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DIMACS Reconnect Conference 2006
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Research
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By Anonymous Hero
Posted Tue Nov 01, 2005 at 06:31:53 AM PDT
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DIMACS Reconnect '06 Conference:
Morgan State University
Simple and Complex Discrete-time Population Models in Ecology and Epidemiology
The Reconnect '06 Conference sponsored by DIMACS (the Center for Discrete Mathematics and Theoretical Computer Science) is geared towards exposing faculty teaching undergraduates to current research topics relevant to the undergraduate classroom, involving them in writing materials useful in the classroom and reconnecting them to the mathematical sciences enterprise by exposing them to new research directions and questions. The program at Morgan State in Baltimore will be held from July 9 - July 15, 2006. It is anticipated that applicants accepted to participate will receive lodging and meals through NSF funding. For more information or an application form, visit our web site at http://dimacs.rutgers.edu/reconnect/. Or, contact the Reconnect Program Coordinator, at reconnect@dimacs.rutgers.edu or (732) 445-4304.
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Partial Proof of the Goldbach Conjecture
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Research
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By Goldbach
Posted Mon Oct 31, 2005 at 09:18:53 AM PDT
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The Goldbach Conjecture can be stated as follows: for every natural number m there exist primes p and q such that T(p)+T(q)=2m, where T(N) is the totient function (the number of relative primes to N less than N; relative primes are numbers that do not share any common divisors, i.e., 9 and 4.) By definition, the totient value of a prime p is p-1, i.e., T(p)=p-1. For instance, let m=1; then T(p)+T(q)=2, (p-1)+(q-1)=2, p+q=4, and since both p and q are prime, p=q=2. Now let us examine the case p=2 and q is odd. We see that T(p)=T(2)=2-1=1, so the Goldbach Conjecture (GC) becomes T(q)=2m-1. Since q is odd, T(q)=q-1 is even; but 2m-1 must be odd (definition of odd.) Therefore the GC does not hold in this case. In other words, it has been shown that the Goldbach Conjecture can be stated as follows: all even numbers greater than 4 are the sum of 2 odd primes. I will proceed by showing all the possible values of m that I have been able to prove.
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Math blogging ... and the PhD
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Research
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By overconvergent
Posted Sat May 21, 2005 at 04:19:37 PM PDT
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There are a few math and education bloggers that I read quite regularly - Moebius Stripper, a Canadian who has been teaching in British Columbia, Learning Curves, who also teaches math, Erin O'Connor, who doesn't teach math but was a professor at Penn until she left to teach at a private high school (here's an interesting post by Prof. O'Connor on mathematics), and Joanne Jacobs, who is also not a mathematician but has interesting things to say about education generally.
One of our kind Anonymous Heroes also mentioned Ars Mathematica, "Dedicated to the mathematical arts" (linking to papers, blogs, interesting proofs, etc).
The second half of this article was inspired by a comment made by Moebius Stripper about the PhD program, in this post.
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Richard Hamming on Research
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Research
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By Emil Volcheck
Posted Mon May 02, 2005 at 03:00:40 PM PDT
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At a talk in 1986, Richard Hamming, the BellCore researcher who was a pioneer of error-correcting codes, gave a talk addressing the question ``Why do so few scientists make significant contributions and so many are forgotten in the long run?''
The transcript to this talk is well worth reading.
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NSF Awards Database
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Research
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By Emil Volcheck
Posted Wed Apr 27, 2005 at 11:44:11 PM PDT
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Ever wonder what research projects the NSF is giving grants for? Then
search the NSF Awards database!
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Goldbach Conjecture Disproved
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Research
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By overconvergent
Posted Fri Apr 01, 2005 at 01:00:48 AM PDT
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In an email message today to the Number Theory mailing list, a counterexample to the Goldbach Conjecture - that every even number bigger than 2 can be written as the sum of two prime numbers - was announced. The method is said to involve the Hardy-Littlewood circle method and to use a magma computation that took several weeks to complete. (The actual, "marvellous" counterexample is too big to fit into this posting).
A senior number theorist said, under the condition of anonymity, "we're in shock. No-one saw this coming."
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Mathematics On Your Webpage
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Research
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By overconvergent
Posted Wed Feb 16, 2005 at 04:31:21 AM PDT
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One piece of advice that I have been able to give my graduate student advisees is to have a webpage with professional information (here are my research interests, this is a list of conferences I have attended, here is my CV).
One problem that mathematicians have is that HTML isn't really suited to the display of mathematics, beyond a simple description in English ("I study non-Riemannian hypersquares and have published an article on them in the Journal of Obscure Results").
There are two rather different solutions that I know of to this problem.
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