Mathematics Half Derivatives and some Intuitive Fractional Calculus of Polynomials As you may or may not know, polynomials are expressions that consists of only addition, subtraction, and multiplication operations.

Mathematics Volume of an n-Dimensional Sphere I remember, when I was an undergrad, at one of the beginner courses for physics, the teacher was lecturing about how to convert coordinates to and from Polar, Cylindrical, and

Mathematics Numerical Methods, Square Roots When calculating square roots computers we can employ various techniques. IntroductionI remember in high school, I had this great math teacher teaching algebra. She taught that a we can find

Mathematics Error Functions, Stochastic Gradient Descent, & Backpropagation oth the Stochastic Gradient Descent and Backpropagation are important concepts to understand when studying Neural Networks. Stochastic Gradient Descent optimizes the weights and Backpropagation finds the gradient of the error function quickly.

Neural Networks Structure, Feedforward Neural Networks A lot of times, Neural Networks are talked about in a purely conceptual way, leaving lea way for someone, who is trying to understand it's mechanics, room for misunderstandings. IntroHere,

Mathematics Image Noise Reduction using SVD Decomposition The greatest Mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure. - Felix KleinI remember, while taking a class in linear algebra, the professor, showing

Mathematics Padé Approximant & LU Decomposition, F# Implementation A Padé Approximant is as the book by George A. Baker, Jr., "Essentials of Padé Approximants", the ratio of two polynomials created from the coefficients of the Taylor series of a function.

Mathematics Monte Carlo Method, Integrals IntroductionFor a while, while learning about Numerical Methods for integral, solutions of differential equation, and some other mathematical object, I've come across the Monte Carlo methods. It seemed like some

Mathematics Approximating the Gamma Function with the Gauss-Laguerre quadrature Introduction In mathematics, when an exclamation mark, called a factorial, is used after a number it represents the multiplication of all the numbers from $0$ up to that number. For

Mathematics Faster Matrix Multiplication, Strassen Algorithm For a really long time it was thought that in terms of computational complexity the naive algorithm for the multiplication of matrices was the optimal one, wrong!