NOTE & BLOG - The personal blog for 但为君故




Equivalence of rectangular and trapezoidal approximations

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

12 April, 2024

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.

12 March, 2024

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.

6 March, 2024

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.

5 March, 2024

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.

2 March, 2024

Some classical ciphers and implementations

This article explores classical ciphers historically used. In the past, amid low productivity and primitive computing, these ciphers offered protection.

23 February, 2024

How to explain The halting problem

How to explains the Halting Problem's unsolvability in computing, referencing Alan Turing's work. Let’s start with a simple Java login function and a example.

22 February, 2024

The await-to-js

Handling asynchronous function errors and result more elegantly.

14 February, 2024

The Usages and traps of useEffect in React

The article discusses the challenges and pitfalls of using useEffect in React, emphasizing its proper application for idempotent view initialization and refresh, cautioning against non-idempotent operations to avoid inconsistencies between data and UI.

5 February, 2024

Why the graphql is better than restful in math conclusion?

This article analyzes GraphQL's unique capabilities in API design, highlighting its advantages over REST, such as optimized data loading, enhanced data model composability, and improved semantic clarity in queries and mutations.

20 January, 2024