EE 3060-1

Brief

This course discusses the basic mathematical models for physical phenomena which possess random features or for problems which can be solved by randomization methods. The aim of this course is to consolidate students' way of thinking from intuitive reasoning to rigorous reasoning with a logical fr<x>amework. This course requires knowledge on calculus, both single and multiple variables.

Description

Course keywords: probability, conditional sample space, probability, conditional probability, statistical independence, random variables, cumulative distribution functions, conditional distribution, expectation, conditional expectation, laws of large numbers, central limit theorem 一、課程說明 (Course Description) This course discusses the basic mathematical models for physical phenomena which possess random features or for problems which can be solved by randomization methods. The aim of this course is to consolidate students' way of thinking from intuitive reasoning to rigorous reasoning with a logical framework. This course requires knowledge on calculus, both single and multiple variables. It is required for students to read Chapter 1: Combinatorial Analysis of the textbook by S. Ross before class begins. Quiz #1 on combinatorial analysis will be held during the 1st recitation class in 19:00-21:00 on Monday February 13, 2023 in Delta 211. This course adopts a 16-week semester so that it is an intense course. 二、指定用書 (Text Book) S. Ross, A First Course in Probability, 10th edn. Pearson Educational international, 2020. (Agent in Taiwan: Hwa Tai Publishing (華泰文化), Tel: (04)2422-3877 ext. 532, Email: sales8@hwatai.com.tw.) 三、參考書籍(References) References will be mentioned in the lectures when cited. 四、教學方式 (Teaching Method) 1. This is an English–teaching course. In class, you are welcome to raise questions in any language. If you speak a language other than English, Taiwanese or Mandarin, please have someone to translate it to any of the above three languages. 2. We will basically follow the contents of the textbook from the axiomatic foundation of probability in Chapter 2 to the limit theorems in Chapter 8. Additional materials, including supplemental lemmas and theorems, will be provided to facilitate and/or enrich the development of the theory. 3. Doing exercise problems is an essential part of learning any mathematical subject, including this course. Recommended exercises will be assigned every week for you to practice the basic concepts and results learned in the classroom and to prepare the quiz which will be held during the recitation class every Monday 19:00 – 21:00 in Delta 211, except holidays and the week right after a midterm. The 1st set of recommended exercises will be announced on NTHU eeclass course website on February 7th, 2023. Students do not need to turn in any solutions of the recommended exercises. 4. There will be a total of 12 quizzes. Only the 10 highest scored quizzes will be counted to calculate the semester quiz average. You may be absent from at most 2 quizzes so that there will be no make-up quizzes. The 1st quiz will be held during the 1st recitation class in 19:00-21:00 on Monday February 13, 2023 in Delta 211. The coverage of the 1st quiz is Chapter 1 of the textbook on combinatorial analysis, which is required for you to study before class begins. 5. It is essential that students attend lecture class each day and if you have to miss a class, you should make every attempt to make up the work by obtaining notes from other students. However it is almost impossible to learn as much on your own from an activity that was carried out and discussed in class. 6. There will be two online make-up classes to be held on March 4th and April 1st Saturdays. The online course website will be announced then. 7. All exams are closed book exams. You are allowed to bring in one A4 sheet of paper for each midterm exam and two A4 sheets of papers for the final exam, filled with hand-written or typed notes. You may write whatever you wish on both sides of the paper. 8. The final exam is cumulative and will cover everything taught in the whole semester. 五、教學進度 (Syllabus) Students are required to read Chapter 1 of the textbook which give a coverage of combinatorial analysis before class begins. The following topics will be covered in the class lectures: 1. Axioms of probability and properties of probability 2. Conditional probability, Bayes’s formula, and statistical independence 3. Random variables, discrete random variables, and distribution functions 4. Continuous random variables and functions of random variables 5. Jointly distributed random variables and conditional distributions 6. Properties of expectation, conditional expectation, moment generating functions, and jointly normal random variables 7. Laws of large numbers and the central limit theorem 六、成績考核 (Evaluation) There are weekly quizzes (30%), first midterm (20%), second midterm (20%), and one final (30%). Alphabetical grade will be given as your final grade. The time schedule is as follows: (1) Recommended exercises will be announced every Thursday on NTHU eeclass course website, which are for students to prepare the quiz to be held during the recitation class every Monday 19:00 – 21:00 in Delta 211, except holidays and the week right after a midterm. The 1st set of recommended exercises will be announced on February 7th, 2023 before class begins. Students do not need to turn in any solutions of the recommended exercises. (2) Midterm I – 12:40 – 15:10, Thursday March 16, 2023. Coverage: Chapters 2-4 of the textbook. (3) Midterm II –12:40 – 15:10, Thursday April 20, 2023. Coverage: Chapters 5-6 of the textbook. (4) Final – 12:40 – 15:10, Thursday June 1, 2023. Coverage: Chapters 2-8 of the textbook. 六、可連結之網頁位址 Course website at http://eeclass.nthu.edu.tw

Prerequisites

Timetable

Scores

Average GPA 3.35

Std. Deviation 0.91

PTT Reviews

Remarks

週一19:00-21:00為演習課。16週課程,每週上課150分鐘,其餘時間由教授彈性運用

Restrictions

電機系大學部2年級3年級4年級,電資院學士班大學部2年級3年級4年級優先，第3次選課起開放全校修習

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization