The NSA has been doing this for years with advertisements in Notices of the American Mathematical Society. The problems were never really explicit though. They would just show you a picture, and then say something like "intrigued?, then contact the NSA...".
One of the problems I remember was balancing uniform blocks on a ledge. If you have one block, you can extend it over the ledge 1/2 of its length without falling. For two identical blocks, you can stack them and extend the blocks out 1/2 + 1/4. If you have three, then it is 1/2+1/4+1/6. For four blocks, you have to stack them in layers of 1, then 2, then 1; so you have a stack only three blocks high. You end up with 1 - 1/(2*Sqrt[2]) + 7/8 - 1/(2*Sqrt[2]). All of this was shown in a picture and the obvious problem is left unstated: find a method of determining the greatest distance that n blocks can be extended over the ledge.
bcrowell provided one counter example above. Another is Allen Hatcher's Algebraic Topology textbook which is used in many classes. It is available both online and in print form. Hatcher has a few other books in progress available as well. Robert Ash has an introductory abstract algebra book available online, along with a couple books on other subjects. I don't know anyone who has used Ash's book but google reveals that it has been used by at least one class. I could go on, but my point is that use of online texts in classes and publishing work in progress online is becoming more and more widespread within mathematics. I have not seen this so much in disciplines other than mathematics, but I am not very close to the other academic communities.
You might not play guitar with a bow, but that doesn't mean other people don't. I don't use a bow, but I have played around with an ebow on a couple of occasions.
You can read the actual theorem from Chapter 3 of Peter Gilkey's book available here. The Aitiyah-Singer Index Theorem is Theorem 3.9.5 on page 233, right at the top of the page. There is a nice explanation of it in easy to understand terms on MIT's press release. Unfortunately, this doesn't seem to capture how impressive the theorem really is.
This is considered a standard portion of a CS curriculum. Every CS grad should be expected to have had some exposure to those topics. Here is the the ACM guidelines showing coverage of digital logic and architecture. I think Patterson and Hennessy covers most of this, except maybe for digital logic.
Actually, it is more complicated than that. The "n-dimensional sphere" or S^n does not have a universally accepted definition. The probem comes from what the word dimension refers to. You can define the n-sphere S^n to be the unit sphere in R^{n+1}, in which case n refers to the dimension of the sphere itself(or, as you said, the sphere is locally diffeomorphic to R^n). You can also define the n-sphere S^n to be a sphere(x1^2 +... + xn^2 = r^2) in R^{n}. Here n refers to the dimension of the space. Most topologists seem to use the former definition. However, I do seem to remember an algebraic topology book using the other definition... I can't remember which book this is though; maybe Maunder. Anyways, the ambiguity is not much of a problem in practice since it is usually obvious which meaning is intended, and the author will generally make a note of this as well.
I have a similar machine, which kernel 2.4.21, XFree86 4.2.0 running at 16 bpp, and a PCI TNT2. One instance of glxgers runs at around 720 fps, and two instances run at 330 fps. As I ran more instances, the fps degraded linearly, so that with 12 running, I was seeing about 55 fps on each one.
Am I really the only one left on this planet that believes that assembly language, C, BASIC, Cobol, Fortran, Forth, Pascal, HTML, and Perl are "good enough" for anything, and there's no need for another billion languages, "standards", plug-ins, etc.?
Perl came about in 1987 or thereabouts. Do you think that it was really needed at that point? We already had sed, sh, awk, C, and the rest of the Unix tools. For that matter when C came out we already had Lisp, Smalltalk, BCPL, Intercal, and dozens of other languages(which you didn't bother to include in your list). You also didn't mention any versions in your list. Which version of Fortran is "good enough"? Is it Fortran I, II, III, 66, 77, or 90? To be honest, I'm inclined to agree with you, up to a point. I think that far too often new technologies are adopted and succeed just by benefit of being new, without actually offering any real improvements over existing technologies. I don't think that this provides an argument to simply dismiss all new technologies though. There definitely has been, and still is, room for improvement.
