Monday, December 03, 2007
I have finally decided to stop writing this math blog. This has no bearing on rest of the contributors. It has been a great journey, I see myself today with a lot more mathematical maturity as I go through old to new posts. The reason to stop is not because I am getting absorbed into more serious math but the lack of purpose for which the blog was created nearly two years ago. ( I feel it is the time to tell the story, how the blog started) I had started messaging friends some curious problems that I normally kept creating for fun, later Sudhir suggested 'why don't you blog?' as it reaches people and people can comment. From then on I have posting problems mostly recreational, though I agree that my recent posts were a bit serious.
But these days there has been no response, comments like before and therefor feel the blog does not serve the purpose it was created for. I did or do not expect that I get comments that are mathematical, but some 'tries' as many of them are reachable to a layman, neither I feel like writing about what problems I am thinking about. So
Thursday, November 22, 2007
You can find a lot of free e-books here.Books range from math classics to recently released ones gracefully violating copyrights.I simply believe knowledge should be free.
Some good books of my interest:
1.The art of Counting - Paul Erdos.
2.Combinatorics - Peter Cameron.
3.A course in combinatorics - van Lint and Wilson
4.Enumerative Combinatorics - R P Stanley
5.Research Problems in Discrete geometry - Peter Brass et al
Tuesday, November 20, 2007
Monday, November 19, 2007
This next one is a classic.
Let there be n integers not necessarily distinct.Prove that we pick k (< (n+1)) integers which is divisible by n.
Let i_1, i_2,..., i_n be the integers.
a_2=i_1 + i_2
If one of the a_j ( j=1,..,n ) is divisible by n we are done,else by php we can find a_r and a_s (r>s)giving same remainder. Then a_r-a_s gives rem 0 and we are done.
Wednesday, November 14, 2007
Friday, November 02, 2007
Tuesday, October 30, 2007
Let the set of vectors be linearly independent. Prove that are also linearly independent given
and so on.
ps: I proved it by proving a certain matrix to be invertible and that was pretty cumbersome. Hoping for a better pretty solution :)