【課程說明】
Course Description
| Basically we shall cover the following topics. | |
| (1) | Cauchy-Riemann equation，Cauchy theorem for holomorphic functions, |
| (2) | Cauchy integral formula, |
| (3) | Maximum modulus Principle, |
| (4) | Laurent series,meromorphic functions, |
| (5) | Calculus of residues, |
| (6) | Harmonic functions of two real variables, |
| (7) | Conformal mappings, Riemann mapping theorem. |
【指定用書】
Text Books
| ♠ |
References
【教學方式】
Teaching Method
| ♠ | Lecture and assignments. |
Evaluation
| ♠ | It will be announced in the first class. |
認知神經科學（Cognitive Neuroscience）是一門新興的研究領域，主要是探索腦與心智的關連 性。從感覺與知覺、學習與記憶、注意力與情緒 、同理與厭惡、決策與執行、乃至意識的產生，都是認知神經科學的範疇。Cognitive Neuroscience is an emerging academic field concerned with the relation of Brain and Mind. Topics such as: sensation and perception, learning and memory, attention and emotion, empathy and disguise, decision-making and execution, and consciousness, all belong to the field of Cognitive Neuroscience.
【課程簡述】
Brief course description
認知神經科學（Cognitive Neuroscience）是一門新興的研究領域，主要是探索腦與心智（Brain and Mind）的關連性。從感覺與知覺（Sensation and Perception）、學習與記憶（Learning and Memory）、注意力與情緒 （Attention and Emotion）、同理與厭惡（Empathy and Disguise）、決策與執行（Decision-making and Execution）、乃至意識（Consciousness）的產生，都是認知神經科學的範疇。瞭解這些認知行為背後的神經科學不僅是本世紀最重要的一項科學探索，也與每個人的有密切的關係。例如：神經經濟學（Neuroeconomics）與消費者行為 及市場調查有關，退化性神經疾病（Neurodegenerative disorders）與老年失智症有關。
在本課程中，我們將依序探討認知神經科學中的主要課題，重點在於介紹最新的研究發展，並討論這些科學發現對個人及社會的衝擊。本課程將以 科學人雜誌過去所發表有關認知神經科學的文章為主，並以影片及期刊論文為輔，使無心理學或生物學背景的學生亦可學習此一課程。
Cognitive Neuroscience is an emerging academic field concerned with the relation of Brain and Mind. Topics such as: sensation and perception, learning and memory, attention and emotion, empathy and disguise, decision-making and execution, and consciousness, all belong to the field of Cognitive Neuroscience.Understanding the neuroscience behind these cognitive behaviors not only marks one of the most significant science discovery in this century but also deeply connects to individual’s daily life. For example, Neuroeconomics involves in consumer behavior and market research; Neurodegenerative disorders is related to Alzheimer's disease.
In this course we’ll introduce some main topics of Neuroscience in order, focusing on the latest research and development, and we’ll discuss the influence on society and individuals from these discoveries. Most of the learning materials come from articles about Cognitive Neuroscience on Scientific American of these years, supplied with films and periodical literature as auxiliaries, so students without psychology or biology background can also participate in this course.
