Hp 50g

I like Hp50g's graphing capability. This was one problem where there were 4 maximas and saddle pts

Bipartite counting , thesis and other things

Its June 14 today and the school has started. I am not taking any class this semester so all my efforts are now concentrated on finishing my thesis. Today i had a meeting with Dr. Porter after that I came to Carbondale library to volunteer. It took almost 2 and half hr to get all the books. The good thing about the meeting with Dr. Porter was that I think I finally understood the labeled bipartite graph calculation. The thesis looks in a lot better shape with about 50 pages.

Party at Pomonna

This was the second time I went to Tom's party in Pomonna. Here are some pictures.

Today June 11, 2009

It's about 22 hrs and I just came to Morris library. Today I picked up few books from the library including "The next 50 years", A book on Infinity and a book on History of Japan. I met Austin today. Watched a bit of NBA basketball between Lakers and Magic. I still have no idea why in spite of 8 years of pleading, goading and threatening I am not able to convince my parents that Covey's book and Vipassana are essential to their well being. I try to put myself in their shoes and fathom what is the reason and I guess its their reluctance to embrace new thing. Kind of reminds me of Jonathan Livingston Seagull. I know I have discovered something invaluable and I want to share. Hopefully some day they will realize the profound effects that these two can bring until then I will keep trying.

Edward Gorey

Today I read this book by Edward Gorey. Its a bunch of short stories. Some are unsettling like "Loathsome Couple", "Stupid Joke", "Blue ". I guess he is more famous for his dark, melancholy writing. There are some which make little sense in what he was trying to convey like the story about one guy loosing his umbrella later to be found by his dog. I enjoyed the rhymes and his take on alphabets.

What I am reading ?

I am updating this from Morris Library. Today has been good so far. I ordered book "Back of the Napkin". I am reading few books including "Zero" by Seife, "Jimmy Corrigan: Smartest kid on Earth", "Darwin's Sacred Cause". I will post the reviews as I am done reading. I have now read numerous books on Darwin and this one is perhaps much different take.

Graphic Witness

I came across this while browsing the graphic novel section at the local library. It includes work by 4 artists frans masereel,Lynd Ward,Gicomo Patri and Laurence Hyde. What was impressive about this novel was the way all those novels were written. First of all the stories were conveyed using pictures only. So there wasn't any balloon text. All 4 stories were set in early 1900-1950s. All 4 meloncholy stories exploring topics like urban sprawl, racism, atomic bomb explosion etc.

Jewish Cartoon book

I am here at Carbondale Library updating this blog. So far today I been relaxing. I did finish this book on Jewish parables. I enjoyed it and would definitely recommend it for an easy read.

Some insight

Its 12:26 and I am here at Carbondale library updating this blog. Yesterday I wrote the Gambler's ruin program in Maple and it was good to go over some of the examples that Dr. Clark did in his combinatorics book.

Any course in combinatorics deals with the Stirling numbers, while I understood the recursive proof of 2nd type of Stirling numbers but I was never comfortable with the argument for proving the Stirling numbers of 1st kind until yesterday when I tried writing down all the permutations of c(4) and c(3)and tried to generalize it and at flash of insight every thing was clear. Just to give you a background

c(n,k) = c(n-1,k-1)+(n-1)*c(n-1,k)

The problem term was the factor (n-1) and it is very easy to see that any c(n-1,k) we have (n-1) places where we can put our chosen 'n' element.

Also I was working on derivation of s(n,k) using ordinary generating function. I am comfortable with the proof one gets using mixed generating functions but in ordinary one, one has to deal with partial fraction. Again if you try the trivial example it becomes clear that why one needs to put x = 1/r as a substitution. The recursive definition gives

Bk = x/(1-k*x)*Bk-1 and B0 = 1 and one needs to fish out the coefficient of x^n ie Bk = x^k/((1-x)(1-2x)... (1-kx)) . Thus we need

[x^n] x^k/((1-x)(1-2x)... (1-kx)) and it turns out one has to deal with partial fractions. Where one can write it as

[x^(n-k)] sum(alpha_i/(1-i*x), i = 1.. k)

At Carbondale library

I am in Carbondale library here to spend some time working on my thesis. Just done with some bill payment here on computer. Yesterday was productive I got done several things. I need some time to peruse over the derivation of Bernoulli's formula. I refreshed my concept of product of sum and sum of product and the generating function derivation of Catalan numbers. Today I should complete the trivial proof of uniqueness of bipartition for a connected bipartite graph and write a function in maple that models the gambler's ruin problem.