108-1_數值拓延法
應用數學系
教學目標
在理論部分需了解延拓法的理論，包含隱函數定理及分歧理論。在計算部分需能利用一種程式語言撰寫程式，追蹤解曲線。
授課形式
理論講述與討論-60.00%;個案分析或作品賞析-0.00%;專題實作與報告-40.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
週次 內容 1-2 Implicit function Theorem 3 Newton's method 4 predictor-solver methods 5 Sard's Theorem 6 Solution sets for regular values. 7 Degree Theory 8 Homotopy Invariance of the degree 9 Bifurcation Theorem 10 continuation method 11 pseudo-arclength continuation method. 12 Multi-parameter problems 13 Paths of periodic solutions and Hopf bifurcation. 14 Algorithm 15-17 Coding 18 期末報告
教科書/參考書
Lectures on Numerical methods in Bifurcatiopn problems
評分標準
一、平時成績 （40％) 二、期末報告 （60％)
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
3
在理論部分需了解延拓法的理論，包含隱函數定理及分歧理論。在計算部分需能利用一種程式語言撰寫程式，追蹤解曲線。
授課形式
理論講述與討論-60.00%;個案分析或作品賞析-0.00%;專題實作與報告-40.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
週次 內容 1-2 Implicit function Theorem 3 Newton's method 4 predictor-solver methods 5 Sard's Theorem 6 Solution sets for regular values. 7 Degree Theory 8 Homotopy Invariance of the degree 9 Bifurcation Theorem 10 continuation method 11 pseudo-arclength continuation method. 12 Multi-parameter problems 13 Paths of periodic solutions and Hopf bifurcation. 14 Algorithm 15-17 Coding 18 期末報告
教科書/參考書
Lectures on Numerical methods in Bifurcatiopn problems
評分標準
一、平時成績 （40％) 二、期末報告 （60％)
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
3
108-1_常微分方程專題(一)
應用數學系
教學目標
本課程將介紹常微分方程中一些常見的分析手法，並以一些物理及生物模型作為講解範例。
授課形式
課程內容與進度
1. 講述動態系統與微分方程領域上的重要理論結果。
2. 講述程式的操作。
3. 研讀與報告相關論文。
4. 尋找與報告研究主題。
教科書/參考書
個人投影片、期刊論文。
評分標準
上台報告(50％) + 課堂討論(50％)。
學分數
3
授課時數(周)
3
開課班級
D10841
修課人數
3
本課程將介紹常微分方程中一些常見的分析手法，並以一些物理及生物模型作為講解範例。
授課形式
課程內容與進度
1. 講述動態系統與微分方程領域上的重要理論結果。
2. 講述程式的操作。
3. 研讀與報告相關論文。
4. 尋找與報告研究主題。
教科書/參考書
個人投影片、期刊論文。
評分標準
上台報告(50％) + 課堂討論(50％)。
學分數
3
授課時數(周)
3
開課班級
D10841
修課人數
3
108-1_動態系統專題(二)
應用數學系
教學目標
This course intends to introduce some recently developed topics in dynamical systems. Starting with one-dimensional symbolic dynamics, we will study one-dimensional cellular automata from the viewpoint of ergodic theory. The ergodicity, weak mixing, and strong mixing property of cellular automata are demonstrated. Then we extend to the investigation of reversible and multidimensional cellular automata.
Tree-shifts were introduced less than 4 year and have been studied in the viewpoint of classification. More specific, two tree-shifts are topological conjugate if and only if the conjugacy can be decomposed into the composition of splitting and amalgamation codes. This course intends to elucidate other topological properties such as topological chaos of tree-shifts, and then consider cellular automata defined on Cayley trees.
Students who are interested in Ergodic Theory are welcome to participate some of projects the instructor is working on.