【教學進度】
Course schedule
| Week | Topic Note |
| Week 1 | ♦ 與心智簡介 簡介各週內容，暴力行為在腦中的運作模式 |
| Introduction to Brain and Mind – To introduce the whole course and the operation modes of violence in brains | |
| Week 2 | ♦感覺&知覺 I 視覺的錯視、視覺訊息的處理 |
| Sensation and Perception I – Optical illusion & the Operation of Visual Signals | |
| Week 3 | ♦感覺&知覺 II 奧妙的色彩如何影響大腦認知 |
| Sensation and Perception II – How do the colors affect our perception? | |
| Week 4 | ♦感覺&知覺 III 原來我們聽到的可能不一樣、基因影響嗅覺辨識! |
| Sensation and Perception III – What we hear may be different & Genes determine our olfactory sensation | |
| Week 5 | ♦學習&記憶 感官、短期、長期，原來有不同的記憶形式 |
| Learning and Memory – Different memory modes | |
| Week 6 | ♦睡眠&夢 我可以都不睡覺嗎? 我為何需要睡覺? |
| Sleep and Dreams – Why we need to sleep? | |
| Week 7 | ♦報償&成癮 為何毒品這麼難戒除，成癮對腦造成的傷害 |
| Reward and Addiction – Why is it so hard to quit drugs & how do drugs harm the brains | |
| Week 8 | ♦溝通&語言 動物們如何溝通，為何電子書無法取代紙本? |
| Communication and Language – The ways animals | |
| Week 9 | ♠♠♠♠♠♠♠ 全 校 運 動 會 停 課 YA! ♠♠♠♠♠♠♠♠♠ |
| Taking a day off – NTHU sports day | |
| Week 10 | ♦理性&感性 動物也會難過，不同情緒由不同腦區控制 |
| Rationality and Sensibility – Emotions are controlled by different parts of the brain | |
| Week 11 | ♦選擇&決策 如何做出選擇，究竟你在選什麼? |
| Choice and Decision-making – How to make choices? | |
| Week 12 | ♦同理心 網路和面對面的霸凌有何不同，你懂我的痛嗎? |
| Empathy – The difference between cyberbullying and face-to-face bullying & Can others understand my pains? | |
| Week 13 | ♦智力&創造力 天才從何而來? 創意如何產生? |
| Intelligence and Creativity – Where does genius come from? & How does creativity be formed? | |
| Week 14 | ♦發育&可塑性 嬰兒天生會做哪些事?學前教育可以如何進行 |
| Development and Plasticity – What can infants do by nature? & Preschool education | |
| Week 15 | ♦老化&疾病 如何優雅的老化，能阻止大腦變老嗎? |
| Aging and Disease – How can we age elegantly?& Is it possible to prevent the brains from aging? | |
| Week 16 | ♦腦科學&科技&社會 男、女頭腦大不同? |
| Brain Science, Technology and Society –The difference between female brains and male brains | |
| Week 17 | ♦意識&自由意志 植物人有意識嗎? |
| Consciousness and Free Will – Do vegetative people contain their free will? | |
| Week 18 | ♦期末考週 繳交期末報告 |
| The week of final exam - Hand in the final project | |
【溫馨小提醒】
| ♠ | 本課程同時採用實體上課與同步遠距教學 ♠ |
| This course is lectured in the classroom as well as through distance learning! |
| ♠ | Grading policy: |
| 課堂參與：40% (每堂課結束後需將課程心得與自我經驗分享上傳至社群軟體 fb、ig) Class attendance：40% (Sharing your experience and thoughts of the course on your fb or ig) | |
| 課堂小考：30% (每個段落皆有課堂小考，以 slido 進行) Quizzes：30% (There are quizzes for each parts, performed with slido) | |
| 期末報告：30% (一份 3 頁 A4 的課程主題延伸報告) Final project : 30% | |
| 課前後總結問卷（加分）：5% Questionnaire ( bonus ) : 5% | |
| ♠ | 課程要求 |
| 1.攜帶行動載具（手機、平版、筆電）來上課 Bring your mobile devices (smartphone, tablet, or laptop) to class | |
| 2.下載 slido Download slido app | |
| 3.擁有任一社群軟體 Having a social media account |
腦科學為21世紀最重要的研究領域，而神經科學即是腦科學的基礎。本課程屬於「神經科學微學程」四個核心課程（細胞神經科學、系統神經科學、認知神經科學及計算神經科學）的其中之一。
【課程概述】
Course Description
腦科學為21世紀最重要的研究領域，而神經科學即是腦科學的基礎。本課程屬於「神經科學微學程」四個核心課程（細胞神經科學、系統神經科學、認知神經科學及計算神經科學）的其中之一。在本課程中，我們將介紹神經細胞的基本構造與功能、神經訊號的產生與傳遞、神經細胞間的溝通與塑性、神經細胞的發育與改變、神經系統的退化與再生。藉由重要觀念的解說與實驗數據的分析，本課程期望所有修習的學生都能對神經細胞的特性有充分的瞭解，做為探索腦功能的重要基礎。
| ♠ | 具備生物學基本概念即可！ |
| Basic biological concepts! |
| ♠ | Eric R. Kandel, James H. Schwartz, Thomas M. Jessell, Steven A. |
| Siegelbaum and A. J. Hudspeth, Principles of Neural Science, 5th Ed., 2012 | |
