Algorithm Notes and Its Formula
Mathematics encompasses a wide range of topics and concepts, so it's
difficult to provide a comprehensive list of algorithms and formulas.
However, here are some important ones that you may find useful:
1. Euclidean algorithm: This algorithm is used to find the greatest
common divisor (GCD) of two integers. The formula for the Euclidean
algorithm is:
gcd(a,b) = gcd(b, a mod b)
where "a mod b" is the remainder when a is divided by b.
2. Pythagorean theorem: This theorem relates the lengths of the sides
of a right triangle. It states that:
c^2 = a^2 + b^2
where c is the length of the hypotenuse (the side opposite the right
angle), and a and b are the lengths of the other two sides.
3. Quadratic formula: This formula is used to find the roots (or
solutions) of a quadratic equation, which is an equation of the form:
, ax^2 + bx + c = 0
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where "±" means "plus or minus," and "sqrt" means "square root."
4. Fourier transform: This algorithm is used to decompose a function
(or signal) into its constituent frequencies. The formula for the Fourier
transform is:
F(w) = ∫ f(t) e^(-iwt) dt
where F(w) is the Fourier transform of the function f(t), i is the
imaginary unit, and the integral is taken over all values of t.
5. Bayes' theorem: This theorem is used to calculate the probability of
an event based on prior knowledge of related events. The formula for
Bayes' theorem is:
P(A | B) = P(B | A) P(A) / P(B)
where P(A | B) is the conditional probability of A given B, P(B | A) is
the conditional probability of B given A, P(A) is the prior probability of
A, and P(B) is the prior probability of B.
Mathematics encompasses a wide range of topics and concepts, so it's
difficult to provide a comprehensive list of algorithms and formulas.
However, here are some important ones that you may find useful:
1. Euclidean algorithm: This algorithm is used to find the greatest
common divisor (GCD) of two integers. The formula for the Euclidean
algorithm is:
gcd(a,b) = gcd(b, a mod b)
where "a mod b" is the remainder when a is divided by b.
2. Pythagorean theorem: This theorem relates the lengths of the sides
of a right triangle. It states that:
c^2 = a^2 + b^2
where c is the length of the hypotenuse (the side opposite the right
angle), and a and b are the lengths of the other two sides.
3. Quadratic formula: This formula is used to find the roots (or
solutions) of a quadratic equation, which is an equation of the form:
, ax^2 + bx + c = 0
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where "±" means "plus or minus," and "sqrt" means "square root."
4. Fourier transform: This algorithm is used to decompose a function
(or signal) into its constituent frequencies. The formula for the Fourier
transform is:
F(w) = ∫ f(t) e^(-iwt) dt
where F(w) is the Fourier transform of the function f(t), i is the
imaginary unit, and the integral is taken over all values of t.
5. Bayes' theorem: This theorem is used to calculate the probability of
an event based on prior knowledge of related events. The formula for
Bayes' theorem is:
P(A | B) = P(B | A) P(A) / P(B)
where P(A | B) is the conditional probability of A given B, P(B | A) is
the conditional probability of B given A, P(A) is the prior probability of
A, and P(B) is the prior probability of B.
