tag:blogger.com,1999:blog-3722233.post4757154296942759709..comments2021-10-18T17:43:52.487-05:00Comments on Computational Complexity: A Review of THE KLEIN FOUR's CDLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-3722233.post-87175425033876724272007-08-05T09:37:00.000-05:002007-08-05T09:37:00.000-05:00Good post, we always enjoy the feedback.By the way...Good post, we always enjoy the feedback.<BR/><BR/>By the way, I am the webmaster for the www.kleinfour.com site. The lyrics to all the songs are posted under Music > Song Lyrics <BR/><BR/>Let me know if you have any problems viewing these.<BR/><BR/>Scott Bailey<BR/>oughter@gmail.comUnknownhttps://www.blogger.com/profile/10441150248554993724noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-24274703324836494062007-07-12T10:05:00.000-05:002007-07-12T10:05:00.000-05:00My favorite math song has always been: Where are t...My favorite math song has always been: <BR/><BR/>Where are the zeros of zeta of s?", to the tune of "Sweet Betsy from<BR/>Pike"; words by Tom Apostol (As I recall it goes into minor key briefly for the verse about the Lindelof function :-) <BR/><BR/><BR/>Where are the zeros of zeta of s? <BR/>G.F.B. Riemann has made a good guess, <BR/>They're all on the critical line, said he, <BR/>And their density's one over 2pi log t. <BR/><BR/>This statement of Riemann's has been like trigger <BR/>And many good men, with vim and with vigor, <BR/>Have attempted to find, with mathematical rigor, <BR/>What happens to zeta as mod t gets bigger.<BR/><BR/><BR/>The efforts of Landau and Bohr and Cramer, <BR/>And Littlewood, Hardy and Titchmarsh are there, <BR/>In spite of their efforts and skill and finesse,<BR/>(In) locating the zeros there's been no success.<BR/><BR/>In 1914 G.H. Hardy did find, <BR/>An infinite number that lay on the line, <BR/>His theorem however won't rule out the case, <BR/>There might be a zero at some other place.<BR/><BR/><BR/><BR/>Let P be the function pi minus li, <BR/>The order of P is not known for x high, <BR/>If square root of x times log x we could show, <BR/>Then Riemann's conjecture would surely be so.<BR/><BR/>Related to this is another enigma, <BR/>Concerning the Lindelof function mu(sigma) <BR/>Which measures the growth in the critical strip, <BR/>On the number of zeros it gives us a grip.<BR/><BR/>But nobody knows how this function behaves, <BR/>Convexity tells us it can have no waves, <BR/>Lindelof said that the shape of its graph, <BR/>Is constant when sigma is more than one-half.<BR/><BR/>Oh, where are the zeros of zeta of s? <BR/>We must know exactly, we cannot just guess, <BR/>In orer to strengthen the prime number theorem, <BR/>The integral's contour must not get too near 'em.<BR/><BR/>New verses:<BR/><BR/>Now Andy has bettered old Riemann's fine guess <BR/>by using a fancier zeta (s). <BR/>He proves that the zeros are where they should be, <BR/>provided the characteristic is p.<BR/><BR/>There's a moral to draw from this sad tale of woe <BR/>which every young genius among you should know: <BR/>if you tackle a problem and seem to get stuck, <BR/>just take it mod p and you'll have better luck.<BR/><BR/><BR/>I went googling for it and found a copy on Robin Pemantle's website, he has a few more at: <BR/><BR/>http://www.math.upenn.edu/~pemantle/<BR/>PersonalHome.html<BR/><BR/>Enjoy!!<BR/><BR/>Lenore CowenAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-14808704557276673192007-07-09T09:50:00.000-05:002007-07-09T09:50:00.000-05:00Michael Sipser's Introduction to the Theory of Com...Michael Sipser's Introduction to the Theory of Computation, Second Edition<BR/>is a somewhat standard introductory text.