|
課程名稱 |
機率論一
Probability Theory (Ⅰ) |
|
開課學期 |
108-1 |
|
授課對象 |
理學院 應用數學科學研究所 |
|
授課教師 |
黃建豪 |
|
課號 |
MATH7509 |
|
課程識別碼 |
221 U3410 |
|
班次 |
|
|
學分 |
3.0 |
|
全/半年 |
半年 |
|
必/選修 |
必修 |
|
上課時間 |
星期二6,7(13:20~15:10)星期四7(14:20~15:10) |
|
上課地點 |
天數101天數101 |
|
備註 |
總人數上限：70人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081MATH7509_1 |
|
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 |
This is a graduate course in measure-theoretic probability theory. We will begin with the review of basic measure theory suitable for the probability theory. Having reviewed measure theory, we can introduce random variables, random processes, distributions, and independence. We will discuss Laws of Large Numbers, Central Limit Theorems, Conditioning, Martingales, Markov processes, Random walks. |
|
課程目標 |
Investigate some basic topics of random phenomena and learn the essential tools for studying such phenomena. |
|
課程要求 |
This course is aiming at GRADUATE students. Students with disciplines other than math are welcome but be prepared with the following prerequisites.
1. Measure theory. (Royden Real analysis 3rd Ch 1-7)
2. Undergraduate probability theory.
More info on my course page https://sites.google.com/site/chienhaouci08/math_2a/gradp |
|
預期每週課後學習時數 |
|
|
Office Hours |
每週二 12:00~13:00
每週一 12:00~13:00 |
|
指定閱讀 |
Durrett. Probability: Theory and Examples |
|
參考書目 |
1. Probability by Varadhan
2. A Course in Probability Theory, by K.L. Chung, second edition, Academic Press, 1974.
3. Probability and Measure, by P. Billingsley, 3rd edition, Wiley, 1995. |
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
Class participation |
10% |
|
2. |
Homework |
20% |
每周作業or上台演習 |
3. |
Midterm |
30% |
W09 11/05 |
4. |
Final |
40% |
W17 12/31 |
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
9/10,9/12 |
Classes on Tuesday and Thursday are cancelled.
#1 Do the following problems and the first two in HW01 to see if you are ready for this course. Ex. 1.4.4, 1.5.7, 1.6.6, 1.6.9, 1.6.10, 1.6.14
#2 Self-reading: Royden 3rd Sec 8.5 product topology, 9.3 Product of compact spaces; Additional reference: Munkres 2nd 19 product topology, 37 Tychonoff theorem; Dudley Ch2 General topology Sec 2.1, 2.2 |
|
第2週 |
9/17,9/19 |
1.1-3, topology |
|
第3週 |
9/24,9/26 |
pi-lambda theorem, 1.4-7; 2.1 Independence
|
|
第4週 |
10/01,10/03 |
2.2, 2.3 |
|
第5週 |
10/08,10/10 |
2.3-4; Holiday |
|
第6週 |
10/15,10/17 |
2.4-5 |
|
第7週 |
10/22,10/24 |
2.5, |
|
第8週 |
10/29,10/31 |
2.1 Kolmogorov extension theorem, examples |
|
第9週 |
11/05,11/07 |
Midterm: Week 1-8; 3.2 |
|
第10週 |
11/12,11/14 |
Self-study |
|
第11週 |
11/19,11/21 |
3.2 |
|
第13週 |
12/03,12/05 |
4.1 |
|
第17週 |
12/31,1/02 |
Final; 溫書 |
|