The course is also offered to the students of the fields other than those the course is directly associated with.
Fields of study the course is directly associated with
there are 16 fields of study the course is directly associated with, display
At the end of this course, students should be able to:
understand and use methods of number theory to solve simple tasks;
understand approximately how results of number theory are applied in cryptography:
understand basic computational context;
model and solve simple combinatorial problems.
divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
Number theory applications:
short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
There are standard two-hour lectures and standard tutorial.
During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
Language of instruction
The course is taught annually.
The course is taught: every week.