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A Mathematical Exploration of the Virial Theorem
Ever wondered how a deep mathematical principle can govern the motion of stars and the behavior of gases? The Virial Theorem is a hidden gem that reveals these connections with an elegant identity equation!
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Recommendations for Rigorous Classical Mechanics Textbooks
As a student of pure mathematics, I have always sought rigor in my studies, especially in natural sciences like classical mechanics. If you’re like me, unsatisfied with textbooks that gloss over crucial foundational concepts, this post might resonate with you.
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Why Aren’t Generalized Coordinates in the Lagrangian Equation Considered Functions of Time?
Ever wondered why generalized coordinates in the Lagrangian formulation are treated as independent of time, despite their obvious connection?
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A Mathematical Exploration of Norton’s Dome and Determinism in Classical Mechanics
Chinese, Classical Mechanics, Differential Equation, Introduction, Latex, Mathematics, Paradox, PhysicsIn classical mechanics, the principle of determinism states that the motion of a system is fully predictable given its initial conditions. However, does this principle always hold?
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Why Use L2 Norm Instead of L1 Norm in Loss Functions?
Algebra, Computer Science, Deep Learning, Latex, Likelihood, Machine Learning, Mathematics, Optimization, Probability, Probability Theory, Regression Analysis, StatisticsHave you guys noticed that, in machine learning, MSE is often the preferred choice…
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Intro to Git, Github and VSCode
Hi, this is Louis Liu. In this tutorial, I will guide you through some basic operations in Git, GitHub, and VSCode.
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How is Diandian (点点) (A cat my family rescued 2 years ago) now?
On February 7, 2022, my family found this poor little kitten in a distressing condition during a heavy rainstorm…
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Cracking the Logic Gates Construction Using the Knowledge from Mathematical Logic
Coding, Computer Science, Introduction, Latex, Logic, Logic Gate, Mathematical Logic, Mathematics, Programming, PythonWhat if I tell you that every complex truth function can be meticulously constructed using just 1 type of logic gates!!??
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Using Raspberry Pi to Build a US VPN Server for My Family in China
Cloudflare, Coding, Computer Science, DDNS, DNS, Github, Great Firewall, Linux, Network, Programming, Raspberry Pi, Server, Software, SSH, Video, VPNAround December 2023, all ChatGPT access node IPs used by our ClashX VPN were blocked by OpenAI. This situation led me to seek alternative methods to restore unrestricted internet access for my family. In this blog post, I’m going to share my experience and detailed process of setting up a Raspberry Pi as a VPN server for my family in China.
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I Switched From Github Pages to WordPress…
Transitioning from one platform to another for your digital presence, especially a blog, is a decision that’s never made lightly. My journey from GitHub Pages to WordPress was guided by a series of revelations and requirements that I believe many content creators might resonate with. In this post, I’ll share why I made the switch, focusing on key aspects such as efficiency, user-friendliness, community support, and interactivity with the audience.
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Competitive Mathematics — Factorization (incomplete)
This article draws heavily on the content from 《数学奥林匹克小丛书》 and incorporates some personal insights and reorganization. Therefore, it can be regarded as a set of notes rather than an entirely original work.
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Why I Don’t Use Chinese Social Media Anymore…
China, Chinese, DDoS Attack, Experience, Freedom of Speech, Github, Great Firewall, Man-on-the-Side Attack, Propaganda, Sensitive Topic, VideoI love China and the culture and people there, as it is where I grew up. However, I am not particularly fond of China’s political environment in certain aspects, especially the excessive control over the internet…
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A guide for preparing for the William Lowell Putnam Mathematical Competition
Are you planning to participate in the Putnam Maths Competition in the future? Come and check it out!
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Why mathematicians choose “A linear subspace must have the additive identity” as one of the condition of the linear subspace but not “A linear subspace must be nonempty” ?
Actually they can do that, but why they don’t? Because from the perspective of modern algebra…
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A simple physical approach to understand the Taylor series
Do you know that the displacement formula with acceleration in one dimension which you had learned in Physics class actually reveals the existence of Taylor series implicitly?
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Intro to the Colemak keyboard layout
The QWERTY layout was designed in the 19th century. Colemak is a modern alternative to the QWERTY and Dvorak layouts, designed for efficient and ergonomic touch typing in English… — www.colemak.com
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My experience of U.S. Visa interview in Guangzhou China
Because of the quarantine policy in Shanghai, the U.S. Consulate in Shanghai, China was closed during that time, and accordingly I choose my VISA appointment at U.S. Consulate in Guangzhou, China…
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Summation by Parts (Abel Transformation)
Want to know what is summation by parts? Check it out!
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Some advice for the new learners to Python
In ‘Learn Python the Hard Way’, it is advised that beginners should not use the IDLE that comes with Python. But I don’t agree with that to a certain extent…
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A Simple Analogy to Understand Terminal, Shell, TTY, and Console
Newcomer to Linux OS? Want to know the difference between Terminal, Shell, TTY, and Console? But don’t want to read the tedious doc? Then this post is made for you 🙂 Check it out!
