Posts of MATHEMATICS

The Stirling Formula

Stirling's formula finds a relationship of n!,nⁿ,eⁿ while n trends to infinity.

Sep 18, 2024
MATHEMATICS

Box-Muller Transformation

The Box-Muller transformation is a method to construct a random variable that follows a Gaussian distribution by using a random variable that follows a uniform distribution.

Sep 12, 2024
MATHEMATICS
CRYPTOGRAPHY

Linear Congruential for Pseudorandom Number

Linear congruential method is a pseudo-random number generation method that generates a random number sequence based on a deterministic mathematical algorithm.

Sep 11, 2024
MATHEMATICS
CRYPTOGRAPHY

The Laplace Theorem for Determinant

Laplace's theorem in determinants and its applications

Aug 27, 2024
MATHEMATICS

The Problem of Weighing Coins with Balance.

The 'Coin Weight Problem' aims to solve the following mathematical problem: Among N coins, one coin has a different weight. with a balance scale, ensure finding the different coin with the fewest number of weighings.

Apr 28, 2024
MATHEMATICS
ALGORITHM

The Introduction to Bernoulli Number

Introduction, derivation and proof of Bernoulli numbers

Apr 23, 2024
MATHEMATICS

Equivalence of Rectangular and Trapezoidal Approximations

Discusses the equivalence and error estimation in integrating piecewise continuous functions using rectangular and trapezoidal approximations.

Apr 12, 2024
MATHEMATICS

Taylor Formula, Taylor Theorem, Taylor Series, Taylor Expansion

This article mainly introduces the content and connection between the four concepts of Taylor's formula, Taylor's theorem, Taylor series and Taylor's expansion.

Mar 6, 2024
MATHEMATICS

Proof of Faulhaber's Formula

Faulhaber's Formula, which provides a method to compute the sum of the p-th powers of the first n positive integers.

Mar 5, 2024
MATHEMATICS

The Catalan Series

The article discusses Catalan numbers, a sequence used in combinatorial problems. It covers their recurrence relation, closed form, and applications in path counting. It provides insights into problem-solving using Catalan numbers.

Mar 2, 2024
ALGORITHM
MATHEMATICS
/ 2