Since I made a post earlier about the undergraduate problem solving contest I figured I might as well do an update post now. As it happens the first problem is the only one that I didn't turn in a solution for (the second one was about efficient encodings and the last one was a relatively easy question about squares) As it happens that actually puts me in third place. As the prize for winning the upsc (thats Undergraduate Problem Solving Competition, I like to pronounce the shortened version as oopsie=upsc) is an expenses paid trip to mathfest 2009 I certainly hope that I continue to pull up in the ranks (an all expense paid nerd vacation awesome). Hopefully at least one or two of the questions posted next semester will be really hard. Otherwise I doubt it will be possible for me to pull into the lead.
More urgently though the Putnam exam is going to be December 6th. It will have been 1 year and 5 days since I took the 2007 exam. It is hard to believe that it has only been one year since then. I have learned a great deal in that time. Looking at the putnam problems now I feel at least somewhat prepared for the test. Last time I took the Putnam I got a score of 1 point out of a possible 120. Which I am eager to say is above the average score. I have a book with some of the old putnam exams in it and perhaps if I have a spare 6 hours tomorrow I should administer one of them to myself and see how I do. Hearteningly if I get 40 points on the test then I would be in the top 100 of test takers (a few thousand mathematics undergrads and assorted others take the test every year, what can I say doing well on the exam looks good). Realistically I am shooting for 20 points. The 2007 test was a little harder than usual and encouragingly I now could solve 3 of the 12 problems from that exam. before I finish this post off and run away I will give you some example putnam exam problems.
(A1-1976) P is an interior point of the angle whose sides are the rays OA and OB. Locate X on OA and Y on OB so that the line sexment XY contains p and so that the product of distances (px)(py) is a minimum.
A1 and B1 are traditionally the easiest problems and A6 and B6 traditionally the hardest.
(A6-1976) Suppose f(x) is a twice continuously differentiable real valued function defined for all real numbers x and satisfying |f(x)| <= 1 for all x and (f(0))2 + (f '(0))2 = 4. Prove there exists a point x0 such that f(x0) + f ' ' (x0) = 0.
Monday, November 10, 2008
Wednesday, November 5, 2008
Now that the election is over I can't help but feel elated. This really is an extra ordinary moment in American history. I thought this merited a bit of space here on the blog. All I really want to do is just say it over and over again Obama won, Obama won, Obama won! Because I have been scared that it wouldn't really happen despite the eventually commanding lead he had. I always thought something terrible would happen before the election and then we would have McCain in office which wouldn't have been the end of the world... until he had a heart attack and Palin took over for him. But I am still rattled by how close the election was in terms of the popular vote. How can it be possible for a McCain Palin ticket to get even 20% of the popular vote let alone 46%? But now that the election is good and truly over I can take a sigh of relief and just wish that January were a little bit closer. I hope this is the beginning of a political movement of change like Obama has said he will try for. As he said after the election "change has come" lets hope so.
The poll closed, and it is now official by a vote of 3 to 2 the universe is going to expand forever. This is actually rather close to the current scientific consensus. Detailed measurements of the rate of expansion of the universe done using supernova actually tell us that the rate of expansion of the universe is getting faster! If you are interested the exact method of using these super nova to give the rate of expansion works something like this. Step 1 you look for a type 1A supernova. I'm not exactly sure how you tell if it is a type 1A nova but I'll trust that it is possible. Steps 2 and 3 record the red shift and brightness of the nova as measured from earth. step next, rinse and repeat. So I am not sure exactly how many type 1A's we have on record but from what we do have we can use to make a measurement of the rate of expansion of the universe and how it has changed over time. The brightness of the supernova as measured from earth gives us info on exactly how far away the nova was because type 1A super novas all have exactly the same brightness when they occur. If memory serves it is because the star that collapses into a black hole accumulates mass from a nearby binary star until in reaches a definite critical mass at which point KAB00M! Since all these events happen when the star reaches the same critical mass the brightness of the explosion is just about the same. So as the apparent brightness from earth drops off we can measure how far away the damn thing was to begin with. Now the light has a particular characteristic spectrum which we would see if the thing were not moving relative to us thanks to good old doppler though the spectrum gets shifted. We can use the spectrum shift to measure how fast these things are moving away from us. There you have it we now have data that gives us how fast things distance x away from us are moving which gives you the rate of expansion of the universe. Course it isn't quite that simple, all the complications come in when you take into account that we don't see the light from the nova's instantaneously but it takes some time for the light to reach us. The farther away stuff is the longer it takes the light to get to us but also the more space has expanded during its flight. When you take this into account you not only get a measurement of the rate of expansion of the universe but a measurement of how that rate of expansion has evolved in time. With each nova being a window to a different epoch of the universe. Turns out the expansion of the universe started to slow down for a while and then started speeding up again! So now what it looks like is all those big crunch theories where the universe eventually ends in one huge gravitational collapse were not meant to be. The universe gets to end as a sea of cold lonely atoms and radiation. The 3 to 2 vote confirms it, sad but true.
Saturday, November 1, 2008
So November is NAtional NOvel WRIting MOnth or nanowrimo for short. The challenge is to write 50,000 words of fiction during the days of november. I have yet to fulfill this goal even once though I have been participating to various degrees in nano for 3 years (this will be my 4th year) This year I'm really going to do it though! Of course I have slightly less than no idea what I am going do to for the novel this year. I am really open, at the moment it could be anything from a book about a group of jumpers orbiting a post implosion Jupiter, which is now a singularity used for warp research to a book about how the only thing known to kill vampires are cigarettes.