Selected topics in applied mathematics

Objectives and competences

The primary goal of this course is to teach students the basics of advanced mathematical topics which are indispensable in science and engineering. The focus is on probability theory and statistics, ordinary differential equations and integral transforms. The topics are mandatory for subjects like "Data mining" and "Introduction to control systems".
The competences gained by students encompass:
- the ability to formulate and solve some problems in natural sciences and engineering by using probabilistic setup
- the ability to solve the systems of ordinary differential equations by means of numerical methods
- sufficient skills to solve linear differential equations in analytical way by using integral transforms.


Basics of mathematical analysis and linear algebra.


  1. Probability and statistics
    a. Probability of an event
    b. Basic concepts in statistics
    c. Sampling
    d. Confidence intervals
    e. Analysis of variance, covariance and linear regression
  2. Ordinary differential equations (ODE)
    a. Linear differencial equations
    b. Qualitative behaviours of systems of differencial equations
  3. Integral transforms
    a. Fourier series
    b. Fourier transform
    c. Laplace transform

Intended learning outcomes

Knowledge and understanding:
- basic knowledge and understanding of how to deal with uncertainty in natural and engineering sciences and engineering,
- acquaintance with basic techniques of calculus with random variables
- distinguishing between linear and nonlinear as well as analytically and numerically solvable DE's
- basic skills for numerical solving of (systems) of nonlinear ordinary differential equations
- understanding the role of integral transforms and basic skills in analytic solving of linear ordinary differential equations


• R. Jamnik, Verjetnostni račun in statistika, DMFA Ljubljana, 1995. Catalogue
• F. Križanič, Navadne diferencialne enačbe, DMFA Ljubljana, 1991. Catalogue
• B. Zmazek: Diferencialna analiza, skripta, Maribor, 2006.
• A. Suhadolc, Integralske transformacije, Integralske enačbe, DMFA Ljubljana, 1994. Catalogue

• D. Freedman, R. Pisani, R. Purves, Statistics, Norton, 1998. E-version
• F.M. Dekking, et al., A modern introduction to Probability and Statistics, Springer 2005, E-version
• C. R. Wylie, Differential equations, McGraw-Hill Singapore, 1985. E-version
• L. Debnath, D. Bhatta, Integral transforms and their applications, CRC Press, 2015.


Written exam, Mandatory homework assignments 75/25

Lecturer's references

Assis. Prof. Dr. Hashem Bordbar, hab. field mathematics

Principal education and research areas: Mathematics, Ordered Algebra, Algebraic Hyperstructures, Algebraic Coding Theory and Cryptography.

Professional career: Assis. Prof. Dr. Hashem Bordbar received a Ph.D. in Mathematics in 2017 from the University of Shahid Bahonar, Iran. His research is related to commutative algebra and algebraic hypercompositional structures. Also, he was awarded a scholarship to carry out part of his Ph.D. research at the Gyeongsang National University, South Korea. As a postdoctoral fellow, he worked at the University of Shahid Beheshti, Iran. His research career in this period focused on applications of algebraic (hypercompositional)structures in computer sciences and coding theory. In December 2019 he joint the University of Nova Gorica, as a postdoc in the Centre of Information Technologies and Applied Mathematics. In March 2022 he got his habilitation as Assistant Professor in mathematics.

Selected bibliography

Hashem Bordbar, “The Structure of the Block Code Generated by a BL-Algebra”, Mathematics (MDPI), Vol. 10, No. 5 (2022), pp 692. [SCIE, Scopus, WoS].

Hashem Bordbar, “BCK codes”, Advances in Computational Intelligence, Vol. 2(1), 2022, pp. 4-16. DOI: [Scopus, WoS].

Hashem Bordbar, Sanja Rašović, and Irina Cristea, “Regular local hyperrings and hyperdomains”, AIMS Mathematics, 7(12): 20767–20780. DOI: 10.3934/math.20221138 [SCIE, Scopus, WoS].

Hashem Bordbar, Irina Cristea, Height of prime hyperideals in Krasner hyperrings. Filomat, ISSN 0354-5180, 2017, vol. 31, iss. 19, str. 6153-6163,[COBISS.SI-ID 4978939]

Hashem Bordbar and Irina Cristea, “Divisible hypermodules”, Analele ştiinţifice ale Universităţii" Ovidius" Constanţa. Seria Matematică, Vol.3, No. 1 (2022), pp. 57-74.[SCIE, Scopus, WoS].

Narjes Firouzkouhi, Abbas Amini, Marziyeh Nazari, Fadi Alkhatib, Hashem Bordbar, Chun Cheng, Bijan Davvaz, Maria Rashidi, “Advanced artificial intelligence system by intuitionistic fuzzy 0‑subring for automotive robotic manufacturing”, Artificial Intelligence Review, pp 1 - 26. [SCIE, Scopus, WoS].