一、課程說明 (Course Desc<x>ription) 
<br>This course discusses the basic mathematical models for physical phenomena which 
<br>possess random features or for problems which can be solved by randomization 
<br>methods. The aim of this course is to consolidate students' way of thinking from 
<br>intuitive reasoning to rigorous reasoning with a logical fr<x>amework. This course 
<br>requires knowledge on calculus, both single and multiple variables. It is 
<br>required for students to read Chapter 1: Combinatorial Analysis of the textbook 
<br>by S. Ross before class begins. Quiz #1 on combinatorial analysis will be held 
<br>during the 1st recitation class in 19:00-21:00 on Monday February 19, 2024 in 
<br>Delta 215. This course adopts a 16-week semester so that it is an intense 
<br>course.
<br>
<br>二、指定用書 (Text Book) 
<br>S. Ross, A First Course in Probability, 10th edn. Pearson Educational Limited, 
<br>2020. (Agent in Taiwan: Hwa Tai Publishing (華泰文化), Tel:(04)2422-3877 ext. 
<br>532, Email: sales8@hwatai.com.tw.) 
<br>
<br>三、參考書籍(References)
<br>References will be mentioned in the lectures when cited.
<br>
<br>四、教學方式 (Teaching Method) 
<br>1.	This is an English–teaching course. In class, you are welcome to raise 
<br>questions in any language. If you speak a language other than English, Taiwanese 
<br>or Mandarin, please have someone to translate it to any of the above three 
<br>languages.
<br>2.	We will basically follow the contents of the textbook from the axiomatic 
<br>foundation of probability in Chapter 2 to the limit theorems in Chapter 8. 
<br>Additional materials, including supplemental lemmas and theorems, will be 
<br>provided to facilitate and/or enrich the development of the theory.
<br>3.	Doing exercise problems is an essential part of learning any 
<br>mathematical subject, including this course. Recommended exercises will be 
<br>assigned every week for you to practice the basic concepts and results learned 
<br>in the classroom and to prepare the quiz which will be held during the 
<br>recitation class every Monday 19:00 – 21:00 in Delta 215, except holidays and 
<br>the week right after a midterm. The 1st set of recommended exercises will be 
<br>announced on NTHU eeclass course website on Tuesday February 13, 2024. Students 
<br>do not need to turn in any solutions of the recommended exercises. 
<br>4.	There will be a total of 14 quizzes. Only the 10 highest scored quizzes 
<br>will be counted to calculate the semester quiz average. You may be absent from 
<br>at most 4 quizzes so that there will be no make-up quizzes. The 1st quiz will be 
<br>held during the 1st recitation class in 19:00-21:00 on Monday February 19, 2024 
<br>in Delta 215. The coverage of the 1st quiz is Chapter 1 of the textbook on 
<br>combinatorial analysis, which is required for you to study before class begins.
<br>5.	It is essential that students attend lecture class each day and if you 
<br>have to miss a class, you should make every attempt to make up the work by 
<br>watching the recording uploaded to "CCLu Online Learning" on Youtube. 
<br>6.	There will be two online make-up classes to be held on March 2nd and 
<br>March 30th Saturdays. Please watch the Youtube channel "CCLu Online Learning" 
<br>then.
<br>7.	All exams (quizzes, midterms, and the final) are closed book exams. You 
<br>are allowed to bring in one A4 sheet of paper for each midterm exam and two A4 
<br>sheets of papers for the final exam, filled with hand-written or typed notes. 
<br>You may write whatever you wish on both sides of the paper.
<br>8.	The final exam is cumulative and will cover everything taught in the 
<br>whole
<br>semester.
<br>
<br>五、教學進度 (Syllabus) 
<br>Students are required to read Chapter 1 of the textbook which give a coverage of 
<br>combinatorial analysis before class begins. The following topics will be covered 
<br>in the class lectures:
<br>1. Axioms of probability and properties of probability
<br>2. Conditional probability, Bayes’s formula, and statistical independence
<br>3. Random variables, discrete random variables, and distribution functions
<br>4. Continuous random variables and functions of random variables
<br>5. Jointly distributed random variables and conditional distributions
<br>6. Properties of expectation, conditional expectation, moment generating 
<br>functions, and jointly normal random variables
<br>7. Laws of large numbers and the central limit theorem
<br>
<br>六、成績考核 (Evaluation) 
<br>There are weekly quizzes (30%), first midterm (20%), second midterm (20%), and 
<br>one final (30%). Alphabetical grade will be given as your final grade. The time 
<br>schedule is as follows: 
<br>(1)	Recommended exercises will be announced every Thursday on NTHU eeclass 
<br>course website, which are for students to prepare the quiz to be held during the 
<br>recitation class every Monday 19:00 – 21:00 in Delta 215, except holidays and 
<br>the week right after a midterm. The 1st set of recommended exercises will be 
<br>announced on Tuesday February 13th, 2024 before class begins. Students do not 
<br>need to turn in any solutions of the recommended exercises.
<br>(2)	Midterm I – 12:40 – 15:10, Thursday March 21, 2024. 
<br>    Coverage: Chapters 2-4 of the textbook.
<br>(3) Midterm II –12:40 – 15:10, Thursday April 25, 2024.
<br>    Coverage: Chapters 5-6 of the textbook.
<br>(4) Final –12:40 – 15:10, Thursday June 6, 2024. 
<br>    Coverage: Chapters 2-8 of the textbook.
<br>
<br>七、可連結之網頁位址(Webpage li<x>nks)
<br>
<br>Course website at http://eeclass.nthu.edu.tw
<br>
<br>八、使用生成式AI之倫理聲明(Ethics Statement on Generative Artificial Intelligence) 
<br>
<br>After careful consideration, the instructor of this course deems it 
<br>inappropriate to use generative artificial intelligence in this class. This is 
<br>because the content within generative AI contains numerous errors and may 
<br>adversely affect students' understanding of foundational knowledge. In 
<br>accordance with the published Guidelines for Collaboration, Co-learning, and 
<br>Cultivation of Artificial Intelligence Competencies in University Education, 
<br>this course adopts the following policy : Prohibited use
<br>
<br>Students enrolled in this course should be aware that they may not submit 
<br>assignments, reports, or personal reflections generated using artificial 
<br>intelligence. If such usage is discovered, instructors, the institution, or 
<br>relevant units have the right to reevaluate the assignment or report or withhold 
<br>scores. Students enrolled in this course agree to the above ethics statement if 
<br>registering for the class.
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