授課形式
理論講述與討論-40.00%;個案分析或作品賞析-0.00%;專題實作與報告-60.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. Symbolic shift spaces
2. Graph presentation of some types of shift spaces
3. Topological entropy of shift spaces
4. Chaos in symbolic dynamics
5. Measure-theoretic entropy of shift spaces
6. Topological and measure-theoretic properties of cellular automata
7. Fundamental properties of tree-shifts
8. Chaos and matrix presentation of tree-shifts
9. Cellular automata on Cayley trees
教科書/參考書
Instructor's Lecture Note
評分標準
1. Presence: 20%
2. Class Discussion: 30%
3. Presentation: 50%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
3
This course intends to introduce some recently developed topics in dynamical systems. Starting with one-dimensional symbolic dynamics, we will study one-dimensional cellular automata from the viewpoint of ergodic theory. The ergodicity, weak mixing, and strong mixing property of cellular automata are demonstrated. Then we extend to the investigation of reversible and multidimensional cellular automata.
Tree-shifts were introduced less than 4 year and have been studied in the viewpoint of classification. More specific, two tree-shifts are topological conjugate if and only if the conjugacy can be decomposed into the composition of splitting and amalgamation codes. This course intends to elucidate other topological properties such as topological chaos of tree-shifts, and then consider cellular automata defined on Cayley trees.
Students who are interested in Ergodic Theory are welcome to participate some of projects the instructor is working on.
授課形式
理論講述與討論-40.00%;個案分析或作品賞析-0.00%;專題實作與報告-60.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. Symbolic shift spaces
2. Graph presentation of some types of shift spaces
3. Topological entropy of shift spaces
4. Chaos in symbolic dynamics
5. Measure-theoretic entropy of shift spaces
6. Topological and measure-theoretic properties of cellular automata
7. Fundamental properties of tree-shifts
8. Chaos and matrix presentation of tree-shifts
9. Cellular automata on Cayley trees
教科書/參考書
Instructor's Lecture Note
評分標準
1. Presence: 20%
2. Class Discussion: 30%
3. Presentation: 50%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
3
108-1_計算生物數學專題(二)
應用數學系
教學目標
To go deeper into specific subjects in mathematical biology - concentrating on computation techniques and background biology. Learning to convert given physiological information into more precise mathematical assumptions, construct mathematical models based on the assumptions. Focus will be on continuum models, their construction and numerical simulations, asymptotic analysis on the model to compare with numerics if possible and the biological interpretation of the results.
授課形式
理論講述與討論-30.00%;個案分析或作品賞析-40.00%;專題實作與報告-30.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
Focus on models that require sufficient amount of computation. ODE models concerning biological oscillators which exhibit periodic solutions (and maybe time delay). Discussion on bifurcation analysis and continuation methods. PDE models describing mass conservation (reaction-diffusion systems, chemotaxis models). PDE models describing mass conservation and force balance equations (tumour models).
教科書/參考書
James Murray : Mathematical Biology I,II Numerical solutions of partial differential equations
評分標準
Report or presentation at the end of the semester
學分數
3
授課時數(周)
3
開課班級
D10841
修課人數
1
To go deeper into specific subjects in mathematical biology - concentrating on computation techniques and background biology. Learning to convert given physiological information into more precise mathematical assumptions, construct mathematical models based on the assumptions. Focus will be on continuum models, their construction and numerical simulations, asymptotic analysis on the model to compare with numerics if possible and the biological interpretation of the results.
授課形式
理論講述與討論-30.00%;個案分析或作品賞析-40.00%;專題實作與報告-30.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
Focus on models that require sufficient amount of computation. ODE models concerning biological oscillators which exhibit periodic solutions (and maybe time delay). Discussion on bifurcation analysis and continuation methods. PDE models describing mass conservation (reaction-diffusion systems, chemotaxis models). PDE models describing mass conservation and force balance equations (tumour models).
