陳捷 Jesse C. Chen

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Popular Mathematics

• 《塔木德》中的公平: 在東西不夠的時候，怎麼分才公平呢？只有「按照比例分」才叫做公平嗎？看看兩位二十一世紀的經濟學家是怎麼解釋千年猶太經典《塔木德》中關於「公平」意想不到的故事吧。
• 你能通過牛津大學的數學面試嗎？: 數學的精神不在於複雜的計算，而是在於找尋規律與邏輯的思考。牛津大學的數學口試的其中一個問題不需要任何的計算就可以回答，你可以通過嗎？
• 一個關於剪紙的定理: 你能把一個圖形剪貼成另一個圖形嗎？
• RPN Calculator: An online Reverse Polish Notation (RPN) calculator that also converts RPN into infix notation.

Statistics

• Definiteness of Covariance Matrices: What do we mean when we compare covariances matrices through positive definiteness? A short intuitive interpretation.
• James-Stein Estimator: A brief introduction to the James-Stein Estimator and its empirical Bayes motivation.
• Generalized Method of Moments: A brief introduction to Generalized Method of Moments, aka GMM.
• Fisher Information: A brief introduction to Fisher Information and some related ideas.
• Metropolis-Hastings Algorithm: An explanation and demonstration of the Metropolis-Hastings algorithm.
• Sufficient Statistics: Short definition and example of sufficient statistics.
• Mallow’s Cp: Motivating Mallow’s \(C_p\) criterion, one of the simplest model selection criterion.
• Akaike Information Criterion (AIC): Motivating AIC, one of the most popular model selection criterion.
• von Neumann’s Ergodicity Theorem: An introduction to von Neumann’s Ergodicity Theroem and its connection with convergence of Markov Chains.
• Weak IV: An overview of some important concepts in weak instrument variables.
• Shannon Entropy: Motivating the definition of entropy in information theroy.

Code

• vindent.nvim: A minimal, modern and highly customizable Neovim plugin that provides indentation-based navigation motions and text objects.
• up.nvim: A Neovim plugin that provides a simple way to navigate up the directory tree.
• vim-bunttex: Minimal syntax highlighting for \(\mathrm{\LaTeX}\).
• del: A minimal and safe alternative to rm.
• whenever: Run a command whenever a file/directory is changed.
• Makefile for Economists: A practical introduction to Makefile for economists.
• LaTeX Setup in Vim/Neovim: A brief description of my \(\mathrm{\LaTeX}\) setup in Vim/Neovim.

Potpourri

• 《出洋肄習錄》：在紐約所見所聞的流水帳。
• 〈李鴻章特輯〉：大清欽差頭等出使大臣太子太傅文華殿大學士一等肅毅伯合肥李鴻章在紐約的一週。
• 《論語雜論》：跟述而不作完全相反一想到就忍不住寫下來的儒家筆記。
• 《申請覺迷錄》：申請碩班、博班的心得。

Miscellanea

• Arrow’s Impossibility Theorem: A one-page summary of Arrow’s Impossibility theroem.
• 中文量詞: 中文裡有很多相似、但是意義卻又微妙不同的量詞，像是「雙、副、對」或「條、根、支」。台灣的母語使用者會怎麼在這幾個量詞之間選擇呢？一個簡單的問卷調查結果。
• Kelighine 遊戲: 我國中莫名其妙發明的一款遊戲， 2020 年的時候想說可以把遊戲規則紀錄一下，以免變老之後就忘記了。
• Punkt Uhr: Making an illustration by one of my favourite artists Anna Kövecses move!
• Gallery: Some graphics I’ve created.