| ♠ | 特別感謝書商麥格羅﹒希爾(McGraw-Hill) |
| 提供書籍圖片授權以俾進行影片製作，以下為此書籍之連結資訊！ |
【授課大綱】
| ♠ Week 1 | Fundamental properties of neurons |
| ♠ Week 2. | Transmission of neural signals |
| ♠ Week 3 | Synaptic transmission: mechanisms |
| ♠ Week 4. | Synaptic transmission: neurotransmitters |
| ♠ Week 5. | Synaptic transmission: plasticity |
| ♠ Week 6 | Development of neurons |
| ♠ Week 7 | Development of synapses |
| ♠ Week 8 | Degeneration and regeneration of neurons |
腦科學為21世紀最重要的研究領域，而神經科學即是腦科學的基礎。在本課程中，我們將介紹神經網絡的結構與功能，這是介於細胞神經科學與認知神經科學的重要基礎課程。
【 課程概述 】
Course Description
腦科學為21世紀最重要的研究領域，而神經科學即是腦科學的基礎。在本課程中，我們將介紹神經網絡的結構與功能，這是介於細胞神經科學與認知神經科學的重要基礎課程。本課程內容特別專注於探討感覺神經系統與運動神經系統。藉由重要觀念的解說與實驗數據的分析，本課程期望所有修習的學生都能瞭解神經系統運作方式的基本法則。
Brain science is the most important research area in 21st century and cellular neuroscience is the basis of brain science. In this course, we are going to introduce the structures and functions of neural network which is a basic but important course in between cellular neuroscience and cognitive neuroscience. This course will be specifically focusing on the sensory nervous system and motor nervous system. With the explanation of important concepts and the analysis of experimental data, we expect the students to understand the basic rules of how the nervous system operates.
| ♠ | 具備生物學基本概念即可！ |
| Basic biological concepts! |
| ♠ | Eric R. Kandel, James H. Schwartz, Thomas M. Jessell, Steven A. |
| Siegelbaum and A. J. Hudspeth, Principles of Neural Science, 5th Ed., 2012 | |
| ♠ | 特別感謝書商麥格羅﹒希爾(McGraw-Hill) |
| 提供書籍圖片授權以俾進行影片製作，以下為此書籍之連結資訊！ |
| ♠ Week 1 | Organization of the nervous systems |
| ♠ Week 2. | Sensation and perception: touch and pain |
| ♠ Week 3 | Sensation and perception: vision I |
| ♠ Week 4. | Sensation and perception: vision II |
| ♠ Week 5. | Sensation and perception: audition, olfaction, and gustation |
| ♠ Week 6 | Movement and action: peripheral mechanisms |
| ♠ Week 7 | Movement and action: central control |
| ♠ Week 8 | Movement and action: coordination and planning |
跟著金導遊探索「感覺與知覺」，將以感覺系統搭配淺顯易懂的文字剖析您的感覺與知覺！這個問題，就讓清大的焦傳金教授回答你！想要抓住「感覺」，更要了解「知覺」的關係！
Brief course description
「感覺與知覺」是一門神經科學的基礎課程，目的是將感覺系統的運作方式用淺顯易懂的方式介紹給大家。在這六周的課程中，每週將會有12的單元，每個單元約5分鐘影片，藉由回答許多與生活相關的有趣問題，各位將能學習到最新的腦科學新知，讓我們在與這個世界進行感官互動時，可以增添一份知識性。
【課程目標】
Course objectives
本課程中將以神經科學領域中的感官系統為基礎，循序漸進介紹人類的感覺與知覺，包括視覺、聽覺、觸覺、嗅覺、味覺等。這些感覺系統是人類接受外界訊息的媒介，除了影響我們的理性與思考，也會觸動我們的情緒與記憶，因此是一般社會大眾會有興趣的科普知識，也很容易引起多數人的關心。本課程的目標是以生動的文字、圖片及影片引發大眾的好奇心，並以淺顯方式將艱澀的神經科學知識轉化成一般人均可理解的切身經驗，在體驗與感受的過程中輕鬆學習科普常識，並將這些知識應用於日常生活中。 In this course, based on the sensory system in the field of neuroscience, we will gradually introduce human sensations and perceptions including the sense of sight, hearing, touch, smell and taste. These sensory systems are the medium of human receiving external information which not only influence our rational and thinking, but also our emotions and memories. Therefore, it is a popular science knowledge that the general public will be interested in and can easily arouse most people’s concerns. The course objective is to trigger public curiosity with vivid text, pictures and videos. And transform difficult neuroscience knowledge into personal experience in a simple way that can be understood by everyone. Let us learn the popular and common science knowledge through experiences and feelings and apply this knowledge to daily life.
