I am a student of Ahuntsic in the natural science program and in this program, our learning is really based on the study of sciences such as mathematics which is divided into 5 compulsory courses. We also have chemistry and physics classes divided into 3 classes each. Finally we also have two biology lessons. All these subjects allow us to accumulate enough knowledge to pursue a career in fields such as medicine, engineering and architecture.
Asymptote
The asymptote is a point on the x or y-axis that the curve will never touch. It's used to simulate what happen at infinity, and it's used in limits and calculus
Example: The inverse function contain 2 asymptote. At y=0 and x=0
en: Asymptote
Basel problem
The Basel problem consists of finding the sum of the infinite series. In 1734, Leonhard Euler showed that this sum is exactly pi square over 6. This was a surprising discovery, because it relates a sequence of integers to π, a geometric number. This resolution marked a major turning point in the study of infinite series.
Example: The Basel problem is one of my favorite problems ever, and I've been able to solve it alone.
en: le problème de Basel
Euler number
Euler number is a constant in mathematics that is used and found everywhere. Interest rate, cohesion between cosines and sinus in the complex spectrum, the exponential growth of something, etc. In general, it's just a fantastic number with a lot of incredible properties and a lot of use in mathematics
Example: The integral of Euler's number to the power of x is itself
en: La constante d'Euler
Euler's identity
One the most beautiful equation in math because it regroups 5 of the most important constant in math. e, pi, I, 0 and 1
Example: Euler's identity is the most beautiful equation in the entire world and its proof is even more beautiful
en: Identité de Euler
function sinus, sin(x)
The function sinus can be described with a lot of example, but my favourite is this one. It's just the variation of the y component around a circle of radius 1. In mathematics, it's used to describe every movement in a circle, every function that repeats itself overtime and to find angles on a triangle.
Example: The derivative of the sinus of x is the cosine of x
en: la fonction sinus
Integral of a function f(x)
The integral is the study of the area under a curve. It's commonly known by students as the inverse of the derivative, because it's found like this in calculus. BUT IT'S NOT THE INVERSE OF THE DERIVATIVE PLEASE
Example: The integral of the inverse function is ln(x)
en: L'intégral d'une fonction f(x)
Number Pi
Ratio between the circumference of a circle and its diameter (3.14159). Irrational and found everywhere in geometry.
Example: The number of pi can be found with the Taylor series
en: Le nombre pi
Pythagorean Theorem
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Example: Pythagorean theorem was not discovered by Pythagore by the way
en: Le théorème de Pythagore
Quadratic formula
This is one of the most important formulae in all of mathematics. It's used everywhere to decompose square equation.
Example: The quadratic formula is used in chemistry, math, physics, engineering, biology, etc
en: La formule de la quadratique
Taylor series
Development of a function in infinite sum of polynomials. Locals approach to complex functions. It's used to describe complex functions into an easier form to work with
Example: The Taylor series of the function e to the x is the sum, for n ranging from 0 to infinity, of x to the power of n divided by the factorial of n.
en: Serie de taylor
The Basel problem to the power of 4
After Euler's incredible discovery of the Basel problem, mathematicians did not stop there. They wanted to find the solution to the sum of the inverse of the powers of 4. It was again Euler who found the solution thanks to the hyperbolic sine
Example: I also managed to solve the problem of Basel to the power of 4. Thanks to the same technique that Euler used. Long lives the hyperbolic sinuses
en: La somme de l'inverse des puissances de 4
The derivative
The derivative is the study of the slope variation of a function f(x)
Example: The derivative of the function ln(x) is the inverse function
en: La derivé
The fundamental trigonometric identity
A very easy but very important identity that is used to prove every other trigonometric identity. It's just the pythagorean theorem where we translate x and y in a function of sin(x) and cos(x).
Example: Personally, I hate fundamental trigonometric identity because it gets way too much credit for what it is.
en: Identité triogonométrique fondamentale
The limit of a function at t
Limits are the study of function when x approaches a value t. It's used to know what happen at infinity and at other indefinite values of the function f(x)
Example: The limit of the inverse function when x approaches 0 is infinity
en: la limite de la fonction f(x) lorsque x tend vers t
the Neperian logarithm
Base logarithm e. Inverse of the function e to the x, used to solve exponential type equations. To isolate x
Example: The Neperian logarithm is one of the most important inventions in mathematics
The sum of every cubic integer
I discover this beautiful proof recently. If you add every cubic integer (1+2^3+3^3+4^3...+n^3). It's equal to the sum of Gauss to the power of two. Isn't that beautiful?
Example: The sum of every cubic integer is just the sum of every integer to the power of 2
en: La somme des cubes des nombres de 1 à n
The sum of every integer to n (Sum of Gauss)
This is the sum of every integer to a value n. So 1+2+3+4+5...+n. It seems simple, but it has a very beautiful proof discover by Gauss. It's equal to n(n+1)/2
Example: Gauss discover the sum of every integer during a school class to impress his teacher
en: La somme de tout les nombres jusqu'a n
Zeta Function
After solving the sum of the inverses to the power of 4. The mathematicians wanted to create a function which would group together all the possible solutions, and they called it the Zeta function. This is an unresolved problem yet.
Example: I will be the one who solves the Zeta function
