fun readings

There are very few books which I have read more than couple of times. There are some books which I have read over 20 times. I just finished rereading  Hardy's book "A Mathematician's Apology"  probably for the 3rd or 4th time. Its not one of the most uplifting book but surely its a book which has shaped the opinion of countless of mathematicians. I also kind of finished "Calculus of Friendship" by Steven Strogatz. It goaded me to get another book by Paul Nahin called "Chases and Escapes". So I might be spending some time to finish both of Paul's book Dr Euler's formula and chases and escapes. I learned about chases and escape problems in another book by Graham but I didn't know that it has such an interesting history. I did a cursory reading of Paul's book and it seems like a lot of fun

Kindle after 1 week of usage

It been over a week since I bought this Kindle. I like it. At the last count I had over 100 ebooks books and I am hoping that by December end I can brag about the number of them I manage to finish. I love the flexibility of dwelling into any book I like and the ability of the device to remember where I left off. I was concerned about the lack of keyboard on the device to take note but it hasn't bothered me much. The highlight feature is a winner. I use this all the time and the neat thing about it is that it keeps all the highlighted text in one place. So you can read the summary of all the highlights you did. Its almost as taking notes.
 Before getting kindle I was overly concerned about its inability to read djvu file however djvu libre can easily export your djvu files to pdf (though size could be more than 3 times the original file). Most of my books were on djvu format which I had to convert to pdf and they read ok. Many other were on pdf and its comfortable to read pdf on kindle. Its best to read the kindle files as they appear to be darker on kindle.The kindle format is borrowed from html format. So if you have a html file its easy to convert it to kindle. Gutteberg.org has a neat collection of kindle books and they read fabulous on kindle. I downloaded Robinson Crusoe and I plan on reading few more classics.  I can check my email using the browser called "Experimental".
  One can change the orientation using the zoom feature and see the text in landscape or portrait mode. I once downloaded Manga statistics and that file is 135 mb but reading on kindle was not a problem. All I had to do was to switch to the darkest settings and read in landscape mode. So all in all a great device to catch up on your reading. Downloading files on kindle is easy it appears as a drive when you plug it into your computer and you shove your files into the document folder. From kindle you can organize your books into categories so they are easy to access.

Short commentary on Ballot Box problem

One of the problem in elementary course in probability is the ballot box problem. The statement of the problem goes as something "There are two candidates A and B competing in an election,  where after counting it is found that A has won the election. Now if we recount it what is the probability that we will find at least a  tie". The easiest way to think about this will be to conjure some numbers. Let there were 5 votes and out of 5 A had 3 and B had 2. We know from multinomial theorem that 5 things (when 3 are of same type and 2 are of other) can be arranged in 5!/(3! 2!) =10.
Lets list all those 10 possibilities

1. AAABB (Bs together)
2. AABAB (Moving 1 B and keeping other fixed)
3. ABAAB (Moving 1 B and keeping other fixed)
4. BAAAB (Moving 1 B and keeping other fixed) (Bs on both extreme)
5. BAABA  (Moving the other B and keeping the other fixed)
6. BABAA  (Moving the other B and keeping the other fixed)
7. AABBA  (Bs together)
8. ABBAA  (Bs together)
9. BBAAA  (Bs together)
10. ABBAA (As on both extreme)

 You should notice that out of these 10 except the first two we always have a tie sometimes during the counting. Question: When do you think when will any tie will happen ? Answer: It will always happen when you have counted some even number of ballots. Notice one more thing when the tie has happened if we replace As by Bs and  Bs by As we get another different way of tying. Also if number of Bs is smaller then we will always have some tie during the course of counting. Let a denote the number of As and b denote the number of Bs then the probability of  tie when we count b first  is b/(a+b) but for every sequence starting with B we saw there is a corresponding sequence starting with A which also gives a tie. Hence the total number of favorable cases is 2b and the corrected probability is 2b/(a+b)

Reading Update

There is an old saying by Sir Francis Bacon that "Some books are to be tasted, others to be swallowed, and some few to be chewed and digested: that is, some books are to be read only in parts, others to be read, but not curiously, and some few to be read wholly, and with diligence and attention." Today I downloaded few more books to go over including the annotated guide to "Alice in Wonderland" by Martin Gardner. I been wanting to read this book for quite sometime and even owned the copy but never got around reading this one. I am currently reading DuSutoy's Symmetry and its pretty appealing. There is an equally fascinating by Saunders McLane on Mathematics form and function.
     

