Faculty: Faculty of Engineering

Department(s): Computer Engineering

Course: Theory of Probability

Weekly hours: Theory: 2 Exercises: 1

ECTS Credits: 5

Semester: Fall/Spring

Lecture Schedules:

Lecturer: Dr. Hiqmet Kamberaj

Room Number: 409

Phone Number of the lecturer: +389 (0)23174010 (ext. 123)

E-mail address of the lecturer: km.ude.ubi|jarebmakh#km.ude.ubi|jarebmakh

**Course Objectives:**

The aim of the course is to give a broad knowledge of the concepts of Probability for students of computer science and engineering first-year graduate-level course in Theory of Probability. In this course student will learn about Measure theory, Laws of large numbers, Central limit theorems, Random walks, Martingales, Markov chains, Ergodic theorems, and Brownian motions.

**Available topics for Master Diploma Thesis**

- Discrete and Continuous-time Markov-processes in gene expressions networks.
- Hidden Markov Models in computational biology.
- Problem of egodicity: Random walks and Monte Carlo.
- Brownian motion of (bio)molecules in solvents.
- Other topics are available upon request.

Skill outcomes | Necessary ( + ) Not Necessary ( –) |
---|---|

Written communication skills | + |

Oral communication skills | + |

Computer skills | + |

Working in laboratory | + |

Working team | + |

Preparing projects | + |

Knowledge of foreign language | + |

Scientific and professional literature analysis | + |

Problem solving skills | + |

Management skills | + |

Presentation skills | + |

**Course Textbooks:**

- R. Durrett, Probability: Theory and Examples, 4.1th edition, Cambridge University Press, 2013.

**Weekly Study Plan**

Weeks | Topics |
---|---|

1 | Measure theory. |

2 | Laws of large numbers. |

3 | Central limit theorems. |

4 | Poisson convergence. |

5 | Random walks. |

6 | Martingales. |

7 | Markov chains. |

8 | Ergodic theorem. |

9 | Bownian motion. |

10 | Ito's formula, Donsker's theorem, and empirical distributions. |

11 | Preparatory week. |

12 | Final exam week. |

13 | Preparatory week. |

14 | Preparatory week. |

15 | Make up 1 Exam. |

In June | Make up 2 Exam. |

**Attendance**

Students are obliged to attend at least 60% of lectures.

**Exams**

- Achieved success in a course shall be evaluated through a final exam and seminar work.
- The topic of the seminar work for each course shall be chosen in the first two weeks of lecture. The seminar work shall be delivered at the last (10th) week of lecture. It shall consist from 7,500-10,000 words (tables, graphs are excluded).
- The maximum number of credit points (a) for final exam is 60% (b) for seminar work is 40% of the total number of points.
- The student who has not passed the exam may enter the exam 2 (two) more times during the make-up exam sessions.

**Student workload:**

Please calculate the “Total Student Work Load” and then distribute that figure to the different engagements. For calculating the Total Student Work Load we multiply the course ECTS credits with standard figure 30. (ECTS Credit: 5) x 30 = 150 hours.

Activities | Hours |
---|---|

Lecture hours for 14 weeks: | 28 |

Laboratory and class exercises for 14 weeks: | 14 |

Student Mentoring for 14 weeks: | - |

Consultation for 14 weeks: | 4 |

Exam preparations and exam hours (Midterm, final, Makeups) : | 20 |

Individual reading work for 14 weeks (Reading assignments/expectations for reading and comprehension is 5 pages per hour. Example: If a book 300 pages, total Individual reading work for 14 weeks 300:5 = 60 hours. | 50 |

Homework and work practice for 14 weeks: | 34 |

Preparation of diploma work, for 14 weeks: | - |