教科書/參考書
James Murray : Mathematical Biology I,II Numerical solutions of partial differential equations
評分標準
Report or presentation at the end of the semester
學分數
3
授課時數(周)
3
開課班級
D10841
修課人數
1
108-1_實變函數論(一)
應用數學系
教學目標
使學生熟悉Lebesgue測度，Lebesgue積分的觀念、性質和操作技巧，以及如何應用在近代分析學和機率論。
授課形式
理論講述與討論-80.00%;個案分析或作品賞析-0.00%;專題實作與報告-0.00%;田野調查-0.00%;實驗-0.00%;其他:演習-20.00%
課程內容與進度
Lebesgue outer measure，Lebesgue measure，non-Lebesgue measurable set，Lebesgue measurable function，Littlewood three principles， Lebesgue integral，Lebesgue dominated convergence theorem，the Minkowski and Holder inequalities， the concepts of convergence and completeness，Riesz-Fisher theorem，Approximation in L^p space，product measure and Fubini theorem。
教科書/參考書
H. L. Royden：Real Analysis，1988 R. L. Wheeden and A. Zygmund：Measure and integral：An introduction to real analysis，1977
評分標準
作業70%，期末測驗30%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
4
使學生熟悉Lebesgue測度，Lebesgue積分的觀念、性質和操作技巧，以及如何應用在近代分析學和機率論。
授課形式
理論講述與討論-80.00%;個案分析或作品賞析-0.00%;專題實作與報告-0.00%;田野調查-0.00%;實驗-0.00%;其他:演習-20.00%
課程內容與進度
Lebesgue outer measure，Lebesgue measure，non-Lebesgue measurable set，Lebesgue measurable function，Littlewood three principles， Lebesgue integral，Lebesgue dominated convergence theorem，the Minkowski and Holder inequalities， the concepts of convergence and completeness，Riesz-Fisher theorem，Approximation in L^p space，product measure and Fubini theorem。
教科書/參考書
H. L. Royden：Real Analysis，1988 R. L. Wheeden and A. Zygmund：Measure and integral：An introduction to real analysis，1977
評分標準
作業70%，期末測驗30%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
4
108-1_偏微分方程及其應用(一)
應用數學系
教學目標
偏微分方程在自然與科學領域中皆有許多應用, 如生物、物理、化學、幾何與財務等。而在這門課將介紹如何以變異法解決非線性橢圓方程式的相關問題為主。
授課形式
理論講述與討論-50.00%;個案分析或作品賞析-0.00%;專題實作與報告-50.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. Introduction and Basic Results: Motivations and Brief Historical Notes; Notation and Preliminaries; A Review of Differential Calculus for Real Functionals; Weak Solutions and Critical Points; Convex Functionals; Some Spectral Properties of Elliptic Operators. 2. Minimization Techniques: Compact Problems Coercive Problems; A min–max Theorem; Superlinear Problems and Constrained Minimization; A Perturbed Problem; Nonhomogeneous Nonlinearities; The p-Laplacian.
教科書/參考書
(1) Marino Badiale Enrico Serra: Semilinear Elliptic Equations for Beginners-Existence Results via the Variational Approach (2) 自編講義
評分標準
平時課堂表現:70%; 上台演練:30%
學分數
3
授課時數(周)
3
開課班級
D10841
修課人數
4
偏微分方程在自然與科學領域中皆有許多應用, 如生物、物理、化學、幾何與財務等。而在這門課將介紹如何以變異法解決非線性橢圓方程式的相關問題為主。
授課形式
理論講述與討論-50.00%;個案分析或作品賞析-0.00%;專題實作與報告-50.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. Introduction and Basic Results: Motivations and Brief Historical Notes; Notation and Preliminaries; A Review of Differential Calculus for Real Functionals; Weak Solutions and Critical Points; Convex Functionals; Some Spectral Properties of Elliptic Operators. 2. Minimization Techniques: Compact Problems Coercive Problems; A min–max Theorem; Superlinear Problems and Constrained Minimization; A Perturbed Problem; Nonhomogeneous Nonlinearities; The p-Laplacian.
教科書/參考書
(1) Marino Badiale Enrico Serra: Semilinear Elliptic Equations for Beginners-Existence Results via the Variational Approach (2) 自編講義
評分標準
平時課堂表現:70%; 上台演練:30%
學分數
3
授課時數(周)
3
開課班級
D10841
修課人數
4
108-1_群試設計
應用數學系
教學目標
Brief introduction of group testing: In the classical group testing, we have a set of items, each of which is either positive or negative. The idea of group testing is to group samples and then apply a test to the group. A group test, also called a pool, is a subset of items that yields a positive outcome if it contains at least one positive item. The task of group testing is to determine the positive items by group tests as few as possible. Group testing has been well-known for its applications in various fields including communication network, image compression, molecular biology and several computer science applications. Group testing also has strong relationships with several disciplines such as coding theory, information theory, and computational learning theory. In this course, we will study various group testing problems.
