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 
<br>course 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 13, 2023 in 
<br>Delta 211. 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 
<br>international, 2020. (Agent in Taiwan: Hwa Tai Publishing (華泰文化), Tel:
<br>(04)2422-3877 ext. 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 mathematical 
<br>subject, including this course. Recommended exercises will be assigned every 
<br>week for you to practice the basic concepts and results learned in the classroom 
<br>and to prepare the quiz which will be held during the recitation class every 
<br>Monday 19:00 – 21:00 in Delta 211, except holidays and the week right after a 
<br>midterm. The 1st set of recommended exercises will be announced on NTHU eeclass 
<br>course website on February 7th, 2023. Students do not need to turn in any 
<br>solutions of the recommended 
<br>exercises. 
<br>4. There will be a total of 12 quizzes. Only the 10 highest scored quizzes will 
<br>be counted to calculate the semester quiz average. You may be absent from at 
<br>most 2 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 13, 2023 
<br>in Delta 211. 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 have 
<br>to miss a class, you should make every attempt to make up the work by obtaining 
<br>notes from other students. However it is almost impossible to learn as much on 
<br>your own from an activity that was carried out and discussed in class.
<br>6. There will be two online make-up classes to be held on March 4th and April 
<br>1st Saturdays. The online course website will be announced then.
<br>7. All exams are closed book exams. You are allowed to bring in one A4 sheet of 
<br>paper for each midterm exam and two A4 sheets of papers for the final exam, 
<br>filled with hand-written or typed notes. You may write whatever you wish on both 
<br>sides of the paper.
<br>8. The final exam is cumulative and will cover everything taught in the 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 211, except holidays and 
<br>the week right after a midterm. The 1st set of recommended exercises will be 
<br>announced on February 7th, 2023 before class begins. Students do not need to 
<br>turn in any solutions of the recommended exercises.
<br>(2) Midterm I – 12:40 – 15:10, Thursday March 16, 2023. 
<br>    Coverage: Chapters 2-4 of the textbook.
<br>(3) Midterm II –12:40 – 15:10, Thursday April 20, 2023.
<br>    Coverage: Chapters 5-6 of the textbook.
<br>(4) Final – 12:40 – 15:10, Thursday June 1, 2023. 
<br>    Coverage: Chapters 2-8 of the textbook.
<br>
<br>六、可連結之網頁位址 
<br>
<br>Course website at http://eeclass.nthu.edu.tw
<br>
<br>