Tea is a stimulant, just as coffee is. It generally has less caffeine than coffee, but it also has theophylline which is another stimulant. Some beverages also have theobromine, which is also in chocolate, as another stimulant. There also seems to be a growing number of fruit flavored beverages with added stimulants of a wide variety, for example guarana, which are on the market.
I agree, and I think much of the misinterpretation comes because many are commenting on Knuth without ever having really read it. This comes from the introduction to TOACP.V3 2nd edition(which is from 1998 by the way, not so ancient):
The title "Sorting and Searching" may sound as if this book is only for those systems programmers who are concerned with the preperation of general-purpose sorting routines or applications to information retrieval. But in fact the area of sorting and searching provides an ideal framework for discussing a wide variety of important general issues:
How are good algorithms discovered?
How can algorithms and programs be improved?
How can the efficiency of algorithms be analyzed mathematically?
How can a person choose rationally between different algorithms for the same task?
In what sense can algorithms be proved "best possible"?
How does the theory of computing interact with practical considerations?
How can external memories like tapes, drums, or disks be used efficiently with large databases?
Indeed, I believe that virtually every important aspect of programming arises somewhere in the context of sorting and searching!
mplayer/mencoder will do both of the things you have asked for. I believe transcode will as well. Basically what you want is something like the following(using mencoder):
SCOX is traded on Nasdaq and has been doing very well as a result of all of the recent happenings. Friday they closed at 4.75, and today they hit 8.04, and are now trading at 6.92. This is a result of the MSFT news. SCO's market cap is currently 84.4 milion. You can find all of this data at finance.yahoo.com by punching in SCOX.
Re:Everything can be related to math.
on
Origami and Math
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· Score: 1
In general if you ask someone in America to name a mathematician, their answer is invariably one of John Nash(American), Andrew Wiles(British), or Theodore Kaczynski(American). Then again, we don't put mathematicians on stamps or money in this country, unless you count Franklin. Anyways, Poincare really should be on your list of French mathematicians as well, possibly replacing Catalan who was not French. That said, five American mathematicians(all dead(like your French), and all well known among non-mathematicians): Norbert Wiener, Alonzo Church, Haskell B. Curry, Claude Shannon, and Richard Hamming.
There are numerous things wrong with Java. If you can only name one(it's not as fast as C++), then you really don't know the language. Oh, and there are people who claim to have examples of Java beating C++ in performance. I have yet to see any of these that actually deliver though.
Slashdot Mirror
That is what drove a mathematician. Hardy is certainly not representative of your typical modern day mathematician. You should still read his book.
The NSA has been doing this for years with advertisements in Notices of the American Mathematical Society. The problems were never really explicit though. They would just show you a picture, and then say something like "intrigued?, then contact the NSA...".
One of the problems I remember was balancing uniform blocks on a ledge. If you have one block, you can extend it over the ledge 1/2 of its length without falling. For two identical blocks, you can stack them and extend the blocks out 1/2 + 1/4. If you have three, then it is 1/2+1/4+1/6. For four blocks, you have to stack them in layers of 1, then 2, then 1; so you have a stack only three blocks high. You end up with 1 - 1/(2*Sqrt[2]) + 7/8 - 1/(2*Sqrt[2]). All of this was shown in a picture and the obvious problem is left unstated: find a method of determining the greatest distance that n blocks can be extended over the ledge.
bcrowell provided one counter example above. Another is Allen Hatcher's Algebraic Topology textbook which is used in many classes. It is available both online and in print form. Hatcher has a few other books in progress available as well. Robert Ash has an introductory abstract algebra book available online, along with a couple books on other subjects. I don't know anyone who has used Ash's book but google reveals that it has been used by at least one class. I could go on, but my point is that use of online texts in classes and publishing work in progress online is becoming more and more widespread within mathematics. I have not seen this so much in disciplines other than mathematics, but I am not very close to the other academic communities.