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-68247950204566659792007-07-08T11:36:00.000-05:002007-07-08T11:36:00.000-05:00Hi,This is off the topic, but I was hoping for som...Hi,<BR/><BR/>This is off the topic, but I was hoping for some advice on learning computational complexity and this seemed like the place to ask. I have a computer Engineering background (doing my PhD), and I just took a course in computability, I was fascinated and decided I needed more. Unfortunately we don't have a complexity course in my school, so I will have to learn on my own. So my question is what is the best book (most recommended) for learning complexity on my own? Ideally I was wondering if there is a book with solutions to the problems in the book. Sorry for switching the topic. <BR/><BR/>Thanks in advance.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-83963016640002015242007-07-08T08:39:00.000-05:002007-07-08T08:39:00.000-05:00How about a book review:http://www.itwire.com.au/c...How about a book review:<BR/><BR/><A HREF="http://www.itwire.com.au/content/view/13339/53/" REL="nofollow">http://www.itwire.com.au/content/view/13339/53/</A><BR/><BR/>HAHAHAHAHA!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-37928639852071620782007-07-06T15:46:00.000-05:002007-07-06T15:46:00.000-05:00Let us not forget the Jimmy Buffet classic, "Math ...Let us not forget the Jimmy Buffet classic, "Math Sucks." I'm not sure if he realizes just how smart the line "There are numbers to big to be named" is. Here's the lyrics:<BR/><BR/><BR/> If necessity is the mother of invention<BR/>Then I'd like to kill the guy who invented this<BR/>The numbers come together in some kind of 3rd dimension<BR/>A regular algebraic bliss.<BR/>Let's start with something simple<BR/>Like one and one ain't three<BR/>And two plus two will never get you five<BR/>There's fractions in my subtraction<BR/>And X don't equal Y<BR/>But my homework is bound to multiply<BR/><BR/>Math sucks (math sucks)<BR/>Math sucks (math sucks)<BR/>I'd like to burn this textbook, I hate this stuff so much!<BR/>Math sucks (math sucks)<BR/>Math sucks (math sucks)<BR/>Sometimes I think that I don't know that much--But math sucks!<BR/><BR/>I got so bored with my homework<BR/>I turned on the T.V.<BR/>The beauty contest winners were all smiling through their teeth<BR/>They asked the new Miss America "Hey babe, can you add up all those bucks?"<BR/>She looked puzzled then just said, "Math Sucks!"<BR/><BR/>Math sucks (math sucks)<BR/>Math sucks (math sucks)<BR/>You don't even have to spell it, all you have to do is yell it<BR/>Math sucks (math sucks)<BR/>Math sucks (math sucks)<BR/>Sometimes I think that I don't know that much--But math sucks!<BR/><BR/>Geometry, trigonometry, and if that don't tax your brain<BR/>There are numbers to big to be named (too big to be named)<BR/>Numerical precision is a science with a mission<BR/>And I think it's gonna drive me insane<BR/><BR/>Parents fighting with their children and the Congress can't agree,<BR/>Teachers and their students are all jousting constantly<BR/>Management and labor keep rattling old sabers,<BR/>Quacking like those Peabody ducks<BR/><BR/>Math sucks (quack quack)<BR/>Math sucks (quack quack)<BR/>You don't even have to spell it, all you have to do is yell it!<BR/>Math sucks (math sucks)<BR/>Math sucks (math sucks)<BR/>Sometimes I think that I don't know that much--But math sucks!<BR/><BR/>Math sucks, math sucks, math sucks the big one<BR/>Math sucks, math sucks, math sucks the big one<BR/><BR/>[repeat until end, fades out]Unknownhttps://www.blogger.com/profile/17144266998977560260noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-63632270468780781072007-07-06T15:00:00.000-05:002007-07-06T15:00:00.000-05:00I wonder - what group theory is mentioned in "Conf...I wonder - what group theory is mentioned in "Confuse Me"? Seems to me like a strictly non-math song...matanhttps://www.blogger.com/profile/16023846623500719671noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-44626314331312896822007-07-05T11:29:00.000-05:002007-07-05T11:29:00.000-05:00Still, the math novelty song business is brutalTha...<I>Still, the math novelty song business is brutal</I><BR/><BR/>That's a gem, well done.Anonymousnoreply@blogger.com