課程名稱 |
或然率理論與模型 Probability Theory and Modeling |
開課學期 |
100-1 |
授課對象 |
工學院 水利工程組 |
授課教師 |
蔡宛珊 |
課號 |
CIE7165 |
課程識別碼 |
521EM7540 |
班次 |
|
學分 |
3 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期四5,6,7(12:20~15:10) |
上課地點 |
土研402 |
備註 |
本課程以英語授課。 總人數上限:30人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1001stochastic |
課程簡介影片 |
|
核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
課程概述 |
WHILE A SOPHISTICATED LEVEL OF QUANTITATIVE ABILITIES OR MATHEMATICAL MODELING IS NEEDED IN BOTH ACADEMIA AND PRACTICE, IT IS OFTEN PROMOTED THAT SUCH COURSES ARE ACADEMICALLY DIFFICULT SUBJECTS, RESERVED FOR THE TRULY GIFTED. WITH THE ADVANCEMENT OF TECHNOLOGY, STUDENTS SEEM TO RESORT TO COMPUTER SOFTWARE AS A PANACEA WITHOUT TRULY UNDERSTANDING THE BASICS OF THE PROBLEM. STUDENTS OFTENTIMES IGNORE THE FACT THAT MATHEMATICAL MODELING SHOULD NOT JUST BE PUNCHING NUMBERS INTO A
MODEL AND WAITING FOR WHAT COMES OUT FROM IT. LACK OF AN APPROPRIATE QUANTITATIVE SKILL COULD RESULT IN POOR DATA INTERPRETATION, INACCURATE MODELING AND IMPROPER ENGINEERING DESIGN. THE MAJOR OBJECTIVES OF THIS COURSE ARE TO STIMULATE STUDENTS’ LEARNING INTEREST IN PROBABILITY MODELING AND IMPROVE THEIR QUANTITATIVE SKILLS.
|
課程目標 |
THE OVERALL OBJECTIVE OF THIS COURSE IS TO FAMILIARIZE STUDENTS WITH FUNDAMENTAL AND EXTENDED CONCEPTS OF PROBABILITY THEORIES. STUDENTS ARE ANTICIPATED TO LEARN RELEVANT TOPICS SUCH A MARKOV CHAINS, POISSON PROCESSES, CONTINUOUS-TIME MARKOV PROCESSES, BROWNIAN MOTION AND SIMULATION TECHNIQUES. THIS COURSE WILL EQUIP STUDENTS WITH FUNDAMENTAL KNOWLEDGE AND QUANTITATIVE APPROACHES ESSENTIAL FOR PROBABILITY MODELING. |
課程要求 |
前置課程
STATISTICS
ENGINEERING MATHEMATICS I AND II OR EQUIVALENT |
預期每週課後學習時數 |
|
Office Hours |
|
指定閱讀 |
|
參考書目 |
INTRODUCTION TO PROBABILITY MODELS” BY ROSS (9TH EDITION), ACADEMIC PRESS (2006)
"INTRODUCTION TO STOCHASTIC PROCESSES" BY HOEL ET AL. HOUGHTON MIFFLIN. (1972) |
評量方式 (僅供參考) |
|
週次 |
日期 |
單元主題 |
Week 1 |
9/15 |
Introduction |
Week 2 |
9/22 |
Uncertainty Analysis and Risk Assessment |
Week 3 |
9/29 |
Introduction to Point Estimate Methods |
Week 4 |
10/06 |
Parameter estimation |
Week 5 |
10/13 |
Introduction to Markov Chains |
Week 6 |
10/20 |
Discrete-time Markov Chains (1) |
Week 7 |
10/27 |
Discrete-time Markov Chains (2) |
Week 9 |
11/10 |
Continueous-time Markoc Chains (1) |
Week 10 |
11/17 |
Revisit to statistical distributions
&
Continueous-time Markov Chains (2) |
Week 11 |
11/24 |
The Exponenetial distribution and the Poisson process (1) |
Week 12 |
12/01 |
The Exponenetial distribution and the Poisson process (2) |
Week 13 |
12/08 |
Gambler's ruin problems |
Week 14 |
12/15 |
Birth and death processes (more examples) |
Week 15 |
12/22 |
A revised point estimate method |
Week 16 |
12/29 |
Dealing with non-detect data
& Introduction to R |
|