You might not play guitar with a bow, but that doesn't mean other people don't. I don't use a bow, but I have played around with an ebow on a couple of occasions.
You can read the actual theorem from Chapter 3 of Peter Gilkey's book available here. The Aitiyah-Singer Index Theorem is Theorem 3.9.5 on page 233, right at the top of the page. There is a nice explanation of it in easy to understand terms on MIT's press release. Unfortunately, this doesn't seem to capture how impressive the theorem really is.
This is considered a standard portion of a CS curriculum. Every CS grad should be expected to have had some exposure to those topics. Here is the the ACM guidelines showing coverage of digital logic and architecture. I think Patterson and Hennessy covers most of this, except maybe for digital logic.
See for example, GAP, or Macaulay2.
Actually, it is more complicated than that. The "n-dimensional sphere" or S^n does not have a universally accepted definition. The probem comes from what the word dimension refers to. You can define the n-sphere S^n to be the unit sphere in R^{n+1}, in which case n refers to the dimension of the sphere itself(or, as you said, the sphere is locally diffeomorphic to R^n). You can also define the n-sphere S^n to be a sphere(x1^2 + ... + xn^2 = r^2) in R^{n}. Here n refers to the dimension of the space. Most topologists seem to use the former definition. However, I do seem to remember an algebraic topology book using the other definition... I can't remember which book this is though; maybe Maunder. Anyways, the ambiguity is not much of a problem in practice since it is usually obvious which meaning is intended, and the author will generally make a note of this as well.
I've coded in Oberon. You can too.
You can see how much tax they paid here. It's not quite all of the same people though, since the latest data that the IRS published is from 2000 .
Here are a few. I've used lsh myself, and found it quite nice.
I have a similar machine, which kernel 2.4.21, XFree86 4.2.0 running at 16 bpp, and a PCI TNT2. One instance of glxgers runs at around 720 fps, and two instances run at 330 fps. As I ran more instances, the fps degraded linearly, so that with 12 running, I was seeing about 55 fps on each one.
Here is the response to the paper which the page you linked is based on.
Tea is a stimulant, just as coffee is. It generally has less caffeine than coffee, but it also has theophylline which is another stimulant. Some beverages also have theobromine, which is also in chocolate, as another stimulant. There also seems to be a growing number of fruit flavored beverages with added stimulants of a wide variety, for example guarana, which are on the market.
IEEE 754/854 has not changed for some time now, but it does have some problems and a revision is currently being worked on. See http://grouper.ieee.org/groups/754/revision.html.
Many are available for free in paper form as well from public libraries.
mencoder movie.asf -o movie.mpg -oac mp3lame -lameopts cbr:br=96:vol=6 -ovc lavc -lavcopts vcodec=mpeg4:vbitrate=1300:vhq:v4mv
You'll have to tweak the options to get desirable results.
That has sugar. You should drink pure grain alcohol and rain water.
SCOX is traded on Nasdaq and has been doing very well as a result of all of the recent happenings. Friday they closed at 4.75, and today they hit 8.04, and are now trading at 6.92. This is a result of the MSFT news. SCO's market cap is currently 84.4 milion. You can find all of this data at finance.yahoo.com by punching in SCOX.
In general if you ask someone in America to name a mathematician, their answer is invariably one of John Nash(American), Andrew Wiles(British), or Theodore Kaczynski(American). Then again, we don't put mathematicians on stamps or money in this country, unless you count Franklin. Anyways, Poincare really should be on your list of French mathematicians as well, possibly replacing Catalan who was not French. That said, five American mathematicians(all dead(like your French), and all well known among non-mathematicians): Norbert Wiener, Alonzo Church, Haskell B. Curry, Claude Shannon, and Richard Hamming.
There are numerous things wrong with Java. If you can only name one(it's not as fast as C++), then you really don't know the language. Oh, and there are people who claim to have examples of Java beating C++ in performance. I have yet to see any of these that actually deliver though.