3. 강의목표
Probability theory is the branch of mathematics, which concerns random phenomena, and this course aims to introduce students to the fundamentals of probability theory (without measure-theoretic concepts). The course covers essential topics including axioms of probability, random variables and their distributions, conditional probability and independence, fundamental limit theorems (Law of Large Numbers and Central Limit Theorem), and an introduction to Markov chains.
4. 강의선수/수강필수사항
Solid knowledge of Calculus and Multivariable Calculus.
If you took Math 230 (Introduction to Probability and Statistics), that would be helpful.
If you did not take Math 230, then I recommend you to read chapter 2 and chapter 3 of "Probability & Statistics for Engineers & Scientists, 9th ed. by Walpole et. al." in advance.
5. 성적평가
Attendance+Participation 5%, Homework 20%, Midterm 35%, Final 40%.
Homework will be assigned every week. You have to solve all the problems, however, not all the problems will be graded. Your TA will choose certain problems to grade.
If you don't take the mid-term exam or the final exam, you will get an F grade.
More than 6 absences will result in an automatic F grade.
6. 강의교재
| 도서명 |
저자명 |
출판사 |
출판년도 |
ISBN |
|
Introduction to probability
|
Anderson, David F., Timo Seppäläinen, and Benedek Valkó
|
Cambridge University Press
|
2017
|
|
|
Markov Chains
|
J. R. Norris
|
Cambridge University Press
|
1998
|
|
7. 참고문헌 및 자료
- Basic Probability Theory, by Robert Ash. An electronic copy of Ash’s book is available at the author’s website.
- A First Course in Probability (10th edition), Sheldon Ross.
- Elements of stochastic processes by Richard Durrett (this book is a reference for Markov chains. The tone of this book is more concise and delicate than the one written by Dr. Norris's book.).
- Introduction to Stochastic Processes by Gregory F. Lawler (this book is a reference for Markov chains).
8. 강의진도계획
In this course, we will cover
- Axioms of Probability
- Independence and conditional probability
- Discrete and continuous random variables
- Joint distributions
- Properties of expectations (moments, conditional expectations, moment-generating functions)
- Law of large numbers
- Central Limit Theorem
- Conditional distribution
- Discrete-time Markov Chains
- Continuous-time Markov chains and Brownian motions (if time permits)
9. 수업운영
- No make-up exams.
11. 장애학생에 대한 학습지원 사항
- 수강 관련: 문자 통역(청각), 교과목 보조(발달), 노트필기(전 유형) 등
- 시험 관련: 시험시간 연장(필요시 전 유형), 시험지 확대 복사(시각) 등
- 기타 추가 요청사항 발생 시 장애학생지원센터(279-2434)로 요청