授課形式
理論講述與討論-40.00%;個案分析或作品賞析-0.00%;專題實作與報告-60.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
教科書/參考書
Primary: Fault-Tolerant Search Algorithms: Reliable Computation with Unreliable Information by Ferdinando Cicalese.
Secondary: 1. D. Z. Du and F. K. Hwang, Pooling Designs and Nonadaptive Group Testing - Important Tools for DNA Sequencing, World Scientific, 2006.
2. D. Z. Du and F. K. Hwang, Combinatorial Group Testing and Its Applications (2nd Edit.), World Scientific, 2000.
3. M. Aigner, Combinatorial Search, John Wiley and Sons, 1988.
評分標準
Participation(20%)
In class discussion (20%)
Paper report (60%)
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
7
Brief introduction of group testing: In the classical group testing, we have a set of items, each of which is either positive or negative. The idea of group testing is to group samples and then apply a test to the group. A group test, also called a pool, is a subset of items that yields a positive outcome if it contains at least one positive item. The task of group testing is to determine the positive items by group tests as few as possible. Group testing has been well-known for its applications in various fields including communication network, image compression, molecular biology and several computer science applications. Group testing also has strong relationships with several disciplines such as coding theory, information theory, and computational learning theory. In this course, we will study various group testing problems.
授課形式
理論講述與討論-40.00%;個案分析或作品賞析-0.00%;專題實作與報告-60.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
教科書/參考書
Primary: Fault-Tolerant Search Algorithms: Reliable Computation with Unreliable Information by Ferdinando Cicalese.
Secondary: 1. D. Z. Du and F. K. Hwang, Pooling Designs and Nonadaptive Group Testing - Important Tools for DNA Sequencing, World Scientific, 2006.
2. D. Z. Du and F. K. Hwang, Combinatorial Group Testing and Its Applications (2nd Edit.), World Scientific, 2000.
3. M. Aigner, Combinatorial Search, John Wiley and Sons, 1988.
評分標準
Participation(20%)
In class discussion (20%)
Paper report (60%)
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
7
108-1_深度類神經網路
應用數學系
教學目標
本課程延續人工智慧課程，作為機器人影像辨識、文字語音互動機器人等實作應用的核心分類與辨識引擎。讓學生利用深度學習進行影像辨識，引導機器人進行特定物件夾取，以體驗AI技術與實體機器人的整合；或讓學生利用深度學習進行文字語音辨識，進行人機互動，以體驗AI技術與實體機器人的整合。
授課形式
理論講述與討論-50.00%;個案分析或作品賞析-30.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
Fundamental Concepts and Models to Artificial Neural Systems
Single-Layer Perceptron Classifier
Multi-Layer Feedforward Networks
Matching and Self-Organizing Network
Hopfield Network and Associate Memory
Introduction to Deep Learning
Feature Extraction with Convolution
Deep Neural Networks
教科書/參考書
Neural Fuzzy Systems, C. T. Lin and C. S. George Lee, Prentice-Hall, Englewood Cliffs, NJ 1996.
類神經網路(4E)，黃國源，全華圖書股份有限公司，2018。
評分標準
TBA
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
25
本課程延續人工智慧課程，作為機器人影像辨識、文字語音互動機器人等實作應用的核心分類與辨識引擎。讓學生利用深度學習進行影像辨識，引導機器人進行特定物件夾取，以體驗AI技術與實體機器人的整合；或讓學生利用深度學習進行文字語音辨識，進行人機互動，以體驗AI技術與實體機器人的整合。
授課形式
理論講述與討論-50.00%;個案分析或作品賞析-30.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
Fundamental Concepts and Models to Artificial Neural Systems
Single-Layer Perceptron Classifier
Multi-Layer Feedforward Networks
Matching and Self-Organizing Network
Hopfield Network and Associate Memory
Introduction to Deep Learning
Feature Extraction with Convolution
Deep Neural Networks
教科書/參考書
Neural Fuzzy Systems, C. T. Lin and C. S. George Lee, Prentice-Hall, Englewood Cliffs, NJ 1996.
