this course will study various techniques for designing and analyzing algorithms. we will mainly focus on problems for which the exact algorithm is not known or not efficient enough and problems with resource constraints. besides designing efficient algorithms, proving the performance guarantees is also a main topic of this course. some topics that we will cover are as follows:

approximation algorithms: algorithms that find near-optimal solutions with provable performance guarantees in polynomial time. this course will mainly focus on approximation algorithms for np-hard problems.

randomized algorithms: algorithms that use random numbers. we will focus on algorithms with provable success probabilities and good expected solution quality.

the following topics will also be briefly described if time permits.

streaming algorithms: algorithms that solve problems on massive datasets. in this type of problem, usually, the algorithm is only allowed to read the data once and use no more than a constant or poly-logarithmic amount of space.

online algorithm: the input to the problem is not known in advance and arrives over time. an online algorithm must decide how to process a specific input before seeing future inputs. the goal is to perform as well as an algorithm that knows all inputs beforehand.

we will cover algorithm design techniques such as hashing, sampling, and linear programming.

內容: 講授高等電腦視覺之基本觀念及立論基礎。
介紹各種高等電腦視覺可能之應用,
並配合各項相關專題課程的需求研發適當之演算法及計算架構並完成軟體模擬。
將涵蓋:
1. 簡介 (introduction),
2. 影像形成 (image formation),
3. 影像處理 (image processing),
4. 模型擬合與最佳化 (model fitting and optimization),
5. 深度學習 (deep learning)
6. 辨認 (recognition)
7. 特徵偵測與配對 (feature detection and matching)
8. 影像對正與縫合 (image alignment and stitching)
9. 運動估計 (motion estimation),
10. 計算攝影學 (computational photography),
11. 由運動求得結構與同步定位與地圖建構 (structure from motion and slam)
12. 深度估計 (depth estimation)
13. 三維重建 (3d reconstruction),
14. 以影像為基礎的繪圖 (image-based rendering),

本課是探討數位訊位處理的理論與應用，來對數位訊號之理論，數位濾波器設器，梅爾倒頻譜，音訊處理，影像壓縮及影像處理，快速演算法設計，正交轉換等領域，做個清楚且有系統的介紹

1. 本學期所有課程將會「實體聚集並支援線上會議室同步參與」，連結為 https://ntucc.webex.com/meet/yenminghuang
2. 歡迎所有對相控陣列雷達系統之實務設計和開發有興趣的同學，自在地加入我們的課程社團一起討論和分享，連結為 https://www.facebook.com/groups/ntuphasedarrayradar/
3. 課程投影片將公告並隨時更新於 https://sites.google.com/view/yenming/teaching
4. 歡迎訂閱課程影片youtube頻道: https://www.youtube.com/@ntuphasedarrayradar
5. 由於本課程的時段和形式較為特殊，若有任何問題，請隨時與授課教師聯絡 yenminghuang@ntu.edu.tw
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algorithm design for phased array radar is a graduate-level course designed for students interested in modern radar systems widely used in vehicle networks, surveillance systems, military applications, satellites, etc. this course is the extension of the course entitled signal processing for phased array radar to provide more insights into high-tech radar systems and applications in recent years. from the aspects of digital signal and data processing algorithms with the aid of artificial intelligence (ai), we explore advanced radar technologies.

外系學生加選請於加退選時向授課老師詢問。總人數限 60人限本系所學生(含輔系、雙修生)

this course provides an introduction to the design and analysis of computer algorithms. we will cover topics including concepts of algorithm complexity, and various algorithms such as divide-and-conquer, dynamic programming, sorting, and greedy algorithms.
for those who would like to add this course (加簽), please fill in this google form and follow the instruction: https://forms.gle/l9of8rfaurnp2he59

本課程以英語授課。外系學生加選請於加退選時向授課老師詢問。總人數限 60人限本系所學生(含輔系、雙修生)

本課程將討論生物資訊學基本原理及實際應用，以使修習同學能充分掌握如何運用電腦的處理能力，有效解決生醫研究上資料分析，生物醫學資料庫應用分析，以及生物分子結構分析與功能預測。

生物資訊與系統生物學程必修課，學程學生優先選。與李建璋、賴亮全、詹迺立、范怡琴、歐陽彥正合授總人數限 80人限學士班三年級以上

這是一門半學期的課程，主要介紹多變數函數的微積分運算，和其豐富的應用。
微分主題包含多變數函數的極限，偏微分，方向導數，切平面，線性逼近，和微分連鎖律；並討論求函數極值， lagrange乘子法等應用問題。積分部分涵蓋多重積分與逐次積分的定義，fubini定理，和變數變換；並以求實體質量、質心等幾何量作為其應用。
課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力；同時會示範微積分在各領域的應用，幫助學生將微積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算並完成學習單上的小型研究題目。

calculus of multivariable functions together with its profound applications are introduced in this half-semester course. especially, topics about differentiation include limits, partial derivatives, directional derivatives, tangent planes, linear approximations, and the chain rule. also, applications such as finding extreme values and methods of lagrange multipliers are discussed. topics about integration involve definitions of multiple integrals and iterated integrals, fubini’s theorem, change of variables, as well as applications such as computing the mass and center of mass of a solid.
definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. practical applications of calculus in various fields are illustrated in order to promote a more organic interaction between the theory of calculus and students own fields of study. this course also provides discussion sessions in which students are able to improve their skills in handling calculations in calculus and complete small projects under the guidance of our teaching assistants.

本課程中文授課,使用英文教科書。密集課程。統一教學.一10為實習課.週末考試.總人數限150人限本系所學生(含輔系、雙修生)

這是一門半學期的課程，主要介紹多變數函數的微積分運算，和其豐富的應用。微分主題包含多變數函數的極限、偏微分、方向導數、切平面、線性逼近、和微分連鎖律。並討論求函數極值、 lagrange 乘子法等應用問題。積分部分涵蓋多重積分與逐次積分的定義、fubini 定理、和變數變換。並以求實體質量、質心等幾何量作為其應用。課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力。同時會示範微積分在各領域的應用,幫助學生將微積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算並完成學習單上的小型研究題目。

本課程中文授課,使用英文教科書。密集課程。統一教學.一10為實習課.週末考試.總人數限150人限本系所學生(含輔系、雙修生)

building upon the foundation laid in math4006-7, which focused on calculus of functions with a single real variable, multivariable calculus (math4008-9) delves into the principles and applications of multivariable calculus, particularly in the context of 2- and 3-variable functions. this course serves as a crucial cornerstone for various disciplines in science and engineering.

key topics include
1. partial derivatives
2. continuous and differentiable functions in multivariables
3. chain rule and directional derivatives:
4. second derivative test and lagrange multipliers
5. double and triple integrations
6. curvilinear coordinates

in this course, definitions are thoroughly discussed, and key theorems are derived during lectures to foster logical deduction and analytical skills among students. practical applications of calculus are highlighted to establish a meaningful connection between theoretical concepts and their relevance to various scientific and engineering fields. to enhance students proficiency in calculus, ta classes are incorporated into the course. here, students have the opportunity to refine their calculation skills under the guidance of experienced teaching assistants. these sessions aim to reinforce theoretical concepts and provide practical insights into problem-solving techniques.

本課程以英語授課。密集課程。統一教學.一10為實習課.週末考試.總人數限130人限本系所學生(含輔系、雙修生)

這是一門半學期的課程，分為「向量微積分」與「泰勒展式」兩大主題。
「向量微積分」討論的主體是定義域、值域皆屬於 r^n的向量場。我們將定義如何在曲線或曲面上積分向量場，並介紹作用在向量場上的兩種微分運算，「散度」與「旋度」。課程將解釋green定理、stokes定理、散度定理如何結合向量場的微分與積分運算，而被理解為高維度的「微積分基本定理」。應用上，我們將推導電磁學中的 gauss 定律，計算封閉曲面的電通量。
「泰勒展式」這主題推廣「極限」的概念，探討如何以多項式逼近複雜的函數。為了達到這個目的，我們將介紹無窮級數與冪級數的收斂性，利用泰勒定理估計餘項，進而推導出常見函數的泰勒展式。最後我們將示範多項式逼近的實際應用。
課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力；同時會示範微積分在各領域的應用，幫助學生將微積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算並完成學習單上的小型研究題目。

本課程中文授課,使用英文教科書。密集課程。密集課程.統一教學.一10為實習課.總人數限150人限本系所學生(含輔系、雙修生)

這是一門半學期的課程，分為「向量微積分」與「泰勒展式」兩大主題。
「向量微積分」討論的主體是定義域、值域皆屬於 r^n 的向量場。我們將定義如何在曲線或曲面上積分向量場,並介紹作用在向量場上的兩種微分運算，「散度」與「旋度」。課程將解釋 green 定理、stokes 定理、散度定理如何結合向量場的微分與積分運算，而被理解為高維度的「微積分基本定理」。應用上，我們將推導電磁學中的 gauss 定律，計算封閉曲面的通量。
「泰勒展式」這主題推廣「極限」的概念，探討如何以多項式逼近複雜的函數。為了達到這個目的，我們將介紹無窮級數與冪級數的收斂性，利用泰勒定理估計餘項，進而推導出常見函數的泰勒展式。最後我們將示範多項式逼近的實際應用。
課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力。同時會示範微積分在各領域的應用，幫助學生將微積分與其他專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算並完成學習單上的小型研究題目。

本課程中文授課,使用英文教科書。密集課程。密集課程.統一教學.一10為實習課.總人數限150人限本系所學生(含輔系、雙修生)

in the final segment of calculus (math4009), two main topics will be discussed.

firstly the course focuses on how calculus can be applied to vector fields. vector fields, which are vector-valued functions originated from physics, will be thoroughly examined with an emphasis on understanding integrals over curves and surfaces. in particular, green’s, stokes, and divergence theorem will be presented as generalizations of the fundamental theorem of calculus for, respectively, line and surface integrals. an application, we will derive the gauss law, offering insights into the flux of an inverse square field across a closed surface.

to conclude our study of calculus, we will introduce the definitions of limits for sequences and series, addressing the theoretical foundations for the introduction of power series. as a generalization of `polynomials, power series find application in representing both elementary and advanced functions, thereby laying the groundwork for a more sophisticated analysis of functions, essential in practical contexts.

the key topics covered include:

1. line integrals
2. green’s theorem and conservative vector fields
3. surface integrals and flux
4. stokes’ and divergence theorem
5. series : definition and convergence tests
6. power series : radius of convergence and their calculus
7. taylors theorem and its applications

本課程以英語授課。密集課程。英文授課.密集課程.統一教學.一10為實習課.總人數限130人限本系所學生(含輔系、雙修生)

本課程介紹以gaas及inp為主的三五族化合物半導體材料系統的磊晶及製程技術。
一、 光電半導體材料的種類及基本特性
二、 塊材成長技術
三、 真空技術
四、 磊晶技術：分子束磊晶法
五、 磊晶技術：有機金屬化學沈積法
六、磊晶技術：液相磊晶法