## Le Monde puzzle [#1063] and le bac’

Posted in Kids with tags , , , on August 21, 2018 by xi'an

As pointed out by Jean-Louis Foulley in his comment on the recent Le Monde puzzle [#1063] post, the questions are heavily inspired by the 2018 high school final exam (known as Le Baccalauréat or Le Bac’) in mathematics in France, as can be checked from the above. Including the denomination of powerful number! In Part A, the students had to study the Diophantine equation x²-8y²=1 (E) and show it had an infinite number of (integer) solutions. While these students did not have access to computing facilities, question 1 was solved by sheer enumeration, providing 8=2³ and 9=3² as an answer. While (2) and (3) are rather straightforward, using the prime number decomposition of a and b for (2), the fact that x² and 8y² are powerful for (3). Brute force search leading to x=99,y=35 for the final question.

## (mis)selection at French universities

Posted in Kids, University life with tags , , , , on June 21, 2016 by xi'an

There was an most relevant article in the weekend edition of Le Monde about the absurd posture of French laws, governments and universities about prohibiting any selection at the entrance to university. Under the current regulation, anyone with the baccalauréat degree can apply to any first year program and expect to be accepted. Since this is impossible, universities have to discriminate based on the current address and, if there still are too many applicants, resort to random sampling. To avoid selecting based on high school records or even the final grades at the State level baccalauréat. Or the same universities have to invent some local degrees that are not recognised as national (State) degrees. This is more than absurd, obviously, as it drives most of the best students away from the university system into private schools or abroad. (Paris-Dauphine chose a few years ago to opt out from being a national university, in order to select its students and is thus private in this respect if public in its funding.)

One extreme [and personal] example of this Kafkaian (dis)organisation is provided by medical studies. Anyone with a baccalauréat with any major (science, humanities, carpentry, …) can on principle enter a medical school! Obviously, there must be some selection before too many patients die or too many doctors graduate and the way it operates is as follows: a huge number of students enter the first year of medical studies where they follow mass teaching, with courses mostly on video and tutoring from second year students. They take two one-day exams in December and May with only multiple answer questions. And about 10% of those students are accepted in second year… Among the 90% who fail, about 40% are allowed to try again. Once. [Our daughter thus spent two years of intense bachotage to enter the second year. Congrats to her for her dedication and success!] In the end, French doctors are certainly not worse than others, but this remains a waste of time, energy and money for a huge number of people, with no other argument than an ideological call to égalité. Which translates in practice into a huge inequality between students who can afford private tuition and massive family logistic support [as we found out!] and those who cannot. Furthermore, some universities are bursting at the seams with the number of first year medical students, in constant augmentation despite the 10% success rate. And are thus considering introducing random sampling as well! Using the (costly) baccalauréat to restrict the number of accepted first years students would seem reasonable and rational, as would a more directive orientation of high school students as advocated by Le Monde. An unlikely move, given the potential political impact of the measure.

## philosophy at the 2015 Baccalauréat

Posted in Books, Kids with tags , , , , , , , , , , on June 18, 2015 by xi'an

[Here is the pre-Bayesian quote from Hume that students had to analyse this year for the Baccalauréat:]

The maxim, by which we commonly conduct ourselves in our reasonings, is, that the objects, of which we have no experience, resembles those, of which we have; that what we have found to be most usual is always most probable; and that where there is an opposition of arguments, we ought to give the preference to such as are founded on the greatest number of past observations. But though, in proceeding by this rule, we readily reject any fact which is unusual and incredible in an ordinary degree; yet in advancing farther, the mind observes not always the same rule; but when anything is affirmed utterly absurd and miraculous, it rather the more readily admits of such a fact, upon account of that very circumstance, which ought to destroy all its authority. The passion of surprise and wonder, arising from miracles, being an agreeable emotion, gives a sensible tendency towards the belief of those events, from which it is derived.” David Hume, An Enquiry Concerning Human Understanding,

## Vivons-nous pour être heureux ? [bacc. 2014]

Posted in Books, Kids with tags , , , , , on June 20, 2014 by xi'an

This year is my daughter’s final year in high school and she is now taking the dreaded baccalauréat exams. Just like a few hundred thousands French students. With “just like” in the strict sense since all students with the same major take the very same exam all over France… The first written composition is in the “mother of all disciplines”, philosophy, and the theme of one dissertation this year was “do we live to be happy?”. Which suited well my daughter as she was hoping for a question around that theme. She managed to quote Plato and Buddha, The Pursuit of Happiness and The Wolf of Wall-street… So sounded happy enough with her essay. This seemed indeed like a rather safe notion (as opposed to ethics, religion, politics or work), with enough material to fill a classical thesis-antithesis-synthesis plan (and my personal materialistic conclusion about the lack of predetermination in our lifes).

## 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

$z^4+4z^2+16=0$

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.