Mark Nelson » Mathematics
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Programming, mostly.Mon, 20 Oct 2014 12:43:36 +0000en-UShourly1http://wordpress.org/?v=3.5.1Data Compression With Arithmetic Coding
http://marknelson.us/2014/10/19/data-compression-with-arithmetic-coding/
http://marknelson.us/2014/10/19/data-compression-with-arithmetic-coding/#commentsSun, 19 Oct 2014 20:50:30 +0000Mark Nelsonhttp://marknelson.us/?p=2088Arithmetic coding is a common algorithm used in both lossless and lossy data compression algorithms. It is an entropy encoding technique, in which the frequently seen symbols are encoded with fewer bits than rarely seen symbols. It has some advantages over well-known techniques like Huffman coding. This article will describe the CACM87 implementation of arithmetic [...]]]>http://marknelson.us/2014/10/19/data-compression-with-arithmetic-coding/feed/11A Big Problem That Doesn’t Need a Bignum
http://marknelson.us/2011/02/14/a-big-problem-that-doesnt-need-a-bignum/
http://marknelson.us/2011/02/14/a-big-problem-that-doesnt-need-a-bignum/#commentsTue, 15 Feb 2011 00:10:37 +0000Mark Nelsonhttp://marknelson.us/?p=292Calculating a probability that involves k-step Fibonacci numbers can be done without resorting to Bignum classes - and the C++ deque container is a perfect class for the job.]]>http://marknelson.us/2011/02/14/a-big-problem-that-doesnt-need-a-bignum/feed/520 Heads In a Row – What Are the Odds?
http://marknelson.us/2011/01/17/20-heads-in-a-row-what-are-the-odds/
http://marknelson.us/2011/01/17/20-heads-in-a-row-what-are-the-odds/#commentsTue, 18 Jan 2011 02:44:35 +0000Mark Nelsonhttp://marknelson.us/?p=187An exercise in probability demonstrates the exact chances of flipping a fair coin k times in a row given n tosses.]]>http://marknelson.us/2011/01/17/20-heads-in-a-row-what-are-the-odds/feed/26Combinatorial Data Compression
http://marknelson.us/2011/01/09/combinatorial-data-compression/
http://marknelson.us/2011/01/09/combinatorial-data-compression/#commentsSun, 09 Jan 2011 23:10:57 +0000Mark Nelsonhttp://marknelson.us/?p=154Newcomers to the world of data compression often stumble on this old idea in hopes of creating a novel and powerful algorithm. In a nutshell, the idea is to create an enumerative coding system that uses combinatorial numbering to identify a message, in hopes of providing a more compact representation . Unfortunately, these schemes always [...]]]>http://marknelson.us/2011/01/09/combinatorial-data-compression/feed/4Innumeracy Revisited
http://marknelson.us/2010/09/12/innumeracy-revisited/
http://marknelson.us/2010/09/12/innumeracy-revisited/#commentsSun, 12 Sep 2010 17:35:39 +0000Mark Nelsonhttp://marknelson.us/2010/09/12/innumeracy-revisited/The New York Times has an interesting article today examining the curious fact that certain types of terrorist organizations have an unusually high ratio of engineers among their members. An interesting point to study, no doubt, but what caught my eye was this little blunder: William A. Wulf, a former president of the National Academy [...]]]>http://marknelson.us/2010/09/12/innumeracy-revisited/feed/11P ≠ NP?
http://marknelson.us/2010/08/10/p-%e2%89%a0-np/
http://marknelson.us/2010/08/10/p-%e2%89%a0-np/#commentsTue, 10 Aug 2010 18:42:47 +0000Mark Nelsonhttp://marknelson.us/2010/08/10/p-%e2%89%a0-np/You may have never heard of Vinay Deolalikar, but there is a chance that he may become next year’s Turing Award winner, not to mention an overnight millionaire. It seems that Vinay dropped the news at the start of this week that he had proven that P does not equal NP. In short, this proof [...]]]>http://marknelson.us/2010/08/10/p-%e2%89%a0-np/feed/05 Trillion Digits of Pi
http://marknelson.us/2010/08/06/5-trillion-digits-of-pi/
http://marknelson.us/2010/08/06/5-trillion-digits-of-pi/#commentsFri, 06 Aug 2010 18:46:27 +0000Mark Nelsonhttp://marknelson.us/2010/08/06/5-trillion-digits-of-pi/Back in 1981, fresh out of school, I was awestruck by Steve Wozniak’s program that calculated over 100,000 digits of e on an Apple II. (Anyone who has a scan of his article in the June 1981 issue of Byte, please email me a copy!) Shortly after reading the article, I ported his program to [...]]]>http://marknelson.us/2010/08/06/5-trillion-digits-of-pi/feed/2Innumeracy Part N
http://marknelson.us/2008/07/20/innumeracy-part-n/
http://marknelson.us/2008/07/20/innumeracy-part-n/#commentsSun, 20 Jul 2008 19:56:27 +0000Mark Nelsonhttp://marknelson.us/2008/07/20/innumeracy-part-n/This isn’t the first time I’ve complained about innumeracy, and I’m sure it won’t be the last. Just to get off on the right foot, let me give the definition of the word from thesite innumeracy.com: A term meant to convey a person’s inability to make sense of the numbers that run their lives. Innumeracy [...]]]>http://marknelson.us/2008/07/20/innumeracy-part-n/feed/5A Floating Point Problem
http://marknelson.us/1996/04/01/a-floating-point-problem/
http://marknelson.us/1996/04/01/a-floating-point-problem/#commentsMon, 01 Apr 1996 14:44:33 +0000Mark Nelsonhttp://test.kewby.com/?p=10An example of how you can run into trouble when performing floating point comparisons.]]>http://marknelson.us/1996/04/01/a-floating-point-problem/feed/0