Instructor: |
Janosch
Ortmann |

Contact: |
janosch dot ortmann at utoronto dot ca |

Dates: |
Mondays 1-3 and Wednesdays 1-2 |

Location: |
Mondays BA 1230, Wednesdays BA B025 |

Office hours: |
Tuesdays 11-12 |

Office: |
ES 4145 (Earth Sciences, 4th floor) |

**Important announcement**: the final exam will take place on
Monday December 16 from 1-4pm in the mathematics exam room BA 6183
(6th floor of Bahen).

You can download the course syllabus here.

MAT 1128 is a course designed for Master’s and Ph.D. level
students in statistics, mathematics, and other departments, who
are interested in a rigorous, mathematical treatment of
probability theory using measure theory. Specific topics to be
covered include: probability measures, the extension theorem,
random variables, distributions, expectations, laws of large
numbers, Markov chains.
If time permits we may cover some basic aspects of ergodic theory.

The course takes the place of STA 2111 for Mathematics graduate
students and will prepare students for Probability II (STA 2211)
and the Qualifying Exam in May.

Students should have a strong undergraduate background in Real Analysis, including calculus, sequences and series, elementary set theory, and epsilon-delta proofs. Some previous exposure to undergraduate-level probability theory is also recommended.

There will be a mid-terms as well as a final exam. In addition there will be roughly biweekly assignments that will be marked and returned. The final exam will count for half of your mark, the rest will be made up by midterm (30%) and assignments (20%).

The mid-term will take place during class on **Wednesday
October 23**.

From time to time I will post handouts on supplementary material.

- Handout
on measure theory: some facts and concepts that you will
need to know for this course. These notes may be slightly
extended as we move through the course.

- List
of topics for the midterm test.

- List
of topics for the final exam.

- Some
extra problems for the final exam.

I will regularly post exercises here. Most will be for you to test your understanding of the course. You are encouraged to work through these and come and ask me if you have problems. Some will be for handing in to me, and you will receive these returned with a grade.

- Exercise
sheet 1: exercises on measure theory. This is for your own
benefit only and does not contain any assessed questions.

- Exercise
sheet 2: exercises on integration and convergence of
random variables. This exercise sheet does not contain any
assessed questions.

- Exercise
sheet 3: exercises on expectation and convergence
theorems. This exercise sheet does not contain any assessed
questions, but you are encouraged to hand in your solutions for
grading by
**Monday, September 30.**

- Exercise
sheet 4: (
**corrected version**) exercises on independence. This is the first assignment that counts towards your course credit. Please submit answers before the lecture on**Wednesday, October 9**. If you are auditing this course you are still encouraged to submit your answers in order to get feedback. - Exercise
sheet
5: exercises on weak laws of large numbers and liminf and
limsup for sets. This is the second assignment that counts
towards your course credit. Please submit answers before the
lecture on
**Wednesday, October 30**. If you are auditing this course you are still encouraged to submit your answers in order to get feedback. - Exercise
sheet
6: (
**typo corrected**) exercises on weak convergence and characteristic functions. This is the third assignment that counts towards your course credit. Please submit answers before the lecture on**Wednesday, November 13**. If you are auditing this course you are still encouraged to submit your answers in order to get feedback. - Exercise
sheet 7: exercises on the CLT and random walks. This is
the fourth and last assignment that counts towards your course
credit. Please submit answers before the lecture on
**Wednesday, November 27**. If you are auditing this course you are still encouraged to submit your answers in order to get feedback.

The text book for the course will be *Probability: Theory and
Examples* by Rick Durrett, fourth edition, published by
Cambridge University Press. You can download a pdf copy of an
earlier edition on his web
site