## Saturday, April 30, 2005

Finally "Holoholona" (the Hawaiian word for giant) our boat is ready here. The day was perfect for the cardboard boat regatta. I enjoyed bit of that. So many different boat designs were there from a single kayak to the monster like ours. I will be uploading the remainning pictures (I have 67 other pictures !!) soon. In this pic you can see starting from the left Bethany, Jason, Bryan, Kelly, Sarah, Matt Kelsey, Rawley, Matt, Stephanie, Nathan, Teresa and Sumant.
Here is the pic at Mississipi bar seen in the pic are Ayako, Aza, David and Sumant. We chatted for almost 3 hours. Especially the discussion about Mike was hilarious !

## Thursday, April 28, 2005

### Boat Regatta, SIUC

This saturday I will be participating in Boat Regatta. It should be fun and the great thing about the history of Cardboard Regatta is that it was an SIUC professor who first came up with this idea in early 1970s and since then this idea grown in popularity and now cardboard races are organized throught out USA may be outside too. We have made a boat out of cardboard. Its almost finished. I will be going there to help with the work. My teammates have done a wonderful work and its great to be a part of such a team. I will be posting the photos of regatta soon. Till then keep your fingers crossed and pray that weather is going to be nice. For past few days weather is colder and rainning.

## Wednesday, April 27, 2005

### April 27, 2005

I am right now in library and decided to update this blog. Well today's morning was sweet as I could prove one more exercise on Golden Number. It was to prove that
F(n-1)*F(n+1) = F(n)^2 + (-1)^n
Another property of Golden numbers is
(Phi)^(n+1) = F(n) + Phi *F(n+1)
More stuff in complex number was discussed today, including one more of hadamard's theorem. I still have to get the grasp of laurent series and residue stuff. Dr. Grimmer discussed more on the higher order differential equations.
I have to return the book Div, Grad, Curl and all that.

Time to go and catch Lou Dobb's tonight and I am hungry too !!

## Tuesday, April 26, 2005

### Sumant's update, Mamiko, Boat regatta, Tau Beta Pi, Pi Mu Epsilon, Papa

I thought to update whats going on here. Japan has recently been struck by several tragidies. Yesterday there was a freak train accident. Killing almost 50 people. Then there have been several major earthquakes in Japan. One of my best friend Mamiko lives there and everytime there is such a tragedy I feel anxious. Two weeks from now I will be wrapping up with my semester. So far so good. I need to step up my study for that. Then there is a boat regatta on coming saturday and Tau Beta Pi induction ceremony. Besides Pi Mu Epsilon induction on wednesday. Though I have not been invited for the induction of Pi Mu Epsilon I certainly want to join it. Yesterday I spend time revising complex analysis and differential equation. I am trying to sleep early but somehow I am sleeping late which leads to getting up late.
One of my other friend Mary is vacationning in Mexico. She will be back on sunday. Lots of new plans I have for the summer. I plan to catch will whole lot of movies. A deeper understanding of complex analysis will surely be there. Haven't travelled for a while so trip to california should be fun. Some experiment with robots and other things. Updates on my web page. I am also thinking of contributing to Wikipedia. It sure is a great project. I am in love with thier website. Pretty cool. I find myself spending hours and hours now browsing it. I am proud of my Papa's recent work in his village. He is now living his passion ! Yesterday got a mail from him that he is organizing a workshop on electrical and electronics there. Bravo Papa !!

### Aleph, AlephZero, AlephOne

I was wondering what I am learning these days !! As I wrote earlier discussion on Infinity was wonderful. Infact I will have to edit what I said earlier about cardinal numbers. The cardinality of natural numbers is alephZero and it is same as the cardinality of N*N which is to be noted. So I repeat again. The cardinality of natural numbers is alephZero and cardinality of N*N is also alephZero. Now the next question one may ask what is the cardinality of N*N*N*...N. Well its also alephZero. As long as the number of Ns are finite its alephZero. Then we have a transition we have alephOne. Which is equal to the all possible subsets of Natural number and its same as cardinality of real numbers.
So
Cardinality of Natural numbers = alephZero
Cardinality of N*N = alephZero
Cardinality of N*N*... N = alephZero if Ns are finite

Cardinality of powerset of Natural number = alephOne
Cardinality of Real numbers = alephOne

I haven't swam for a while and tommorow I will definitely swim. Yesterday I was glad that I could solve the general fibonacci series solution. That the ratio of consecutive terms approach Golden Ratio. That thing is neat. Start with any seed, infact the first two terms can be different instead of assuming the seed to be the single number. The proof can be had by induction method. Assuming that lim n-> infinity Fn+1/Fn approaches golden ratio. Dr Jerzy Kocik also discussed some more properties of golden ratio. Now I should spend some time learning complex analysis stuff.

