| Area of Mathematics: | Algebra & Geometry (EAG) | ||
| Semester: | 2nd | ||
| Course ID: | 22201 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | For the course’s material, click here. | ||
| Insctructors: | Giorgos Kapetanakis | ||
Description
- Prime numbers and the fundamental theorem of arithmetic.
- Divisibility, greatest common divisor, least common multiple, the Euclidean algorithm.
- Linear Diophantine equations, Pythagorean triples.
- Arithmetic functions, Euler’s phi function, reciprocity law.
- Congruences, the Chinese remainder theorem.
- Recursive solution of polynomial equations modulo a prime power.
- Introduction to Cryptography and the RSA cryptosystem.
- Primitive roots, indices, Fermat’s little theorem.
- Quadratic residues, law of quadratic reciprocity, computations with Legendre’s and Jacobi’s symbols.
Bibliography
- T. Apostol. Introduction to Analytic Number Theory. Springer, 2010.
