Discrete Mathematics 1
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
801DIM1 | Z | 2 | 2+0 | Czech |
- Garant předmětu:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Software Engineering
- Synopsis:
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The seminar is devoted to elementary number theory and applications. It includes individual problem solving.
- Requirements:
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Knowledge of grammer school mathematics is assumed.
- Syllabus of lectures:
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1. Divisibility, congruences, Femat's little theorem.
2. Euler's function, Moebius function, inclusion exclusion principle.
3. Perfect numbers, Mersenne's primes, Fermat's numbers.
4. Primality testing. Public key cryptographic systems: RSA, knapsack problem.
- Syllabus of tutorials:
- Study Objective:
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Acquired knowledge:
Students learn to solve some types of elementary number theoretical problems.
Acquired skills:
The emphasis is put on correct formulation of mathematical ideas and logic process.
- Study materials:
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Compulsory literature:
[1] Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concrete Mathematics: A Foundation for Computer Science, Reading, Massachusetts: Addison-Wesley, 1994
[2] 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.
Recommended literature:
[3] P. Erdös, J. Surányi, Topics in the Theory of Numbers, Springer-Verlag, 2001.
[4] 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.
- Note:
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
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- Applications of Informatics in Natural Sciences (compulsory course in the program)