most recent 30 from http://mathoverflow.net 2013-05-22T20:31:44Z http://mathoverflow.net/feeds/question/62677 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62677/applications-of-commutative-algebra Berry 2011-04-22T22:54:16Z 2011-04-23T01:16:41Z

<p>Hi. I'm preparing a thesis in commutative algebra, and when I say this to my friends they always ask me what are the applications to "real-world", and I don't know what to answer. This let me think that I'm studying something useless. I'm studying on the Matsumura and on the Herzog-Bruns. Any of you know some applications of this abstract algebra to the real-world?</p>

http://mathoverflow.net/questions/62677/applications-of-commutative-algebra/62679#62679 Igor Rivin 2011-04-22T23:58:58Z 2011-04-22T23:58:58Z

<p>Google "Gunnar Carlsson" and "Rob Ghrist" and "Berndt Sturmfels" and "John Canny", and...</p>

http://mathoverflow.net/questions/62677/applications-of-commutative-algebra/62685#62685 quid 2011-04-23T00:53:45Z 2011-04-23T00:53:45Z

<p>Commutative Algebra and Algebraic Geometry are of relevance to Statistics and in recent years there was quite a lot of activity on this.</p> <p>See e.g. <a href="http://en.wikipedia.org/wiki/Algebraic_statistics" rel="nofollow">http://en.wikipedia.org/wiki/Algebraic_statistics</a> (and scroll down, the beginning is perhaps also interesting for your purpose, but what I mean is rather at the end of the page).</p> <p>For example there is this book L. Pachter and B. Sturmfels. Algebraic Statistics for Computational Biology from 2005.</p> <p>And there is a fairly recent (I believe) Activity Group of SIAM (Society for Applied and Industrial Mathematics) for Algebraic Geometry (which perhaps is close enough CA), about to hold its first conference <a href="http://www.siam.org/meetings/ag11/" rel="nofollow">http://www.siam.org/meetings/ag11/</a> (looking up the planery speakers should yield further details; there is a considerable intersection with names I. Rivin gives).</p> <hr> <p>Another topic at the borderline of commutative algebra and number theory is Elliptic Curve Cryptography see <a href="http://en.wikipedia.org/wiki/Elliptic_curve_cryptography" rel="nofollow">http://en.wikipedia.org/wiki/Elliptic_curve_cryptography</a> and also other cryptographic problems, but in part they feeel perhaps too number theoretic for you.</p> <hr> <p>Finally, not really your question, but apparently the motivation: to convince your friends, depending on the background of your friends, I suggest to explain them the (simple) congruence arithmetic behind the final digit of the ISBN numbers. This was the only thing that I found that I felt had some real impact on the opinion of some of my friends on the usefulnes of pure mathematics. </p>

http://mathoverflow.net/questions/62677/applications-of-commutative-algebra/62688#62688 Hailong Dao 2011-04-23T01:13:15Z 2011-04-23T01:13:15Z

<p><a href="http://d-mathnet.preprints.org/staff/phpages/brunsw/Allahabad.pdf" rel="nofollow">Counting (partially) magic squares</a> (and in fact combinatorics and commutative algebra have had really fruitful interactions). </p> <p>One should also look at <a href="http://mathoverflow.net/questions/2556/real-world-applications-of-mathematics-by-arxiv-subject-area" rel="nofollow">this question</a>.</p>

http://mathoverflow.net/questions/62677/applications-of-commutative-algebra/62690#62690 danseetea 2011-04-23T01:16:41Z 2011-04-23T01:16:41Z

<p>The book "Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra" by Cox, Little &amp; O'Shea, contains some "real world" applications, specifically chapter 6 (of the 3rd edition) is titled "Robotics and Automatic Geometric Theorem Proving".</p>