schedule
Brief course description
Applied Mathematics is a two-semester course, emphasizing the basic mathematical training encountered in science and engineering. Facing the modern frontiers with brand-new challenges, the course contains the following key modules:
| (1) | Complex Analysis |
| (2) | Partial Derivative |
| (3) | Linear Algebra |
| (4) | Quantum Operators |
| (5) | Fourier Transform |
| (6) | Vector calculus |
Syllabus
| (1) | Preliminary |
| (2) | Partial differentiation |
| (3) | Matrices and vector spaces |
| (4) | Vector calculus |
| (5) | Ordinary differential equations |
| (6) | Integral transforms |
| (7) | Operators and special functions |
| (8) | Partial differential equations |
| (9) | Probability and statistics |
| (10) | Numerical methods |
| ♠ | Mathematical Methods for physics and engineering (3rd edition) |
| by Riley, Hobson and Bence |
to dynamical readjustments:
| (1) | Preliminary (4 lectures) – chap 1,2,3,4 |
| (2) | Partial differentiation (2 lectures) – chap 5 |
| (3) | Matrices and vector spaces (8 lectures) – chap 7,8,9 |
| (4) | Vector calculus (6 lectures) – chap 10,11 |
| (5) | ntegral transforms (4 lectures) – chap 12,13 |
| (6) | Ordinary differential equations (6 lectures) |
| – chap 14,15,16 | |
| 1. | Differentiable Mappings |
| 2. | The Inverse and Implicit Function Theorems and Related Topics |
| 3. | Integration |
| 4. | Fubini's Theorem and The Change of Variables Formula |
| 5. | Fourier Analysis |
| ＊ | |
| second edition. |
| ＊ | D. Widder, Advanced Calculus. |
| ＊ | T. Apostal, Advanced Calculus. |
【教學方式/教學進度】
This is an introductory course on the theory of curves and surfaces in the three dimensional Euclidean space. After developing the theory of curves, we will study the geometry of a surface from both intrinsic and extrinsic point of view. Topics include first and second fundamental forms, various notions of curvature, and the famous Gauss-Bonnet theorem.
| * | Differential geometry of curves and surfaces, by Manfredo P. Do |
| Carmo. Prentice Hall. |
| * | Elementary Differential Geometry, 2nd edition, A. Pressley, Springer, 2010. |
| * | Elementary Differential Geometry, 2nd Edition, by Barrett O'Nell. |
www.math.nthu.edu.tw/~cjsung/course/ug2018s.html
人類對於周遭事物，如何隨時間與環境而變化，都充滿好奇心。我們要如何用物理學推敲出萬物的變化，或基於系統性的觀察而提出新的想法....
