- Description:
-
The seminar is devoted to elementary number theory and applications. It includes individual problem solving.
- Contents:
-
1. Divisibility, congruences, Femat's little theorem.
2. Linear diofantic equations, linear congruences, Chinese remainder theorem.
3. Euler's function, Euler´s theorem, Moebius function, inclusion exclusion principle.
4. Perfect numbers, Mersenne's primes, Fermat's numbers.
5. Primality testing. Public key cryptographic systems: RSA, knapsack problem.
- Recommended literature:
-
Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concrete Mathematics: A Foundation for Computer Science, Reading, Massachusetts: Addison-Wesley, 1994
J. Herman, R. Kučera, J. Šimša,
Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory. 1. vyd. New York : Springer-Verlag,
2000. 355 s. Canadian Mathematical Society Books in Math.
P. Erdös, J. Surányi, Topics in the Theory of Numbers,
Springer-Verlag, 2001.
M. Křížek, F. Luca, L. Somer,
17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New
York, 2001.
- Keywords:
- Modular arithmetics, Euler's function, primes, RSA
Abbreviations used:
Semester:
- W ... winter semester (usually October - February)
- S ... spring semester (usually March - June)
- W,S ... both semesters
Mode of completion of the course:
- A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
- GA ... Graded Assessment (a grade is awarded for this course)
- EX ... Examination (a grade is awarded for this course)
- A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)
Weekly load (hours per week):
- P ... lecture
- C ... seminar
- L ... laboratory
- R ... proseminar
- S ... seminar