Numerical Mathematics, Probability Theory and Mathematical Statistics

Study programs

Teaching information

Teachers

doc. RNDr. Marián Klešč, PhD. RNDr. Mária Hutníková, PhD. RNDr. Emília Draženská, PhD. doc. RNDr. Helena Myšková, PhD. RNDr. Zuzana Gibová, PhD.

Schedule

Prerequisites

26001210 - Mathematics I

Learning outcomes

To provide basic knowledge of numerical mathematics and its use in solving practical problems. Develop logical thinking by solving problems from probability. Introduce students to the basics of mathematical statistics.

Course outline

1. Separation of roots of a nonlinear equation. Numerical solution of nonlinear equations by bisection method. 2. Numerical solution of nonlinear equations by Newton's method and iteration method. 3. Solving a system of nonlinear equations by Newton's method. 4. Approximation of functions by interpolation and least squares method. 5.Numerical calculation of a definite integral by trapeziodal method and Simpson's method. 6. Random events and probability. 7. Conditional probability, independent events,Total probability law and Bayes' theorem. 8. Random variable and its characteristics. Expective value and variance. 9. Some probability distributions of a discrete random variable - binomial, hypergeometric and Poisson distributions. 10. Probability distributions of a continuous random variable - exponential and Gaussian (normal) distribution. 11. Mathematical statistics - basic concepts and characteristics of random selection. 12. Confidence intervals for random characteristics. 13. Testing statistical hypotheses.

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%. credit 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 form 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

1. Buša J., Pirč V., Schrötter Š.: Numerické metódy, pravdepodobnosť a matematická štatistika, 2006, ISBN 80-8073-632-4. (http://web.tuke.sk/fei-km/sites/default/files/prilohy/1/statnumo.pdf, http://web.tuke.sk/fei-km/sites/default/files/prilohy/1/statnuma4.pdf ) 2. Daňo I., Ostertagová E.: Vybrané kapitoly z numerických metód, pravdepodobnosti a matematickej štatistiky, Equilibria, s.r.o., Košice, 2012, ISBN 978-80-8143-012-1. 3. Doplňujúce materiály k cvičeniam vytvorené v rámci projektu IT4KT (http://it4kt.cnl.sk/c/nm/student/01.html)

Grade distribution

Total graded students: 4155