類神經網路(4E)，黃國源，全華圖書股份有限公司，2018。
評分標準
TBA
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
25
108-1_數學建模與生物數學
應用數學系
教學目標
Aims: (i) To investigate mathematical models of biological systems and introduce various techniques for analysing them, (ii) To enable students to understand how mathematics can be used to study biological systems. Objectives: On completion of this course students should be able to formulate ODE and PDE models to describe elementary biological systems and to be able to use a range mathe- matical techniques to analyse them.
授課形式
理論講述與討論-80.00%;個案分析或作品賞析-0.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. Single species population models. - Population growth - Insect outbreak 2. Models for interacting populations. - Competition - Predator-prey 3. Reaction kinetics and molecular biology. - Biological reactions - Biological oscillators 4. Population dispersal - Outcome and speed of population invasion 5. Pattern formation. - Turing theory for morphogenesis 6. Infectious Diseases (if time allowed) - Brief introduction on SI, SIS,SIR models. Mathematical techniques: - Mathematical modelling: formulating equations, units, non-dimensionalisation. - Qualitative analysis of differential equations: linear stability for ODEs (sections 1-3) and PDEs (4,5), phase-lines (1), hysteresis (1), phase-planes (2-3), bifurcation analysis (2,3,5), Law of mass action (3), travelling wave analysis (4), Turing theory (5).
教科書/參考書
N. F. Britton : Essential Mathematical Biology L. Edelstein-Keshet : Mathematical Models in Biology James Murray : Mathematical Biology I,II
評分標準
midterm exam or assessment 50% final exam 50%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
2
Aims: (i) To investigate mathematical models of biological systems and introduce various techniques for analysing them, (ii) To enable students to understand how mathematics can be used to study biological systems. Objectives: On completion of this course students should be able to formulate ODE and PDE models to describe elementary biological systems and to be able to use a range mathe- matical techniques to analyse them.
授課形式
理論講述與討論-80.00%;個案分析或作品賞析-0.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. Single species population models. - Population growth - Insect outbreak 2. Models for interacting populations. - Competition - Predator-prey 3. Reaction kinetics and molecular biology. - Biological reactions - Biological oscillators 4. Population dispersal - Outcome and speed of population invasion 5. Pattern formation. - Turing theory for morphogenesis 6. Infectious Diseases (if time allowed) - Brief introduction on SI, SIS,SIR models. Mathematical techniques: - Mathematical modelling: formulating equations, units, non-dimensionalisation. - Qualitative analysis of differential equations: linear stability for ODEs (sections 1-3) and PDEs (4,5), phase-lines (1), hysteresis (1), phase-planes (2-3), bifurcation analysis (2,3,5), Law of mass action (3), travelling wave analysis (4), Turing theory (5).
教科書/參考書
N. F. Britton : Essential Mathematical Biology L. Edelstein-Keshet : Mathematical Models in Biology James Murray : Mathematical Biology I,II
評分標準
midterm exam or assessment 50% final exam 50%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
2
108-1_大型矩陣計算
應用數學系
教學目標
矩陣計算是科學計算的基石，主要分為求解線性系統以及特徵值問題的數值方法。在課程中，將訓練學生矩陣分析以及計算的能力。
授課形式
理論講述與討論-80.00%;個案分析或作品賞析-0.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. symmetric eigenvalue problem 2. unsymmetric eigenvalue problem
教科書/參考書
1. Lecture Notes of Matrix Computations, Wen-Wei Lin 2. Matrix computations /Gene H. Golub, Charles F. Van Loan.
評分標準
1. 期中考或期中報告 2. 期末考或期末報告 3. 平常成績
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
12
矩陣計算是科學計算的基石，主要分為求解線性系統以及特徵值問題的數值方法。在課程中，將訓練學生矩陣分析以及計算的能力。
授課形式
理論講述與討論-80.00%;個案分析或作品賞析-0.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. symmetric eigenvalue problem 2. unsymmetric eigenvalue problem
教科書/參考書
1. Lecture Notes of Matrix Computations, Wen-Wei Lin 2. Matrix computations /Gene H. Golub, Charles F. Van Loan.
評分標準
1. 期中考或期中報告 2. 期末考或期末報告 3. 平常成績
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
12
108-1_組合學專題（一）
應用數學系
教學目標
This is a research-oriented course. We will go through various research topics such as two-sided group testing, fault tolerant search algorithms, compressed sensing, et al. Some papers or course materials will be assigned according to students' interest. Students enrolled in this course require prior knowledge of elementary combinatorics.
授課形式
理論講述與討論-30.00%;個案分析或作品賞析-0.00%;專題實作與報告-70.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
as in the introduction.
教科書/參考書
I will give students some papers.
評分標準
In Class Report and Discussion: 80 %
Participation: 20 %
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
2
This is a research-oriented course. We will go through various research topics such as two-sided group testing, fault tolerant search algorithms, compressed sensing, et al. Some papers or course materials will be assigned according to students' interest. Students enrolled in this course require prior knowledge of elementary combinatorics.
授課形式
理論講述與討論-30.00%;個案分析或作品賞析-0.00%;專題實作與報告-70.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
as in the introduction.
教科書/參考書
I will give students some papers.
評分標準
In Class Report and Discussion: 80 %
Participation: 20 %
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
2
108-1_偏微分方程數值方法(一)
應用數學系
教學目標
This subject will introduce numerical methods for three basic types of partial differential equations which relate to many mathematical models arising from real problems. My expectation is to help you to develop the skill of solving practical ordinary and partial differential equations numerically and efficiently.
授課形式
理論講述與討論-50.00%;個案分析或作品賞析-0.00%;專題實作與報告-0.00%;田野調查-0.00%;實驗-0.00%;其他:in-class discussion and assignments-50.00%
課程內容與進度
Eighteen weeks in this semester: Two to three weeks a topic. Systematical procedures for each topic are shown as follows: 1. Terminology explanation 2. Background and derivation of mathematical models 3. Numerical methods (and stability analysis if possible) 4. Implementation and demo results
教科書/參考書
1. Randall J. LeVeque, Finite Difference Methods for Differential Equations 2. J. D. Faires and R. Burden, Numerical Methods, 4th edition. 3. J. David Logan, Applied Mathematics, 3rd Edition. 4. Steven C. Chapra & Raymond P. Canale, Numerical Methods for Engineers, 6th Edition.
評分標準
Grading: in-class discussion (40%), assignments (40%), and final report (20%)
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
3
This subject will introduce numerical methods for three basic types of partial differential equations which relate to many mathematical models arising from real problems. My expectation is to help you to develop the skill of solving practical ordinary and partial differential equations numerically and efficiently.
授課形式
理論講述與討論-50.00%;個案分析或作品賞析-0.00%;專題實作與報告-0.00%;田野調查-0.00%;實驗-0.00%;其他:in-class discussion and assignments-50.00%
課程內容與進度
Eighteen weeks in this semester: Two to three weeks a topic. Systematical procedures for each topic are shown as follows: 1. Terminology explanation 2. Background and derivation of mathematical models 3. Numerical methods (and stability analysis if possible) 4. Implementation and demo results
教科書/參考書
1. Randall J. LeVeque, Finite Difference Methods for Differential Equations 2. J. D. Faires and R. Burden, Numerical Methods, 4th edition. 3. J. David Logan, Applied Mathematics, 3rd Edition. 4. Steven C. Chapra & Raymond P. Canale, Numerical Methods for Engineers, 6th Edition.