Mutually Exclusive or Not

 I was thinking about mutually exclusive and independent events and one of the easy example one can conjure up is with two coins.
Experiment: Tossing two coins

Mutually Exclusive

E1: Head on both coins => 1/4
E2: Tails on both coins => 1/4
E3: E1 or E2
P(E3) = P(E1)+P(E2) => 1/4+1/4 = 1/2

Not Mutually Exclusive
E4: Head on one coin => 3/4
E5: Tail on one coin => 3/4
E6: E4 or E5
P(E6) = P(E4)+P(E5) = 3/4+3/4 = 3/2 which is ><
The reason is the above two are not mutually exclusive as both E4 and E5 could happen when we have a {HT, TH} 

Kindle

 Finally after months of scouting around for Kindle I managed to get one in Siem Reap. "Rogue" is selling Kindles here in Amazon. They are getting them shipped from United States via DHL. I wrote a blog about kindle when it came out in 2008 and ever since then had been fascinated by it. I am getting back to my reading and hopefully will be able to finish lot more books before this year ends.

“If you want to build a ship, don’t drum up the people to gather wood, divide the work, and give orders. Instead, teach them to yearn for the vast and endless sea” Antoine De Saint-Exupery, author of The Little Prince.

  This thought is one of my all time favorite and conveys my teaching philosophy. Too often the math classes become nothing more than a course in techniques of symbol manipulation. While there is no denying its an important skill unless one knows where those symbolic manipulation skills are taking you the motivation to continue is easily lost. I had some terrific instructors such as Dr. Kammler, Dr Porter, Dr. Kocik and Dr. Lane Clark who knew this truth very well who motivated me to become a better student.

Pictures from Sumant

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Number Mysteries (Repeated Numbers)

Repeated Number trick
15873 * 7 = 111111
12345679 * 9 = 11111111
1443 * 7 = 101010

Look closely the above three results. You can ask people to pick up a number between 1 and 9 and then let them multiply by 15873 and then for magic ask them to multiply by 7. Their number will be repeated 6 times. For example let say the person decides to go with 3 then you will have 15873 *3 = 47619. Now multiply that number by 7 and you will get 333333.

If you want to repeat 8 times a number between 1 and 9 ask them to multiply by 12345679 and then multiply by 9.For example let say the person decides to go with 3 then you will have 12345679 *3 = 37037037. Now multiply that number by 9 and you will get 33333333.

The third one is for 2 digit number. Here you can ask someone to find a number between 9 and 99 and then repeat the same procedure as above and then multiply by 7. It will be repeated 3 times.

In Chiang Mai doing math

My Ashok Hall Class 6, 2011-12

This pic was taken in the Dining Hall of Ashok hall after my class 6 did an evening assembly. It was a flamboyant performance and the principal acknowledged that. There were many other teachers who helped who are not here. In the picture you can see Avani Kedia, Another kedia, Tanushree Agarwal, Shreya Rungta, Diksha Chabbaria,Sakshi Rungta,  Khushi, Sumant, Vishaka Singh, Muskan Kapoor, Sristi Jaiswal, Muskan Chabbaria, Saasha Sanadi, Anjali Pandey, Bhavna Jalan, Shraddha Gupta, Laiba Ahmad. It was one of the best vacation I had. The whole class bonded so well. The farewell they gave me was over the top. Miss these guys. I wish them all the best and I am pretty sure they will do great in life.