## Monday, April 25, 2005

### Sumant's Friends in STMicroelectronics

Right now I am talking to one of my cool friend Subhasis Das. I still recall my good old days in STMicroelectronics. My buddy Naveen and I used to get up early in the morning to catch the office bus from Jia Sarai in South Delhi. I happenned to make lots and lots of friends in ST and I am still in touch with many. Some of the cool people like Subhasis Das, Vivek Khaneja, Shalini Miyan, Nabarun Dasgupta, Mohit Jain are still in regular touch. Others like Rajat Chauhan, Subhasis Rudra, Manisha Sharma, Juhee Mala, Deepu Arora, Rahul Pandey, Sidharth Batra, Sunil Kasanyal do keep in touch with wonderful mail we call junk mail. Its amazing when one looks back at the number of people we meet and then we may never see them again. The years in ST were fun. Working with Saibal Dutt. Kaushik Saha was the person I idolized he was truly remarkable. His thirst for knowledge had a profound influence on me. So was Vivek Sir. He has the leadership skills and same thirst like Kaushik to learn.

### Books overdue to be returned

I just recived a mail from Augusta college that I have to return "Visual Complex Analysis" . I checked on my library website and now I have around four books in overdue and they cannot be renewed anymore. So tommorow I should be returning those. The news on our boat building endeavour is good. Its joy to see so many people making contribution and taking decisions. Never thought that one can build a boat out of cardboard and now I am doing that. Recently there was also a math club meeting and I am glad that I attended. Dr. Donald Mills was there and he was open about suggestions. So it should be an exciting time. Already he has taken a lot of initiatives to improve the club and its a pretty dynamic club with lots of guest speaker coming in. I enjoy all those talks.
Dr. Philip Feinsilver is cool and interesting person. I find his lectures pretty interesting. He goes out of his way to help people understand things. His notes are clear. We learned some pretty interesting stuff in his class like lim sup, lim inf, inf, sup, contraction mapping, cauchy sequence, convergence, bolzanno wierstrass. I wrote a paper on Riemann. Did get to learn Tex with his help and Dr. Kocik's help. It was fun to use it.

### Power Series, Fourier Series, Laurent Series

In my complex analysis class we just finished the Fourier series. Well fourier series are remarkable. They are just Trigonometric series and thier usefullness in solving the classic problems of heat and wave was fascinating to learn. We learned how to find Fourier coefficients of the series. Its easy to understand because integration between -L to L for combination of sin(nPix/L) and cos(nPix/L) gives you either zero or L and you can have sine series and cosine series. Also if the function is in fourier series its easy to find the fourier coefficients. Dr. Grimmer explained it so well in the class. Now we are taking a look at the Power series. Now these are interesting. It was interesting to see that any polynomial can be expressed in terms of power series at different points. For example the ploynomial x can be reperesented as x only at point 0. But becomes 1+(x-1) at 1 and 2+(x-2) at 2 and so on. Well power series work for only positive powers and not fraction. So what we do if we have to find negative exponents and then you get what is called Laurent series. Still Laurent series don't have a fractional powers. One good thing about power series is that inside their radius of convergence they are differentiable and hence continious.

### Golden Number and Different Infinities

Recently in my class on Transition to higher mathematics Dr. Jerzy Kocik has been giving lecture on Golden Numbers and its really fascinating. I liked his wooden divisor with three legs that divides any piece into golden ratio. The history behind it is interesting and the wonderful thing is its relation to Fibonacci numbers. Even though I know fibonacci numbers for now quite a while. It is this lecture by Dr. Kocik that helped me appreciate these numbers more fully. Another thing he talked about was Infinities which too was pretty neat. The numbers can be classified in two ways. Ordinal numbers and Cardinal numbers. Ordinal numbers have position or ranking. Cardinal numbers measure amount. And it is this concept of cardinal numbers that helps us define different infinities. Now the concept of natural numbers is one of the central one in number theory. Natural numbers are ordinal and integers are not. We say that the cardinality of natural numbers is aleph. I love the way this letter is written and Dr. Kocik's way of writing it. Now to count anything else we use bijection mapping. So in this way we can show that integers have the same cardinality as natural numbers. Even numbers, odd number and even rational numbers also have the same cardinality as natural number ie aleph. Here is how the numbers are defined in terms of set theory Zero is {}. One is {{}}. Two is {{},{{}}} and three you can guess is {{},{{}}, {{},{{}}} } and so on. This is the way ordinal numbers are defined. And also leads to the famous property "Well ordering principle". Which say natural numbers are well ordered. The cardinal numbers are based on aleph concept. Which is a power set concept. That alephZero (Yes there are alephOne, alephTwo and so on thanks to Cantor) is equal to Power set of Natural numbers. Then size of real numbers is equal to alephOne as one can show that there are more irrational numbers than rational numbers and there you see those cantors diagrams of counting. Indeed its fascinating to learn about infinity and zero and thats a huge revealation that there are levels of infinites. Bigger infinities. Cool kind of stuff we engineers don't get to learn.
While browsing through wikipedia math website I came across the concept of Bertrand russels objection and the barber paradox which reads like "There is a town in which there is a male barber who shaves every men who doesn't shave himself and no one else". Such a town couldn't exist. This paradox is called as Russell's Paradox.
Also I came to know that there are two kinds of set theory. One is called "Naive set theory" and other is called "Axiomatic set theory". The Naive set theory is based on set as a collection of elements whereas the "Axiomatic set theory" is based on axioms. The Goodel showed there are still discrepancies in the theory of sets. So far it remains a field open to more research.