Integration problem from pAt84

Posted by tpc at December 27th, 2005

My latexrender (installed by my wife with much pain) has gone to disuse. So I’m putting up this problem posted by pAt84.

Version 1
\mbox{\Large \mu = \int_0^1 \frac{ \big( \sum_{j=0}^n a_j t^j \big) \big( \sum_{i=1}^n i b_i t^i \big) } { \sqrt{\big( \sum_{j=1}^n j a_j t^j \big) ^2 + \big( \sum_{i=1}^n i b_i t^i \big)^2 }} dt}

Version 2
\mbox{\Large \mu = \int \frac{p(x) q\prime (x)}{ \sqrt{ p\prime (x)^2 + q \prime (x)^2} } dx}

Posted in Calculus/Analysis, Problems| 1 Comment | 

A Calendar Puzzle

Posted by tpc at December 25th, 2005

A simple little puzzle. Suppose you are given two ordinary 6 sided dice. Is it possible to put the numbers 0-9 (with repetition) onto the faces of both dice, such that using both dice you can display all the days of the month i.e. 01 - 31 .

Posted in Combinatorics, Fun Stuff, Problems| 9 Comments | 

Friday the 13th

Posted by tpc at December 25th, 2005

I was looking at the schedule for the next year, there is a possibility that my first lecture will be on Friday the 13th. It got me doing a little back of envelope calculation to see how often does the 13th fall on a Friday.
(more…)

Posted in Fun Stuff| 2 Comments | 

Arts Or Science

Posted by tpc at December 8th, 2005

I remembered the first time I was aware that there were people who thought mathematics was an art, I was quite offended. This has probably something to do with being Singaporean. Our country is tiny and we are where we are due to a conscious effort of the government to promote science and technology in the 70s. (Some think that it was such a rousing success that we are now a cultural desert and hence the current emphasis on the arts.) Back in school, if your result was good you go to the science stream as opposed to the arts or commerce streams. That was then, things are quite different now, although there is an unhealthy (at least to me) push towards life sciences.

Yet, as my interest in mathematics grew, I began to see and feel otherwise. Pure mathematics is no different from arts. I study numbers because they are interesting and beautiful to me, without any recourse as to what uses they would have. Much like someone who studies Tolkien’s work and researches middleearth.

An interesting blog whose title evoked the question Ars Mathematica.
Anyway the answer is right there.
Mathematics = Arts V Science. (Not XOR)

Posted in General| No Comments |