Elementary Number Theory

Course code

MLM6206.DT

old course code

MLM6206

Course title in Estonian

Arvuteooria

Course title in English

Elementary Number Theory

ECTS credits

4.0

approximate amount of contact lessons

56

Teaching semester

spring

Assessment form

Examination

lecturer of 2019/2020 Spring semester

Tatjana Tamberg (eesti keel) tavaline kursus

lecturer of 2020/2021 Autumn semester

lecturer not assigned

Course aims

Major. To study concepts of numbers, divisibility theory and arithmetical functions in general.

Brief description of the course

Introduction to number theory. Basic properties of divisibility. Number theoretic functions. Continued fractions. Linear diophantine equations. Continued fractions and approximation of real numbers. Basic properties of congruences. Modular arithmetic. Linear congruences. The Chinese remainder theorem. High-order congruences. Quadratic residues. Orders and primitive roots. Index Calculus. Some applications of Number Theory in cryptography.

Independent work

Acquiring of the theory, solving problems

Learning outcomes in the course

Knows mathematical facts and is able to use methods in volume of a subject.

Assessment methods

Two in-class tests and individual home tests (together 50 points). The oral examination (50 points) contains presentations on two topics.

Teacher

dots Tatjana Tamberg

The course is a prerequisite

Replacement literature

Ebbinghaus, H. D. et al. 1991 Numbers. Berlin: Springer;

Kivistik, L.; Gabovitš, J. 1974 Arvuteooria. Tartu: TRÜ;

Vinogradov, I. M. 2003 Elements of number theory. New York, Mineola: Dover Publications.

Kivistik, L.; Gabovitš, J. 1974 Arvuteooria. Tartu: TRÜ;

Vinogradov, I. M. 2003 Elements of number theory. New York, Mineola: Dover Publications.