評分標準
Grading: in-class discussion (40%), assignments (40%), and final report (20%)
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
3
108-1_數據科學專題
應用數學系
教學目標
透過研讀應用數據科學與因果關係解決實際問題的相關論文，讓學生了解數據科學與因果關係在實務上的應用，並針對資料的特徵與分析結果以 R 軟體進行視覺化的互動式呈現。
授課形式
理論講述與討論-0.00%;個案分析或作品賞析-50.00%;專題實作與報告-50.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. 研讀、歸納並整理相關文獻
2. 對資料進行視覺化呈現
3. 建立因果關係
4. 分析結果整理與報告
教科書/參考書
無
評分標準
書面報告: 60%; 口頭報告: 40%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
5
透過研讀應用數據科學與因果關係解決實際問題的相關論文，讓學生了解數據科學與因果關係在實務上的應用，並針對資料的特徵與分析結果以 R 軟體進行視覺化的互動式呈現。
授課形式
理論講述與討論-0.00%;個案分析或作品賞析-50.00%;專題實作與報告-50.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
1. 研讀、歸納並整理相關文獻
2. 對資料進行視覺化呈現
3. 建立因果關係
4. 分析結果整理與報告
教科書/參考書
無
評分標準
書面報告: 60%; 口頭報告: 40%
學分數
3
授課時數(周)
3
開課班級
M10841
修課人數
5
108-1_書報討論(一)
應用數學系
教學目標
培養學生對於作研究這件事情的基本概念：包含如何發現問題、如何以數學的方式描述問題、如何用數學工具解決問題，及如何呈現研究成果。
授課形式
理論講述與討論-10.00%;個案分析或作品賞析-70.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
本學期會有１０～１４專題演講（出席率占學期總成績７０％），在學期最後兩週為期未報告。
教科書/參考書
無。
評分標準
出席率：７０％ 期末報告：３0% ＊修本課程學生請務必於開學第一週出席，故請於201９年９月１１日1４:10到理學院4０８教室。
學分數
1
授課時數(周)
2
開課班級
M10841
修課人數
7
培養學生對於作研究這件事情的基本概念：包含如何發現問題、如何以數學的方式描述問題、如何用數學工具解決問題，及如何呈現研究成果。
授課形式
理論講述與討論-10.00%;個案分析或作品賞析-70.00%;專題實作與報告-20.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
本學期會有１０～１４專題演講（出席率占學期總成績７０％），在學期最後兩週為期未報告。
教科書/參考書
無。
評分標準
出席率：７０％ 期末報告：３0% ＊修本課程學生請務必於開學第一週出席，故請於201９年９月１１日1４:10到理學院4０８教室。
學分數
1
授課時數(周)
2
開課班級
M10841
修課人數
7
108-1_專題實作(二)
應用數學系
教學目標
培養學生思考問題、解決問題以及上台報告、撰寫報告之能力。
授課形式
理論講述與討論-10.00%;個案分析或作品賞析-30.00%;專題實作與報告-60.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
採分組方式進行，每組挑選一研究議題，於2019年10月2日進行研究提案報告；期中提案報告後需定期回報研究進度，有問題隨時提出；期末報告暫定於2019年12月25日，報告三天前需繳交口頭報告電子檔。（所有修課同學皆須參與第一週2019年9月11日的修課要求說明。如果當天無法參加，請另行找時間與修課教師說明。）
教科書/參考書
無
評分標準
期中提案報告（10%）＋期末報告與結案報告（90%）
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
8
培養學生思考問題、解決問題以及上台報告、撰寫報告之能力。
授課形式
理論講述與討論-10.00%;個案分析或作品賞析-30.00%;專題實作與報告-60.00%;田野調查-0.00%;實驗-0.00%;其他-0.00%
課程內容與進度
採分組方式進行，每組挑選一研究議題，於2019年10月2日進行研究提案報告；期中提案報告後需定期回報研究進度，有問題隨時提出；期末報告暫定於2019年12月25日，報告三天前需繳交口頭報告電子檔。（所有修課同學皆須參與第一週2019年9月11日的修課要求說明。如果當天無法參加，請另行找時間與修課教師說明。）
教科書/參考書
無
評分標準
期中提案報告（10%）＋期末報告與結案報告（90%）
學分數
3
授課時數(周)
3
開課班級
A10541
修課人數
8