Archive for integrals

a maths mansion!

Posted in Books, Kids, pictures, Travel with tags , , , , , , , , , on October 11, 2015 by xi'an

I read in The Guardian today about James Stewart’s house being for sale. James Stewart was a prolific author of many college and high-school books on calculus and pre-calculus. I have trouble understanding how one can write so many books on the same topic, but he apparently managed, to the point of having this immense house designed by architects to his taste. Which sounds a bit passé in my opinion. Judging from the covers of the books, and from the shape of the house, he had a fascination for the integral sign (which has indeed an intrinsic beauty!). Still amazing considering it was paid by his royalties. Less amazing when checking the price of those books: they are about $250 a piece. Multiplied by hundreds of thousands of copies sold every year, it sums up to being able to afford such a maths mansion! (I am not so sure I can take over the undergrad market by recycling the Bayesian Choice..!)

Bayes at the Bac’ [again]

Posted in Kids, Statistics with tags , , , , , , , , on June 19, 2014 by xi'an

When my son took the mathematics exam of the baccalauréat a few years ago, the probability problem was a straightforward application of Bayes’ theorem.  (Problem which was later cancelled due to a minor leak…) Surprise, surprise, Bayes is back this year for my daughter’s exam. Once again, the topic is a pharmaceutical lab with a test, test with different positive rates on two populations (healthy vs. sick), and the very basic question is to derive the probability that a person is sick given the test is positive. Then a (predictable) application of the CLT-based confidence interval on a binomial proportion. And the derivation of a normal confidence interval, once again compounded by  a CLT-based confidence interval on a binomial proportion… Fairly straightforward with no combinatoric difficulty.

The other problems were on (a) a sequence defined by the integral

\int_0^1 (x+e^{-nx})\text{d}x

(b) solving the equation


in the complex plane and (c) Cartesian 2-D and 3-D geometry, again avoiding abstruse geometric questions… A rather conventional exam from my biased perspective.