【課程說明 / Description of the course】
人類對於周遭事物，如何隨時間與環境而變化，都充滿好奇心。我們要如何用物理學推敲出萬物的變化，或基於系統性的觀察而提出新的想法，這就是普通物理(ㄧ)的課程目標。那要如何養成研究問題的邏輯與方法呢?本課程以牛頓提出的力學為例，除了學習力學定律之外，也鼓勵同學探討牛頓提出這些理論的原因，同時思考章節之間的關聯性，例如在牛頓的向量力學架構下，已經可以解釋物體的運動，為何還需學習新的能量概念等等。
課程內容涵蓋基礎牛頓力學、功與能量概念，在熟悉單粒子運動後，將建構簡單的多粒子系統（剛體）所遵守的物理規則（轉動運動），基於以上的物理知識，詳細探討日常生活中常見的物理現象，如重力、固體與流體、振盪、波動等。同時也將探討愛因斯坦為何會提出不同於牛頓力學的特殊相對論，以及在特殊相對論中架構下，為何在不同慣性座標系的觀察者們，對時間、空間的認知會有所不同。
【課程教材 / Course Material】
| * | 物理學系吳國安教授教學投影片 |
| Lecture notes (PPT) from Dr. Wu,Kuo-An (Dept. of Physics) |
| 1. | The Feynman Lectures on Physics |
| 2. | "Physics", Volume1, by R.Resnick, D.Halliday, and K. S. Krane. |
| 3. | "University Physics", 2nd revised edition by H. Benson. |
| * | 對生活中的物理現象有好奇心者，敬邀您一同探索日常生活中物理的奧秘！ |
| This course is for people who have curiosity for anything or everything! |
| * | 課程共 13章節，每一章節包含數個單元。 |
| This course consists of 13 chapters; each chapter includes several segments.
| |
| * | 每單元為10~15分鐘的教學影片，針對單一概念講解，透過例題熟悉單元重點。 |
| Each segment contains a 10-to-15-minitue video and focuses on a specific physics topic.
| |
| * | 全程由授課教師精製之投影片，最佳化課程單元影片，提供融會貫通之學習效果。 |
| This course offers PPTs that are available for downloading.
| |
| * | 著重物理定律背後的意義，及思索問題的邏輯性與一致性，在課堂外，希冀能思辨不同問題 |
| 之間的共通性，舉一反三，解決問題。 | |
| This course emphasizes the reasoning of physical laws and nurturing the logical reasoning | |
| ability, so that students can apply this training to solve problems outside the classroom. |
【教學進度 / Schedule】
What do you expect to learn in this course
| 1. | 動態系統與向量力學 Dynamical Systems & Vector Mechanics |
| —從牛頓力學談起（向量力學）Starting from Newtonian Mechanics
| |
| 2. | 功與能Work & Energy |
| — 純量的角度來思考牛頓定律
| |
| 3. | 位能與力學能守恆 Potential Energy & Conservation of Mechanical Energy |
| —純量力學好簡單 Nothing is Simpler Than Scalar Mechanics
| |
| 4. | 線性動量 Linear Momentum |
| —守恆量與物理問題的簡化 Conservation Laws and How do They Simplify Physical Problems | |
| 5. | 多粒子系統 Many-particle System |
| — 邁向真實世界的第一步 The First Step Towards The Real World | |
| 6. | 剛體轉動 Rigid-body Rotation |
| — 如何設計容易轉動的輪子 A possible new design for Wheels | |
| 7. | 角動量 Angular Momentum |
| — 如何設計容易轉動的輪子 A Possible New Design for Wheels | |
| 8. | 重力與行星運動 Gravity & Planetary Motion |
| — 不會砸落在牛頓頭上的月球（但是蘋果會） The Moon Doesn*t Fall on Newton*s Head, but Apples Do. | |
| 9. | 固體與流體 Solid and Fluid |
| — 巨觀的物理世界 The Macro-scopic Physical Word | |
| 10. | 振盪 Oscillation |
| — 彈簧振盪＊單擺運動＊金融市場有關係嗎？ Is There a Common Feature for Spring Oscillator, Pendulum and Financial Marker? | |
| 11. | 波動(力學波) Waves (Mechanical Waves) |
| —力學波的普世性 The Universality of Mechanical Waves. | |
| 12. | 聲波 Sound Waves |
| — Sound waves for dummies | |
| 13. | 特殊相對論 Special Relativity |
| — 站在月台上的你似乎瘦了？！
|
本課程著重訓練思考邏輯及解決問題的思維方式；培養聽說讀寫的能力，以奠定自學的能力。