課程資訊
課程名稱
 機率導論
Introduction to Probability Theory 
開課學期
 106-2 
授課對象
 理學院  數學系  
授課教師
 黃建豪 
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/1062MATH2502_ 
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課程概述

Contents : Axioms of probability, conditional probability, independence, random variables, jointly distributed random variables, expectation, moment generating functions, limit theorems, Poisson processes, Markov chains. 

課程目標
 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, economists, industrialists, social scientists, 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 many examples. 
課程要求
 需要一點數學分析基礎. Be familiar with mathematical analysis.
外系要加簽先看; For non-math major students,
https://en.wikipedia.org/wiki/Probability_axioms
then email the instructor

Homework set 8-10題, 小考從裡面出2-4題;
期考出8-9題包含上課內容, exercise, HW 
預期每週課後學習時數
  
Office Hours
 另約時間 備註： WF 3:30-4:30 
指定閱讀
 教科書: David Stirzaker : Probability and Random Variables A Beginner’s Guide 1999

For Poisson processes, lecture note.

For Markov chains,
Ch 11 in Grinstead and Snell’s Introduction to Probability 2006 2nd (Free probability ebook)
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf 
參考書目
 Richard Durrett : The Essentials of Probability 1994
Sheldon Ross : A First Course in Probability 2012 9th edition
Grinstead and Snell : Introduction to Probability 2006 2nd
H. Pishro-Nik : Introduction to Probability, Statistics and random processes (Free online textbook) https://www.probabilitycourse.com/ 
評量方式
(僅供參考)
  
No.
項目
百分比
說明
1. 
 Quizzes 
15% 
 6 quizzes, drop the lowest one. 
2. 
 Midterm 
35% 
  
3. 
 Final 
40% 
  
4. 
 Homeworks 
5% 
  
5. 
 class participation 
5% 
  
 
課程進度
週次
日期
單元主題
第1週
 2/27,3/01  Introduction; Ch 2 Rules of probability 2.1-2.5
2.5-7 
第2週
 3/06,3/08  Ch 2 Rules of probability 2.7-9;
Recitation; 2.9-13 
第3週
 3/13,3/15  Ch 3 Counting and gambling 3.1-10
Recitation HW1 due ;
HW1 ch2 #5,10,14,15,19,20,26,31
Grinstead and Snell 4.1 #1-5a, 55,56,58,60 
第4週
 3/20,3/22  Ch 4 Distributions 4.1-8;
Recitation Quiz 1(HW1),
HW 2 due
ch3 ex 9.1 problem #4,7,14,15,16,19,20, 3-state; 
第5週
 3/27,3/29  Ch 5 Random variables 5.1-6
Recitation Quiz 2 (HW 2);  
第6週
 4/03,4/05  Holidays 
第7週
 4/10,4/12  Ch 5 Random variables inequalities, 5.8-9
Recitation HW 3 due ch4 ex 9.1, Poisson to normal, 11.1, 11.2, 12.1
#9,10,11,12,25 
第8週
 4/17,4/19  Ch 6 Jointly 6.2-3; Polya urn model, random permutation, convergence in distributions
Recitation Quiz 3
HW 4 due ch5 #4,6,10,11,15,16,20a,23b,27,28,31 
第9週
 4/24,4/26  6.4 6.7 Review
Midterm (Ch 2,3,4,5,6.2, Applications) 
第10週
 5/01,5/03  自主學習周; Ch6 6.5-8 
第11週
 5/08,5/10  Ch 6 Jointly 6.9-10; 6.11
Recitation 檢討期中 
第12週
 5/15,5/17  6.12-13,Law of large numbers, Borel-Cantelli lemma;
Recitation HW5 due Ch6 ex 3.1, 4.3 # 1,3,10,12,15,19,21,22 
第13週
 5/22,5/24  Momemt generating functions; Central limit theorems
Recitation Quiz 4(HW 5); HW6 due Ch 6 ex12.1,13.1bc #4,28,31,32,42 +SLLN*3 
第14週
 5/29,5/31  Branching processes, 11.1 Markov Chains ;
Recitation Quiz 5(HW 6) 
第15週
 6/05,6/07  no class on 6/5;
11.2 Absorbing MC 
第16週
 6/12,6/14  11.3 Regular MC,Poisson processes;
Recitation Quiz 6(HW 7) #4,8,9,12,15,20, notes*4 
第17週
 6/19,6/21  Review ;
6/21 Final (Ch 6, SLLN, Ch 7, Markov Chains, Poisson processes)