Posts of 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.
The Introduction to Bernoulli Number
Introduction, derivation and proof of Bernoulli numbers
Equivalence of Rectangular and Trapezoidal Approximations
Discusses the equivalence and error estimation in integrating piecewise continuous functions using rectangular and trapezoidal approximations.
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.
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.
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.
The Master Theorem For Time Complexity
In this article, we will model the time complexity of divide and conquer using mathematical methods, analyze its asymptotic properties, and provide three methods of calculation.
Fast Inverse Square Root
The article introduces an algorithm called Fast Inverse Square Root, which is used to quickly calculate the inverse square root of a floating point number.
How Do Computer Calculate the Log-Function
Use Differential Equation Method and Matrix Method to Find Fibonacci Sequence General Formula
This article gives two methods to derive Fibonacci sequence: matrix method and difference equation method