Probability 1 at CEU -- fall semester 2016

Results of the semester are here for those who requested that I publish them online

This was the final exam, and here are the solutions.
This was the midterm exam, and here are the solutions.
These were the questions of the "placement test".

Homework sheet 1. Solutions here.
Homework sheet 2. Solutions here.
Homework sheet 3. Solutions here.
Homework sheet 4. Solutions here.
Homework sheet 5. Solutions here.
Homework sheet 6. Solutions here. An error in Exercise 6.6 corrected - sorry.
Homework sheet 7. Solutions here.
Homework sheet 8. Solutions here.

No. of Credits: 3
No. of ECTS credits: 6
Time Period of the course: Fall Semester
Prerequisites: basic probability
Course Level: introductory MS
Official syllabus: here.
Classes: Mondays from 09:00 in room 310/A.
Course Coordinator: Imre Péter Tóth.

Schedule (planned):
week #whentopicremark
week 1-22016.09.19,26Review of basic notions of probability theory. Measure-theoretic language. Some famous problems and paradoxes.
week 32016.10.03Different types of convergence for random variables. Borel-Cantelli lemmas.
week 4-52016.10.10,17Laws of Large Numbers. The method of characteristic functions in proving weak convergence: the Central Limit Theorem.
week 6-72016.10.24,31Conditional expectation with respect to a sub-sigma-algebra. Martingales. Some martingale convergence and optional stopping theorems.
week 8-92016.11.07,14Applications of martingales: Galton-Watson branching processes. Asymptotic results. Birth and death process. ABRACADABRA problem.
week 10-112016.11.21,28,12.05Random walks on the integers. Construction and basic properties of Brownian motion.
week 122016.12.05Probabilistic methods in combinatorics - an example.

Suggested literature (References):
  1. To catch up with the missing basics: W. Feller: An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition, Wiley, 1968.
  2. For most of the course: R. Durrett: Probability. Theory and Examples. 4th edition, Cambridge University Press, 2010.
  3. For the short combinatorics part: N. Alon, J. H. Spencer: The Probabilistic Method. 3rd edition, Wiley, 2008.
Midterm, exam:
The midterm will be on Tuesday, the 25th of October 2016 from 10:00 to 12:00, in the study room of the Math Department at CEU.

Grading rules:
There will be weekly homework assignments wort 30% of the total score. The midterm will also be worth 30%, while the final exam is worth 40%.
In detail:

Material for learning:
Some notes about the measure theoretic basics of Probability