## LATEST POSTS

### 中文的常态与变态

地道的中文，包括文言文与民间文学的白话文，和我们的关系日渐生疏，而英文的影响，无论来自直接的学习或是间接的潜移默化，则日渐显著，因此一般人笔下的白话文，西化的病态日渐严重。

### 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

### System Reliability Model

Outlines computer system reliability, including series, parallel components, and N-modular redundancy.

### Equivalence of Rectangular and Trapezoidal Approximations

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

### Data Table Relation's Normalization

Introduces functional dependencies, and the database paradigms 1NF, 2NF, 3NF, BCNF, and 4NF. and use examples to explain their concepts and connections.

### 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.

### Some Definitions for Time Complexity.

Give five symbolic and mathematical definitions related to time complexity.