**1. The brachistochrone.
** The shortest path is not the fastest. It's crazy,
but it's absolutely true! With knowledge of the integrals, the variational
calculation, you will find that this trivial question lead to an amazing
response and a lot of valuable information.

**2. The
unidimensional ballistic shooting**. It was a classic
problem in high school, but you will find that this variant - presented in a
fun way - is useful.

**3. The bidimensional
ballistic shot**. This is the improved version of the
one-dimensional problem with a lot of new concepts such as bilinear
interpolation, the grid ... and a lot of passion.

**4. The Chinese
remainder theorem.** A problem dated from 2000 years
but modeled as a game. You will understand why our ancestors came to solve very
complicated calculations, and why now this knowledge is still useful.

**5. The
cycloid.** Do you know the trajectory of the moon seen
from… the sun ? And if the earth suddenly changes the direction of rotation
around the sun? It’s not necessary to go to the sun, because the answer is
here, in this exercise.

**6. Djiskstra
algorithm.** Finding the shortest path in a directed
graph is a classical problem but with many applications. One of the fastest
algorithm is the Djiskstra, but its principle is not easy to understand. This
exercise helps you to get rid of this trouble.

**7. Elliptic
curves.** This is a fairly new concept and is the
subject of many research since its application field is wide. What is
interesting here is that a 2000 years old principle is used to solve problems
in 2000.

**8. Fractal.** Beautiful and vibrant images
in nature or things around us such as blood vessels, the market changes are
also subjects of exciting mathematical
research. These are fractal structures that are found here in this exercise.

**9. The
three laws of Kepler.** They explain the movements of
the celestial body in the universe. We will understand why our ancestors could
to calculate the trajectories of comets with their semi-major axes greatly
exceed the limits of our solar system.

**10. Newton’s
laws of cooling.** This exercise presents a variant
of a classic application of differential equation first degree, the problem of
heat exchange between two and several different environments.

**11. Leapsheep.** This is certainlya very familiar game when you're little, but here
is a little different. You must provide knowledge of numerical sequences,
linear algebra ... and with all that, you will have less than 1% to win.

So! You try ?

**12. Tris
in main memory.** We know (almost) linear sort but
little on how to sort-merge. This exercise explain detailed way the steps of
these two methods and animated diagrams clearly show the superiority of our
method tri-fusion.

**13. Calculation
of extrema without gradient.** This exercise explains
detailed and graphic manner the steps to determine the extrema of functions of
one variable by numerical methods.

**14. Chain
matrix multiplication.** This is a very interesting
topic in optimization. Not only because it shows an error that was always
believed to be true, but it shows that the most powerful computers are still
far behind the human imagination.

**15. Finding
roots by numerical methods.** This exercise explains
detailed and graphic manner the steps to determine the roots of functions one-variables
by numerical methods.

**16. Runge-Kutta
methods.** exercise explains detailed and graphic
manner steps to solve the problem initial values (or Cauchy problem) by Euler
and Heun (improved Euler) methods.