MATH525 ANALYTIC NUMBER THEORY
| Course Code: | 2360525 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. ALİ ULAŞ ÖZGÜR KİŞİSEL |
| Offered Semester: | Fall Semesters. |
Course Objectives
The course aims to cover the classical theory of analytic methods in number theory. Particular emphasis is placed on the Riemann zeta function and how it is used to understand the distribution of prime numbers. In addition, L functions and their role in understanding primes in arithmetic progressions is discussed.
Course Content
Dirichlet series, Dirichlet L-functions, Chebychevs y and q functions, prime number theorem, distribution of primes, functional equations.
Course Learning Outcomes
At the end of the course the student is expected to:
- Relate properties of the Riemann zeta function and Dirichlet L-functions to the distribution of primes
- Use methods from complex analysis, in particular contour integration to obtain properties of the zeta function and L-functions.
- Prove equalities about infinite sums using Poisson's summation formula
- Infer results from the prime number theorem
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 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 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 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 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