05 - Calculating - Pourquoi calculer ? - 05

1 My computer tricked me!

Which numbers do we use in everyday life?
For counting, we used integers, then decimals, real and complex numbers. What about today? If one uses a calculator or a computer?
At the market, it is better to know how to do fast mental calculations. The computer itself uses only decimals numbers to a limited number of decimal points.
The laws of mathematics are no longer respected.

From the bookkeeper to the aeronautical engineer, errors of approximation must be mastered, from the infinitesimal to the infinitely large. It is in this area that computers are not reliable tools.

2 Secure, @-commerce?

Can we buy on the Internet with complete security?
With the development of the web, cryptography -the science of coding- has become an important tool for the protection of banks and for on-line purchases.
The secret of our cheque cards is based on numbers of more than 100 figures, the product of 2 prime numbers*.

But the progress of information technology today allows one to find, more and more quickly, the divisors of larger and larger numbers!
Mathematicians, physicists and computer scientists look for new unbreakable codes, using, in particular, the strange laws of quantum physics.

• An integer is "prime" if it has only two divisors: 1 and itself.
• The first examples : 2, 3 ,5 ,7 ,11 ,13,17,19...

3 Denoising in Corfou

How do you recover digital images which were damaged due to camera, transmission or reception problems?
How do you send and receive images of good quality by high-speed Internet?
For that purpose, mathematicians introduce algorithms for noise removal which are easily illustrated by cartographer methods: the luminous intensity of every pixel of the image is translated into a “height”.
The image is translated into a relief map, the noise causing a rough surface. The relief is then regularized keeping the main “level lines” and one recovers a nice image.

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