Mathematics with Statistic

Objectives and competences

Meet and complement the basic concepts and principles of mathematical analysis, algebra and statistics and their applications in science.


High school mathematic knowledge.



Arithmetics and Algebra

  1. Operations with sets
  2. Natural, integer, rational and real numbers
  3. Fractions and percenteges
  4. Powers and roots
  5. Logarithms
  6. Linear and quadratc equations
  7. Linear systems
  8. Disequations


  1. Vectors in the space
  2. Scalar, vectorial and mixed product
  3. Lines and planes
  4. Conics: circle, ellipse, hyperbola, parabola


  1. Elementary functions (polynomials, rational functions, exponential and logarithmic functions, trigonometrical functions)
  2. Limit of function
  3. Rules and derivatives of elementary functions
  4. Indefinite and definite integrals


  1. Basic concepts and algebra of events
  2. Conditional probability
  3. Statistical parameters (arithmetical mean, median, mode, dispersion, variance, standard deviation).
  4. Mathematical hope
  5. Quantiles
  6. Correlation coefficient
  7. Regression
  8. Random sampling
  9. Intervals of trust


Calculating exercises based on the course lectures.

Intended learning outcomes

Knowledge and understanding:
By the end of this course students will be able to:
-do operations with numbers and sets
-calculate logarithms, roots, powers
-solve linear and quadratic equations and systems
-solve problems with vectors, lines and planes in the space
-calculate limits, derivatives, integrals
-determine the probability of an event
-calculate statistical parameters (average, variance, median, mode, dispersion, variance, standard deviation, etc.)


  1. Wrede, R.C., Spiegel, M. (2002). Advanced Calculus, 2nd Edition, Schaum’s Outlines Series. E-version
  2. TOMŠIČ, Gabrijel, OREL, Bojan, MRAMOR KOSTA, Neža. Matematika I. Ljubljana: Fakulteta za elektrotehniko: 2004. E-version
  3. TOMŠIČ, Gabrijel, MRAMOR KOSTA, Neža, OREL, Bojan. Matematika II. 4. Ljubljana: Fakulteta za elektrotehniko, 2005.
  4. OBLAK, Polona. Matematika. Ljubljana: Založba FRI, 2017. E-version
  5. Košmelj K. (2007) Uporabna statistika, Biotehniška fakulteta, Ljubljana. E-version


Seminar work, homework tasks examination (20 %)/written examination (80 %)

Lecturer's references

Prof. dr. Bojan Orel is a full professor at the Faculty of Computer and Information Science, University of Ljubljana, where he teaches mathematics. In his research work he is engaged in numerical analysis, he is mainly interested in methods for solving differential equations.

  • OREL, Bojan. Extrapolated Magnus methods. BIT (Nord. Tidskr. Inf-Behandl.), 2001, vol. 41, no. 5, str. 1089-1100. [COBISS.SI-ID 11459929]
  • CELLEDONI, Elena, ISERLES, Arieh, NØRSETT, Syvert Paul, OREL, Bojan. Complexity theory for Lie-group solvers. J. complex., 2001, vol. 18, no. 1, str. 242-286. [COBISS.SI-ID 11529305]
  • TURKOVIĆ, Aleksandra, OREL, Bojan, LUČIĆ-LAVČEVIĆ, Magdi, DUBČEK, Pavo, PAVLOVIĆ, Mladen, CRNJAK OREL, Zorica, BERNSTORFF, Sigrid. GISAXS study of temperature evolution in nanostructured CeVO[sub]4 films. Sol. energy mater. sol. cells. [Print ed.], 2007, vol. 91, no. 14, str. 1299-1304. [COBISS.SI-ID 3749658]
  • OREL, Bojan. Accumulation of global error in Lie group methods for linear ordinary differential equations. Electron. trans. numer. anal., 2010, vol. 37, str. 252-262. [COBISS.SI-ID 15731801]
  • LUČIĆ LAVČEVIĆ, Magdi, TURKOVIĆ, Aleksandra, DUBČEK, Pavo, CRNJAK OREL, Zorica, OREL, Bojan, BERNSTORFF, Sigrid. GISAXS view of induced morphological changes in nanostructured CeVO [sub] 4 thin films. J. nanomater., 2011, vol. 2011, str. 303808-1-303808-7, ilustr., doi: 10.1155/2011/303808. [COBISS.SI-ID 4561690]
  • OREL, Bojan, PERNE, Andrej. Computations with half-range Chebyshev polynomials. Journal of Computational and Applied Mathematics. [Print ed.]. 2012, vol. 236, iss. 7, str. 1753-1765. ISSN 0377-0427.[COBISS.SI-ID 16107609]
  • OREL, Bojan, PERNE, Andrej. Chebyshev-Fourier spectral methods for nonperiodic boundary value problems. Journal of applied mathematics. 2014, vol. 2014, article id 572694, str. 1-10, ilustr. ISSN 1687-0042.[COBISS.SI-ID 10832212]