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課程名稱 |
機率導論
Introduction to Probability Theory |
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開課學期 |
107-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
張志中 |
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課號 |
MATH2502 |
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課程識別碼 |
201 49740 |
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班次 |
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學分 |
4.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期二6,7(13:20~15:10)星期四6,7(13:20~15:10) |
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上課地點 |
新203新303 |
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備註 |
限本系所學生(含輔系、雙修生)
總人數上限：110人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1072IntrProb |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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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. |
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課程目標 |
待補 |
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課程要求 |
First semester of "introduction to analysis" and basic matrix theory
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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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.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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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 |
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週次 |
日期 |
單元主題 |
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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 |
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第2週 |
2/26,2/28 |
2/26: 1.5 Independence and 1.6 conditional probability
Read the rest of Chapter 1 yourself |
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第3週 |
3/05,3/07 |
3/5: 2.2 Introduction of random maps
3/7: 2.3 classification of random variables |
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第4週 |
3/12,3/14 |
3/12: 2.3
3/14: 2.4 - 2.7 |
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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 |
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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 |
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第7週 |
4/02,4/04 |
No class |
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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
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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 |
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第10週 |
4/23,4/25 |
No class (tempered week) |
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第11週 |
4/30,5/02 |
4/30: 4.5
5/2: Midterm exam. |
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第12週 |
5/07,5/09 |
5/7: properties of characteristic functions
5/9: properties of characteristic functions (more than 5.3) |
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第13週 |
5/14,5/16 |
5/14: moments and the derivatives of characteristic functions, moment problems
5/16: convergence in distribution |
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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 |
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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 |
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第16週 |
6/04,6/06 |
6/4: Central limit theorem
6/6: Central limit theorem |
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第17週 |
6/11,6/13 |
6/11: Central limit theorem and applications
6/13: Recitation
6/18: Final exam |
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