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Story Problem
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Research
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By coryking
Posted Tue Sep 26, 2006 at 11:22:50 AM PDT
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A 302 metric ton train leaves station A at 3:12am pacific standard time. It must arrive at station B, 103 kilometers away, at exactly 4:32am, PST.
The train has been modified so that it can only accelerate or de-accelerate. The train cannot travel at a constant velocity.
The engineer would like the train to have a constant acceleration for the first half, and a constant negative acceleration for the last half.
Ignoring friction or wind resistance, what should he use for a rate of acceleration? How much energy will the train consume over the entire trip? If, instead, the train could travel at a constant speed, would the engineer use less fuel if he were to travel the majority of the trip at a constant velocity? If we account for wind or friction, which train would be more efficient?
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Researchers find new prime number
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Research
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By Anonymous Hero
Posted Wed Jan 04, 2006 at 01:46:35 PM PDT
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Here's the story plus link:
http://news.yahoo.com/s/ap/20060104/ap_on_sc/largest_prime_number
By GARANCE BURKE, Associated Press Writer
Tue Jan 3, 10:09 PM ET
KANSAS CITY, Mo. - Researchers at a Missouri university have identified the largest known prime number, officials said Tuesday.
The team at Central Missouri State University, led by associate dean Steven Boone and mathematics professor Curtis Cooper, found it in mid-December after programming 700 computers years ago.
A prime number is a positive number divisible by only itself and 1 -- 2, 3, 5, 7 and so on.
The number that the team found is 9.1 million digits long. It is a Mersenne prime known as M30402457 -- that's 2 to the 30,402,457th power minus 1.
Mersenne primes are a special category expressed as 2 to the "p" power minus 1, in which "p" also is a prime number.
"We're super excited," said Boone, a chemistry professor. "We've been looking for such a number for a long time."
The discovery is affiliated with the Great Internet Mersenne Prime Search, a global contest using volunteers who run software that searches for the largest Mersenne prime.
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Folding Paper in Half 12 Times
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Research
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By Anonymous Hero
Posted Fri Nov 18, 2005 at 02:01:40 PM PDT
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I just came across the following somewhat interesting link and thought I'd share.
Mathworld also has some info and mentions how in December of 2001 Britney Gallivan, a High School student, derived a formula for the limit of paper folding and then proceeded to set a new world record by folding first gold foil and then paper in half a whopping 12 times in January of 2002, thus debunking the assertions of that paper cannot be folded in half more than eight times.
Enjoy!
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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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