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: | |
| 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