beachy<br /> <a class="Tab5" href="http://www.math.niu.edu/~beachy/abstract_algebra/study_guide/contents.html"> Abstract Algebra online study guide </a> &nbsp; John A. Beachy and William D. Blair</p> <p><a href="http://www.thiel.edu/mathproject/atps/default.htm"> Algebra Through Problem Solving </a> &nbsp; A non-traditional Algebra text, for high school and early college levels, placed on the Web by the Science Education Team at Los Alamos National Laboratory. Browse it on the Web or download a PDF version. </p> <p><a href="http://www.abstractalgebra.net/"> Algebraic Structures I </a> &nbsp; MA441, Loyola College Department of Mathematics. Good material: exams with answers. Good links. </p> <p><a href="http://theory.cs.uvic.ca/amof/"> AMOF: The Amazing Mathematical Object Factory </a> A teaching tool which generates permutations, subsets and combinations by having the user define the parameters of discrete objects. The Object Server returns a list of all objects that satisfy those parameters. </p> <p><a href="http://www.math.csusb.edu/notes/advanced/algebra/gp/gp.html"> Groups </a> &nbsp; From <a href="http://www.math.csusb.edu/notes/cgi/contents.cgi"> Math Notes</a>, Department of Mathematics, California State University, San Bernardino </p> <p><a href="http://www.jmilne.org/math/"> J.S. Milne's Mathematics Site </a> &nbsp; Graduate-level course notes on <a href="http://www.jmilne.org/math/CourseNotes/gt.html"> Group Theory </a> and related topics. </p> <p><a href="http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/partial.html"> Partial fractions </a> &nbsp; by Don Methven. Worth looking at because it covers a method, here called the cover-up method, not usually found in textbooks. </p> <p><a href="http://www.stewartcalculus.com/data/default/upfiles/AlgebraReview.pdf"> Review of Algebra </a> &nbsp; James Stewart. Check also the homepage, <a href="http://www.stewartcalculus.com/"> Stewart Calculus </a> for excellent Calculus resources. </p> <p><a href="http://www.d.umn.edu/~jgallian/"> Resources for Abstract Algebra </a> &nbsp; By Joseph A. Gallian, University of Minnesota. </p> <p><a href="http://www.central.edu/MAANotes/ITAASoftware.asp"> Software Tools for Working with Abstract Algebra </a></p> </div></div> <div id="articles"><span class="Subhead2"> Articles </span> <div class="Tab5"> <p><a href="http://plato.stanford.edu/entries/algebra/"> Algebra </a> &nbsp; Vaughan Pratt, Stanford Encyclopedia of Philosophy. </p> <p><a href="http://www.maa.org/pubs/nov01web.pdf"> Happy Abstract Algebra Classes </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; John Fraleigh. Excellent advice for teachers and students alike. Also available <a href="http://www.abstractalgebra.net/Misc/Fraleigh_FOCUS.pdf"> here</a>.</p> </div></div> <div id="grouptheory"><span class="Subhead2"> Group theory </span> <div class="Tab5"> <p><a href="http://nrich.maths.org/public/viewer.php?obj_id=1422"> An Introduction to Galois Theory </a> &nbsp; By Dan Goodman. An introductory article, aimed to high school students seriously interested in mathematics. </p> <p><a href="http://www.usna.edu/Users/math/wdj/tonybook/gpthry/tonybook.html"> An Introduction to Group Theory </a> &nbsp; Tony Gaglione, U.S. Naval Academy </p> <p><a href="http://groupexplorer.sourceforge.net/"> Group Explorer </a> &nbsp; Mathematical visualization software. It helps to visualize group theory, build intuition, and and enables experimentation with groups. </p> <p><a href="http://plus.maths.org/content/os/issue48/package/index"> Teacher package: Group theory </a> &nbsp; Plus Magazine. Plus teacher packages give teachers and students easy access to Plus content on a particular subject area. While accessible, Plus articles go far beyond what is usually taught at school. </p> <p> Theory of Groups, by Alexander G. Kurosh. <br /> <a class="Tab5" href="http://books.google.com/books?id=rp9c0nyjkbgC&amp;printsec=frontcover#v=onepage&amp;q&amp;f=false"> Volume 1 </a><br /> <a class="Tab5" href="http://books.google.com/books?id=B3lHYIuqPuQC&amp;printsec=frontcover&amp;source=gbs_ge_summary_r&amp;cad=0#v=onepage&amp;q&amp;f=false"> Volume 2 </a></p> </div></div> <div id="misc"><span class="Subhead2"> Miscellaneous </span> <div class="Tab5"> <p><a href="http://www.theory.csc.uvic.ca/~cos/root.html"> The Combinatorial Object Server </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; For researchers and educators who wish to easily produce list of combinatorial objects such as permutations, combinations, and subsets. Some source code can be downloaded. </p> </div></div> <div id="software"><span class="Subhead2"> Software - Abstract Algebra </span> <div class="Tab5"> <p><a href="http://www.gap-system.org/"> GAP - Groups, Algorithms, Programming </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; A system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides an extensible programming language that can be interpreted or compiled, an interactive environment, including an optional graphical user interface, and mathematical capabilities through a library of thousands of functions, packages, and data libraries. </p> <ul class="noLineBreak"> <li><a href="http://www.gap-system.org/Manuals/doc/htm/index.htm"> GAP 4 Manual </a> &nbsp; Includes tutorial, reference manual, and programming manual</li> <li><a href="http://www.math.colostate.edu/~hulpke/CGT/howtogap.pdf"> Abstract Algebra in GAP </a></li> <li><a href="http://www.math.colostate.edu/~hulpke/CGT/cgtnotes.pdf"> Notes on Computational Group Theory </a></li></ul> <p><a href="http://magma.maths.usyd.edu.au/magma/"> Magma </a> &nbsp; A large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatorics. It provides a mathematically rigorous environment for defining and working with structures such as groups, rings, fields, modules, algebras, curves, graphs, and many others. </p> <p id="parigp"><a href="http://pari.math.u-bordeaux.fr/"> PARI/GP </a> &nbsp; A computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. <br /> <a class="Tab5" href="http://www.ma.utexas.edu/users/villegas/gpbook/gpbook-scripts.gp"> GP scripts </a> from the book <a href="http://www.math.utexas.edu/users/villegas/gpbook/"> Experimental Number Theory </a> by Fernando Rodriguez Villega. </p> <p><a href="http://www.sagemath.org/"> Sage </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; A viable free open source alternative to Magma, Maple, Mathematica and Matlab. <br /> <a class="Tab3" href="http://wiki.sagemath.org/quickref">Sage Quick Reference Cards</a></p> <p><a href="http://www.central.edu/MAANotes/ITAASoftware.asp"> Software Tools for Working with Abstract Algebra </a></p> </div></div> <div id="textbooks"><span class="Subhead2"> Textbooks </span> <div class="Tab5"> <p><a href="http://www.math.uiuc.edu/~r-ash/Algebra.html"> Abstract Algebra: The Basic Graduate Year </a> &nbsp; Robert B. Ash, University of Illinois </p> <p><a href="http://abstract.ups.edu/"> Abstract Algebra: Theory and Applications </a> &nbsp; Thomas W. Judson, Austin State University. A text intended for a one- or two-semester undergraduate course. An <a href="http://abstract.ups.edu/download.html"> annual edition </a> can be freely downloaded: PDF format, GNU free documentation license. </p> <p><a href="http://www.math.miami.edu/~ec/book/"> Elements of Abstract and Linear Algebra </a> &nbsp; By Edwin H. Connell, University of Miami. A foundational textbook on abstract algebra with emphasis on linear algebra. You may download parts of the book or the entire textbook. </p> </div></div> <div class="Quote1"> <hr class="myLine" /> Any idiot can learn anything in mathematics. It requires only patience. <br /> Now, to create something -- that is another matter. <br />-- Alonzo Church <hr class="myLine" /> </div> </div> <div class="MyCopyright"> <hr class="myLine" /> Copyright &copy; 2003-2011 by Edgar R. Ch&aacute;vez. All rights reserved. <hr class="myLine" /> </div> </body> </html>