Applied Mathematics

Study programs

Teaching information

Teachers

doc. RNDr. Marián Klešč, PhD.

Schedule

Learning outcomes

To study basic knowledge of mathematical theory, which is used in cryptography and computer networks.

Course outline

1. Properties of whole numbers, divisibility, congruences. 2. Modular arithmetic. 3. Prime numbers and composite numbers. 4. Special properties of prime numbers. 5. Fermat's theorem, Euler's function and Euler's theorem. 6. Probabilistic methods of generating large prime numbers. 7. Groups and their properties, decompositions of groups. 8. Fields and finite fields. 9. Polynomial arithmetic, multiplicative inversion. 10. Weighted graphs. 11. Transport networks. 12. Ford-Fulkerson maximum flow algorithm in the transport network.

Completion conditions

Assessment and completion of the course: Credit test and examination Continuous assessment: Student passes the continuous assessment and receives credits when he or she meets the requirement to obtain at least 1u out of 1u16% out of 30%. Written test Final assessment: Student passes the final assessment and passes the examination when he or she meets the requirement to obtain at least 36% out of 70%. Oral exam Overall assessment: Overall assessment is the sum of the assessments obtained by students in the assessment period. The overall result is determined in accordance with the internal regulations of the Technical University in Košice. (Study Regulations, the internal regulation principles of doctoral studies)

Recommended literature

Bučko M. - Klešč, M., Diskrétna matematika, elfa, Košice, 2003 Harminc, M., Elementárna teória čísel, UPJŠ, Košice, 1999 Levický, D., Kryptografia v informačnej a sieťovej bezpečnosti, elfa, Košice, 2010 Kolář, J. a kol., Logika, algebry a grafy, SNTL, Praha, 1989

Grade distribution

Total graded students: 1087