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
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.