MATH781 ALGORITHMIC NUMBER THEORY
| Course Code: | 2360781 |
| 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. ÖMER KÜÇÜKSAKALLI |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
The algorithmic number theory connects the classical number theory topics and the theory of computational complexity. In this course, we will study algorithms for finding integer solutions to certain equations, polynomial factorization, primality testing, and integer factorization. We will also study how the objects in question can be efficiently implemented on a computer. The algorithmic number theory problems are important for their mathematical interest and application to secure information exchange, such as RSA and elliptic curve cryptography.
For more information, visit the course webpage: https://users.metu.edu.tr/komer/781/
Course Content
Fundamental number-theoretic algorithms. The Euclidean algorithm and the greatest common divisor. Computations modulo n. Computations in finite fields. Algorithms on polynomials. A survey of algorithms for linear algebra. Algorithms for algebraic number theory. Factoring algorithms.Primality tests.
Course Learning Outcomes
At the end of the course, students are expected to learn
- basic examples of number-theoretic algorithms
- fast computations modulo n
- integer and polynomial factorization
- various primality tests
- efficient implementation of various mathematical objects on a computer
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