研究 (Research)

Journal articles:

• P.-S. Chen, H.-Y. Liu, and C.-H. Hsu, Economic Order Quantity of Deteriorating Drugs with New and Redistributed Demands in a Closed-loop Supply Chain: From the Viewpoint of a Hospital Pharmacy, International Journal of Systems Science: Operations & Logistics, 2026, Vol. 13, No. 1. (SCIE) 
• P.-S. Chen, J. Lyu,  C.-W. Chen, I.-H. Yu, and C.-H. Hsu, The Social-economic Value of a Renewable Energy Power Generation and Energy Storage System: A Case Study, International Journal of Systems Science: Operations & Logistics, 2026, Vol. 13, No. 1. (SCIE)
• H.-A. Bui, C.-H. Hsu, H.-W.V. Young, Y.-Y. Chen, and Y.-A. Liou, Advanced Semi-Supervised Learning for Remote Sensing-Based Land Cover Classification in the Mekong River Delta, Vietnam, Remote Sensing, 2026, 18, 989. https://doi.org/10.3390/rs18070989. (SCIE)

改變世界的17個方程式

Ian Stewart, In Pursuit of the Unknown: 17 Equations That Changed the World, Basic Books, 2012.

李政崇譯，改變世界的17 個方程式 (第2版)，商周出版，2025

學習數學的四個層次：(3) 在許多行業的應用

學習數學的四個層次：(0) 如何學數學，(1) 代表具備基礎的知識與能力，(2) 邏輯推理和抽象思考的能力，(3) 在許多行業的應用，(4) 純粹滿足好奇心或求知慾。

2015/12/1 初稿，持續更新中。

一般性說明

• 數學是科學之母，科學則是工業的基礎，所以大學工學院的數理化課程總學分超過 1/3。可以參考如何選填大學志願。
• 應用在不同的領域 (理工商醫農、教育)，如財務工程、設計電腦、貨物產銷、工程師、使用統計學分析學習成效等等。
• 抽象的模式與思考的方式，適用於現在與未來的應用，以微分為例，物理學的距離微分是速度，經濟學中成本的微分是邊際成本，電子學的電荷微分是電流。也就是說，可以使用函數表示任何待解的問題，函數的微分便可以研究其變化和極值的情況，例如機器學習中，超參數 (hyperparameter) 的學習 。
• 基本的原則變動不大，微積分、機率和統計學、和線性代數已經有 200 年以上的歷史，可幫助未來的自我學習。許多人說學校學的東西，畢業後立即過時或沒用，我覺得很疑惑。大學只是基礎教育，必須不斷地學習新的東西，以因應產業和職務的變化；最近熱門的大數據 (big data) 和人工智慧 (artificial intelligence)，其數學基礎正是這些課程。
  

Bridging physics-based and data-driven modeling for COVID-19 forecasting

Rui Wang, Danielle Robinson, Christos Faloutsos, Yuyang Wang, and Rose Yu, AutoODE: Bridging physics-based and data-driven modeling for COVID-19 forecasting, NeurIPS 2020 Workshop on Machine Learning in Public Health. (best paper award at the NeurIPS Machine Learning in Public Health Workshop)

As COVID-19 continues to spread, accurately forecasting the number of newly infected, removed and death cases has become a crucial task in public health. While mechanics compartment models are widely-used in epidemic modeling, data-driven models are emerging for disease forecasting. In this work, we investigate these two types of methods for COVID-19 forecasting. Through a comprehensive study, we find that data-driven models outperform physics-based models on the number of death cases prediction. Meanwhile, physics-based models have superior performances in predicting the number of infected and removed cases. In addition, we present an hybrid approach, AutoODE, that obtains a 57.4% reduction in mean absolute errors of the 7-day ahead COVID-19 trajectories prediction compared with the best deep learning competitor.

Numerical Python

Robert Johansson, Numerical Python: Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib, Apress, 2019. (code)

 Leverage the numerical and mathematical modules in Python and its standard library as well as popular open source numerical Python packages like NumPy, SciPy, FiPy, matplotlib and more. This fully revised edition, updated with the latest details of each package and changes to Jupyter projects, demonstrates how to numerically compute solutions and mathematically model applications in big data, cloud computing, financial engineering, business management and more. 

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics

Justin Solomon, Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics,  1st Edition, A K Peters/CRC Press, 2015. (pdf)

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into the theoretical tools needed to support these skills.

The book covers a wide range of topics—from numerical linear algebra to optimization and differential equations—focusing on real-world motivation and unifying themes. It incorporates cases from computer science research and practice, accompanied by highlights from in-depth literature on each subtopic. Comprehensive end-of-chapter exercises encourage critical thinking and build students’ intuition while introducing extensions of the basic material.

The text is designed for advanced undergraduate and beginning graduate students in computer science and related fields with experience in calculus and linear algebra. For students with a background in discrete mathematics, the book includes some reminders of relevant continuous mathematical background.

Probabilistic Machine Learning

 "Probabilistic Machine Learning" - a book series by Kevin Murphy

Kevin Patrick Murphy, Probabilistic Machine Learning: An Introduction, MIT Press, 2021. (Python codes)

新的版本，作者花了很多時間整理。以第一部分的數學基礎為例，使用機器學習說明相關的概念。也納入時事，例如 2.3.1 節的 Testing for COVID-19。 

(高中) 數學與資訊工程

馬來西亞的學校提案，準備今年 5 月，開授相關線上演講，以便吸引高中生就讀資訊相關科系。去年12月中開校內協調會的時候，學校長官指派我，負責「數學與資訊工程 」。 月底到了，忙著提科技部計畫和撰寫研究的程式，但是，各種點子不斷地進入我的腦袋裡，只好趕緊把它寫下來，不然半夜進入我的夢鄉，擾人清夢。花了兩天，寫下初稿；最近又多次修正，前後花了不下 20 小時，決定提前定稿 ，以便改作其他教學和研究事務。

後來想一想， 既然這是一個有意義的工作，就準備把他錄成影片，並上傳 YouTube，以幫助有需要的年輕人。追求新知並傳授給學生，一直是我當老師快樂的泉源。

歡迎指正和提供寶貴意見。(pdf in 1) (pdf in 4，如果需要列印， 請雙面列印此版本，環保救地球)

初稿 2021/1/15。

Mathematics for Machine Learning

Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, Mathematics for Machine Learning, Cambridge University Press, 2020. (pdf)

The book assumes the reader to have mathematical knowledge commonly covered in high school mathematics and physics. For example, the reader should have seen derivatives and integrals before, and geometric vectors in two or three dimensions. Starting from there, we generalize these concepts. Therefore, the target audience of the book includes undergraduate university students, evening learners and learners participating in online machine learning courses.

Linear Algebra and Optimization for Machine Learning: A Textbook

Charu C. Aggarwal, Linear Algebra and Optimization for Machine Learning: A Textbook, Springer, 1st ed, 2020.

This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout the book. A solution manual for the exercises at the end of each chapter is available to teaching instructors. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows: 

台灣本土火箭 要讓太空旅行夢想成真

 吳宗信，台灣本土火箭 要讓太空旅行夢想成真，TEDxTaipei，2015 (吳教授的台語真棒)

3Blue1Brown 驚人的視覺化數學影片

But what *is* a Neural Network? | Chapter 1, deep learning 

(主頁面，所有的主題都有好幾部影片)

多變數生產函數

連結未知的點

這週的微積分進度是多變數生產函數和偏微。

除了解釋公式的管理意涵外，依照往例，我會說明完整的故事，例如如何利用行銷，找到影響需求量的關鍵因素；利用網路技術，搜尋相關的數據；利用經濟學，了解可能的需求函數；利用統計學，找到需求曲線，以驗證假設和資料間的相關性；利用微積分和作業研究， 找到合適的價格； 最後，使用程式實現之。

有了這樣的基礎 ，就可以了解價格變化對需求的影響，連動到後端的供應鏈和存貨管理。 這種精準的預測能力，是大數據和機器學習火紅的根本原因之一。

當然，完成這樣的系統不容易。 不過，我請同學退一萬步想 ，同儕間有多少人有這種本事。 和大學畢業文憑數相比，就可知道兩者之間的差距。

地震預警 App MyShake

譚偉晟，抓住救命瞬間！ 柏克萊大學推出地震預警 App「MyShake」，自由時報，2016/2/13

為了減輕地震帶來的災害，各界都努力試圖以科技預測大地震的到來。而現在一款名為「MyShake」的 App，能夠利用智慧型手機的加速儀 (accelerometers)，偵測地震獨有的震動模式，提前警告用戶地震即將來襲，替用戶爭取到珍貴的避難時間！ 

台北 101 阻尼器於蘇迪勒颱風來襲晃動情況

台北 101 阻尼器於 2015/08/08 蘇迪勒颱風來襲晃動情況

Seventeen Equations that Changed the World

Ian Stewart, Seventeen Equations that Changed the World, Profile Books, 2013.

Larry Phillips 畫的圖

Andy Kiersz 有進一步的說明。

單變數微積分

函數有三大類，冪函數 (power function，x^n)、指數對數、和三角函數。透過五種規則變成更複雜的函數，分別為加、減、乘、除、和複合函數 (composite function)，例如
(加) x^3 + x (是多項式)
(減) exp (x) - log (x)
(乘) sin (x) * x^3
(除) x^3 / (cos (x) + 1) 或 2 x / (x^2 + 1) (是有理式)
(複合) sqrt(3 x) 或 sin ( 2 x ) 

線積分 (Line integral) 在斷層攝影術 (Tomography) 的應用

可以參考 Keegan Go, Ahmed Bou-Rabee, and Stephen Boyd, Tomography, EE103, Stanford University, August 16, 2014

後半段的進似解需要 (大二的) 線性代數。

計算螺絲的體積

台灣是螺絲生產大國，接單時必須根據螺絲形狀計算其體積和成本 (註 1)。如果報價太高，可能接不到單；如果報價太低，接單生產的利潤低、甚至虧錢。

許多老闆沒學過微積分，常常根據經驗來估計成本，所以事後才能得知新產品的利潤。朋友使用微積分 (註 2)，可以事前得知新螺絲的體積；但是，一套數萬元的軟體常常被廠商殺價，所以建議朋友的業務向廠商報告時，第一張投影片採用下表來說明該軟體的價值

表的橫軸代表訂購量，縱軸代表體積計算的誤差量，空白處代表成本的誤差量。如果訂購量是 1 千萬，誤差 1%，誤差成本是 1 萬元，接單數次該軟體就回本 (註 3)。

(註 1) 根據體積和生產螺絲材料的成本，可以得知單一螺絲的物料直接成本。
(註 2) 使用公式或數值積分計算之。關於數值積分，講義  11-16 頁計算面積誤差，計算體積 (講義  15-2 頁) 時也有類似的公式，只要取樣點 m 和 n 夠大，誤差就會很小。
(註 3) 假設誤差 1% 的單位成本是 0.1 元。根據廠商實際的經驗，誤差 5% 或更高也發生過。