課程資訊
課程名稱
機率導論
Introduction to Probability Theory 
開課學期
107-2 
授課對象
理學院  數學系  
授課教師
張志中 
課號
MATH2502 
課程識別碼
201 49740 
班次
 
學分
4.0 
全/半年
半年 
必/選修
必帶 
上課時間
星期二6,7(13:20~15:10)星期四6,7(13:20~15:10) 
上課地點
新203新303 
備註
限本系所學生(含輔系、雙修生)
總人數上限:110人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1072IntrProb 
課程簡介影片
 
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課程概述

Probability theory, originated in the consideration of games of chance, is the language to study commonly observed random phenomena. It has become a fundamental tool used by nearly all scientists, including engineers, econometricians, industrialists, jurists, medical practitioners, physicists, statisticians, etc. The main objective of this course is to provide students, who possess the prerequisite calculus background, with a solid mathematical treatment of the fundamental concepts and techniques of probability theory. Another goal is to demonstrate the many diverse possible applications of the subject through examples.
Contents
Axioms of probability, conditional probability, independence, random variables, jointly distributed random variables, expectation, moment generating functions, limit theorems, Poisson processes, and Markov chain.

Recitation is on each Tuesday 13:20 - 14:10. 

課程目標
待補 
課程要求
First semester of "introduction to analysis" and basic matrix theory
 
預期每週課後學習時數
 
Office Hours
 
參考書目
Text (tentative):
Basic probability theory by Robert B. Ash

Several books, including "Basic probability theory",
by R. Ash can be downloaded at
https://faculty.math.illinois.edu/~r-ash/

References:

1. Introduction to Probability by Charles Grinstead and Laurie Snell. Visit
the website http://www.dartmouth.edu/~chance for download.
2. Introduction to Probability by D. P. Bertsekas and J. N. Tsitsiklis, 2nd
edition, 2008, Athena Scientific.

 
指定閱讀
待補 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Exam. 1 
30% 
Chapters 1 - 4 (basic probability) of the text (暫定) 
2. 
Exam. 2 
25% 
Chapters 5 and 6 (limit theorems) of the text (暫定) 
3. 
Exam. 3 
25% 
Chapter 7 (Markov chains) of the text (暫定) 
4. 
Homework 
10% 
(暫定) 
5. 
Recitation 
10% 
(暫定) 每周二第6堂為演習課 
 
課程進度
週次
日期
單元主題
第1週
2/19,2/21  2/19: No class on 13:20-14:10. The class starts at 14:20
2/19 and 2/21: 1.3 probability spaces
Read 1.1, 1.2, 1.4, 1.7 and 1.8 yourself 
第2週
2/26,2/28  2/26: 1.5 Independence and 1.6 conditional probability
Read the rest of Chapter 1 yourself 
第3週
3/05,3/07  3/5: 2.2 Introduction of random maps
3/7: 2.3 classification of random variables 
第4週
3/12,3/14  3/12: 2.3
3/14: 2.4 - 2.7 
第5週
3/19,3/21  3/19: 2.7 (independence and joint distribution/density/mass functions), 2.8 (functions of (one or more than one) random variables)
3/21: 2.8 (sum of independent random variables), 3.2, 3.3 
第6週
3/26,3/28  3/26: 3.4 correlation, 3.5, 3.7 Chebyshev's inequality and the weak law of large numbers
3/28: order statistics  
第7週
4/02,4/04  No class 
第8週
4/09,4/11  4/9: Technical preliminaries of conditional probability and expectation
4/11: Fubini theorem and definition of conditional density and probability
 
第9週
4/16,4/18  4/16: definition and properties of conditional probability and expectation
4/18: properties and examples of conditional probability and expectation 
第10週
4/23,4/25  No class (tempered week) 
第11週
4/30,5/02  4/30: 4.5
5/2: Midterm exam. 
第12週
5/07,5/09  5/7: properties of characteristic functions
5/9: properties of characteristic functions (more than 5.3) 
第13週
5/14,5/16  5/14: moments and the derivatives of characteristic functions, moment problems
5/16: convergence in distribution 
第14週
5/21,5/23  5/21: A necessary and sufficient condition for weak convergence
5/23: 6.6 Borel-Cantelli lemma and an application to convergence in probability 
第15週
5/28,5/30  5/28: More properties of convergence in probability, and Borel zero-one law
5/30: Strong law of large numbers 
第16週
6/04,6/06  6/4: Central limit theorem
6/6: Central limit theorem 
第17週
6/11,6/13  6/11: Central limit theorem and applications
6/13: Recitation
6/18: Final exam