國立成功大學「邁向頂尖大學計畫」
延攬優秀人才工作報告表
NCKU’s “Aim for the Top University Project”
Work Report Form for Distinguished Scholars
□續聘continuation of employment ■離職resignation
100 年 7 月 13 日更新
受聘者姓名
Name of the Employee 江中宙 ■男 □女
Male Female
聘 期 Period of Employment
from 年(y) 月(m) 日(d) to 年(y) 月(m) 日(d) 研究或教學或科技研發與
管理計畫名稱 The project title of research,
teaching, technology development and management
邁向頂尖大學計畫 計畫主持人
（申請單位主管）
Project Investigator (Head of Department/Center)
柯文峰
補助延聘編號
Grant Number HUA １０２-２５-２-３０９
一、研究、教學、科技研發與管理工作全程經過概述。（由受聘人填寫）
Please summarize the entire research, teaching, or science and technology R&D and management work process (To be completed by the employee)
1.
微積分(一)、（二）
(一)
由函數的極限及連續性的探討開始討論微分積分之根本理論方法及應用，強調某些基本理論，例如:Root-location Theorem、Newton Method 等在後續高年級課程中 (如: 數值分析、數值微分方程等)的重要性。接下來談到反導函數、Riemann 積分的一些 基本計算方法。
（二）
介紹積分在物理、幾何及機率上的應用以及一些基本的常微方程。再來談到無窮級數的歛散性質及Taylor Series，最後進入多變數函數、偏微分、多重積分、線積分與面積 分。
2.
解析幾何與矩陣
本課程目的在於介紹向量、座標、矩陣以及相關的幾何內容。為使學生
熟悉矩陣的
基本運算與幾何意義，使學生能銜接微積分後半部份及二年級以上數學系進階
課程。
1. Vector Geometry:
Inner/cross product
Conic Section
Quadratic form 2. Polar Coordinates:
Curve Plotting
Converting to and from Polar Coordinates
Polar Forms for Lines and Conics 3. Linear Transformations
Linear combinations of vectors
Linear independence of vectors
Basis and dimension
Translation
Rotation
Inverse transformations
Inverse matrices
4. Eigenvalues and Eigenvectors Orthogonality
3.
應用機率
The goal of this course is to introduce the elementary probability theory and stochastic processes. It is particularly well suited for those wanting to see how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research.
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a. Random Variables
b. Conditional Probability and Conditional Expectation
Discrete & Continuous Cases
Computing Expectations by Conditioning
Some Applications
c. Markov Chains
Chapman-Kolmogorov Equations
Limiting Probabilities
Some Applications
d. The Exponential Distribution & the Poisson Process
Properties of the Exponential Distribution.
Convolutions of Exponential Random Variables.
The Poisson Process.
e. Brownian Motion and Stationary Processes
Brownian Motion.
Hitting times, Maximum Variable, Gambler’s Ruin Problem.
White Noise.
f.
Gaussian Processes.4.
組合及圖論
The goal of this course is to introduce basic knowledge on graph theory and develop facility at combinatorial reasoning, which are the bases for analyzing a wide of problems in computer science and discrete applied mathematics.
a. Elements of Graph Theory
Graph Models
Isomorphism
Edge Counting & Planar Graphs
b. Covering Circuits and Graph Coloring
Euler & Hamilton Circuits
Coloring Theorems
c. Trees and Searching
Properties of Trees
The Traveling Salesperson Problem
Tree Analysis of Sorting Algorithms
d. Generating Functions
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e. Additional Topics
Burnside’s Theorem
The Cycle Index
f. Polya’s Formula
5. 賽局理論導論
賽局理論 (game theory，或譯博弈理論、競局理論、對局論、局論、對策論)由 80 年代 起 已 經 逐 漸 成 為 主 流 經 濟 學 的 一 部 份 。 它 所 探 討 的 中 心 是 策 略 互 動 行 為(strategic interaction)：研究決策主體的行為發生直接相互作用（影響）時決策問題以及此種決策 的均衡問題。決策者（個人或是企業）在考量策略時必須將其他主體（個人或是企業）得策 略一併考量。當這些相互影響的因素放在一起考慮時，會有什麼結果？會也有結論嗎？該下 何種決策？需要互動式的計算來處理這些因素。賽局理論的應用隨處可見，從數學、哲學、資 訊科學、生物學到各類社會科學都可發現其蹤跡。
1. 生活中的賽局理論
1. 七大困境 2. 信任與合作 3. 改變賽局
2. 賽局理論與經濟學
3. 合作與非合作賽局理論
4. 完全信息靜態賽局
1. 那許平衡
2. 混和策略那許平衡
5. 完全信息動態賽局
1. 賽局的擴展是表述
2. 賽局的擴展是表述的那許平衡 3. 子賽局精煉那許平衡
6. 不完全信息靜態賽局 1. 貝斯那許平衡
2. 貝斯賽局與混和策略平衡 7. 不完全信息動態賽局
1. 精煉貝斯那許平衡 2. 信息傳遞賽局及應用舉例
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二、研究或教學或科技研發與管理成效評估（由計畫主持人或單位主管填寫）
Please evaluate the performance of research, teaching or science and technology R&D and management Work: ( To be completed by Project Investigator or Head of Department/Center)
(1)是否達到延攬預期目標？
Has the expected goal of recruitment been achieved?
(2)研究或教學或科技研發與管理的方法、專業知識及進度如何？
What are the methods, professional knowledge, and progress of the research, teaching, or R&D and management work?
(3)受延攬人之研究或教學或科技研發與管理成果對該計畫(或貴單位)助益如何？
How have the research, teaching, or R&D and management results of the employed person given benefit to the project (or your unit)?
(4)受延攬人於補助期間對貴單位或國內相關學術科技領域助益如何？
How has the employed person, during his or her term of employment, benefited your unit or the relevant domestic academic field?
(5)具體工作績效或研究或教學或科技研發與管理成果：
Please describe the specific work performance, or the results of research, teaching, or R&D and management work:
(6)是否續聘受聘人? Will you continue hiring the employed person? □續聘Yes □不續聘No
※此報告表篇幅以三～四頁為原則。This report form should be limited to 3-4 pages in principle.
※此表格可上延攬優秀人才成果報告繳交說明網頁下載。
This report form can be downloaded in http://scholar.lib.ncku.edu.tw/explain/
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