高等機率論(博)

The aim of this course is to provide the students with a fairly thorough treatment of the main body of basic and classical probability theory, preceded by an introduction to the mathematics which is necessary for a solid treatment of the material. This means that we begin with basics from measure theory after which we turn to the Borel-Cantelli lemmas, inequalities, transforms, and the two classical limit theorems: the law of large numbers and the central limit theorem. A final chapter on martingales is one of the most efficient, important, and useful tools in probability theory.

None.

(1) Please only download rather than print out the pdf files of the textbook and the reference from the website of our university library. (2) By the e-mail "20220514陽明交大防疫通報 NYCU Epidemic Prevention Announcement" from our university on May 14, remote learning for this course will be from May 18 to the end of this semester. Please study the uploaded mp4 files for this course by yourself from May 18 to the end of this semester. If you have any questions about this course, please send me an e-mail, or just come to my office during office hour.

作業部份: None 考試部份: It is required for every student to present a published paper by June 17, 2022 (i.e., Friday of the 18th week in this semester). The paper should be chosen from "References" of the textbook. The presentation time should be about 15 ~ 30 minutes for undergraduates or master students and about 30 ~ 60 minutes for Ph.D. students. Questions and Answers (Q and A) are about 15 minutes for undergraduates or master students and about 30 minutes for Ph.D. students. 評量部份: (1) Attendance at class. (2) Presentation of a published paper from "References" of the textbook.

• Chapter 1 Introductory Measure Theory
• Chapter 2 Random Variables
• Chapter 6 The Law of Large Numbers
• Chapter 7 The Central Limit Theorem
• Chapter 10 Martingales

Textbook: Allan Gut (2013). "Probability: A Graduate Course", Second Ed. Springer Science+Business Media, New York. Reference: Rick Durrett (2019). "Probability: Theory and Examples", Fifth Ed. Cambridge University Press, Cambridge.

地點

A416

時間

Every Thursday from 10:10 a.m. to 12:00 p.m.

聯絡方式

cchen@stat.nctu.edu.tw (03)571-2121 Ext. 31794 or (03)573-1794