# MA8704 Probability Theory and Asymptotic Methods (Fall 2015)

## Messages

- [19.11] Oral exam will be Monday November 30.
- [24.09] The lectures on October 6 and 7 are cancelled. (Lecturer is abroad)
- [18.09] The lecture on Tuesday September 22 will start at 11:15 due to Petter Arnesen's trial lecture at 10:15-11:00.
- [02.09] The lecture on Wednesday September 9 must be completely cancelled due to collision With trial lecture and interview With applicant to Onsager Fellowship.
- [25.08] The lectures on Tuesdays is moved to 10:15-12 in room 656.
- [20.08] The lectures will be on Tuesdays and Wednesdays 9:15-11:00, starting next week. See below for room. Note that room 656 is not available on September 22, 23. Room for these days will be announced.
- [17/08] If you will take the course, but is not able to come to the first meeting on Thursday, then please send me an email before the meeting.
- [22/06] Welcome to the home page of MA 8704 Probability Theory and Asymptotic Methods. Our first meeting will be Thursday, August 20 in room 822, Sentralbygg 2, at 14:15. Welcome!

## Textbook

Alan F. Karr. Probability, 1993, Springer Verlag.

The book can be downloaded from NTNU freely from Springer Link

## Curriculum

- Chapter 1: 1.1-1.5
- Chapter 2: 2.1-2.6
- Chapter 3: 3.1-3.4, 3.6
- Chapter 4: 4.1-4.5
- Chapter 5: 5.1-5.5
- Chapter 6: 6.1-6.6
- Chapter 7: 7.1-7.3, 7.4 (knowledge of main results only), 7.5.1-7.5.3
- Knowledge of main ideas of exercises studied in the lectures

## Lectures (X = cancelled)

Date | Topic | Textbook | Exercises | |
---|---|---|---|---|

25.08 | Probability | Chapter 1.1-1.2 | 1.3,1.9 | |

26.08 | Chapter 1.3-1.5 | 1.10, 1.18, 1.19, 1.21 | ||

01.09X | Random variables | Chapter 2 (self-study) | ||

02.09 | Chapter 2 (until Sec. 2.2.4) | |||

08.09 | Chapter 2 (rest, except 2.7) | 2.1, 2.2, 2.3, 2.5, 2.11, 2.12 | ||

09.09X | Independence | Chapter 3 (self-study) | ||

15.09 | Chapter 3 (except 3.5, 3.7) | |||

16.09 | Expectation | Chapter 4 from beginning to Theorem 4.8 | 3.5, 3.7, 3.9, 3.10, 3.13, 3.14 Solution 3.5 | |

22.09 | Chapter 4 from Theorem 4.9 to Theorem 4.19 | |||

23.09 | Exercises Ch. 3 (1 hr) | |||

29.09 | Chapter 4 finish chapter | 4.2, 4.14, 4.16, 4.19 Solution 4.2 | ||

30.09 | Convergence of random variables | Chapter 5 from beginning to proof of Theorem 5.8 | ||

06.10X | Self study Chapter 5 | |||

07.10X | Self study Chapter 5 | |||

13.10 | Chapter 5 (until Section 5.2.4) | |||

14.10 | Chapter 5 (rest) | 5.1, 5.2, 5.5, 5.6, 5.7, 5.11, 5.15, 5.27 | ||

20.10 | Characteristic Functions | Chapter 6 | ||

21.10 | Chapter 6 | |||

27.10X | Self study Chapter 6 | |||

28.10 | Chapter 6 | |||

03.11 | Finish Chapter 6 | 6.5, 6.7, 6.11, 6.12 | ||

04.11 | Classical Limit Theorems | Chapter 7 | ||

10.11 | Chapter 7 | |||

11.11 | Chapter 7 | |||

17.11 | Chapter 7 | 7.2, 7.3, 7.9, 7.12, 7.25 | ||

18.11 | Final lecture | Chapter 1-7 |

## Lecturer

Professor Bo Lindqvist. Office: 1129, Sentralbygg 2. Email: bo@math.ntnu.no

## Schedule

- Tuesdays 10:15-12:00, Room 656, SB2
- Wednesdays 9:15-11:00, Room 656, SB2