MATH332 THEORETICAL ASPECTS OF STOCHASTIC PROCESSES
| Course Code: | 2360332 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Spring Semesters. |
Course Objectives
This course is intended to serve as a first introduction to stochastic processes, with an emphasis on theoretical aspects and proofs, without requiring full measure theoretical foundations, but only requiring a background course in basic probability theory such as Math 301. The course provides the students with an introduction to examples of stochastic processes much sought for in the industry, such as discrete and continuous time Markov chains, martingales and Brownian motion. In addition, connection with other areas of mathematics such as the amenability problem in group theory and various applications in random geometry will be discussed. The course will equip students intending to continue in diverse pure or applied areas such as group theory, random geometry, financial mathematics, dynamical systems, probabilistic aspects of data science or telecommunication networks, with essentials of the subject.
Course Content
Introduction to stochastic processes. Emergence and applications of stochastic processes in various areas of mathematics such as geometry and group theory. Finite and countable Markov chains. Classification of states with proofs. Continuous-time Markov chains; Poisson process. Conditional expectation. Martingales. Brownian motion. Fractal nature of zero sets of Brownian motion.
Course Learning Outcomes
At the end of the course, students are expected to:
- calculate the large time behavior of finite Markov chains and classify their states,
- decide whether a countable Markov chain is recurrent or transient,
- use the optional sampling theorem for martingales to compute expectations,
- understand the basics of Brownian motion in one and several dimensions.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution