B8.1 Probability, Measure and Martingales (2023-24)
Section outline
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Course materials include: Live lectures videos, Panopto pre-recorded videos, Lecture Notes, Problem Sheets, an R code, additional slides.
Lectures will be streamed live and available to watch later.
In course's Panopto folder, you will find a subfolder MT2020. In there are 26 videos of my 2020 pre-recorded lectures of various length. They cover specific sections of the lecture notes and follow a uniform naming convention: video XY is the Yth video on the contents of Chapter X. All videos are accessed via Panopto and all have attached PDFs with the complete set of notes made during the video. Please note: these videos are from MT2020 and are only an aid, they may miss some examinable material while covering some non-examinable material.
Lecture Notes will be updated as the term goes on - I remove typos when/if those are spotted and I try to add on more of the non-examinable material.
There are four problem sheets, see below, and each is clearly linked to the relevant chapter in the Lecture Notes and the videos.
Finally, I post here some additional materials, e.g., R Code for SSRW examples (covered in 02 - Introduction), notes on percolation or applications further afield. Stay tuned!
PS. At this stage of your education, I think it is useful to include materials which allow those who are interested to undertake guided excursions beyond the syllabus. This is reflected in the length of the lecture notes and wealth of other material here. I should stress that the examinable material is summarised in the syllabus and covered in the lectures.
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The first problem sheet out of four. The questions correspond to the material covered in Chapters 1 & 2.
It contains three sections:
A) warm-up problems (with solutions) that will not be discussed in class unless asked for
B) main part with problems for handing in
C) additional problems worth trying. Some of these may be discussed in classes.
I will update the sheet later on making solutions to problems in part C) visible. -
The second problem sheet out of four.
The problems correspond to the material covered in Chapters 3, 4 & 5.1-5.3.
It contains three sections:
A) warm-up problems (with solutions) that will not be discussed in class unless asked for
B) main part with problems for handing in
C) additional problems worth trying. Some of these may be discussed in classes.
I will update the sheet later on making solutions to problems in part C) visible. -
The third problem sheet out of four.
It may appear longer than usual but many problems are simple and/or short.
The problems correspond to the material covered in Chapters 6, 7 & 8.1.
It contains three sections:
A) warm-up problems (with solutions) that will not be discussed in class unless asked for
B) main part with problems for handing in
C) additional problems worth trying. Some of these may be discussed in classes.
I will update the sheet later on making solutions to problems in part C) visible. -
The fourth problem sheet out of four.
The problems correspond to the material covered in Chapters 8 & 9.
It contains three sections:
A) warm-up problems (with solutions) that will not be discussed in class unless asked for
B) main part with problems for handing in
C) additional problems worth trying. Some of these may be discussed in classes.
I will update the sheet later on making solutions to problems in part C) visible.