Business Mathematics (n)

Meet and complement the basic concepts and principles
of higher mathematics and their applications in science
and technology. Developing thinking skills specific to
problem solving: understanding the problem, finding
appropriate data rescue plan, rescue, checking
compliance solutions and analysis solution. Expression of
the mathematical reasoning and use it in the science and
technical research.

1. Vectors in the space
   • Real and complex numbers
   • Definition of vector and pricipal operations between vectors
   • Scalar, vectorial and mixed product
   • Equation of a line and of a plane in the space

2. Matrices
   • Addition and multiplication of matrices
   • Determinant and the inverse matrix
   • Eigenvalues and eigenvectors

3. Systems of linear equations
   • Solving systems
   • Gauss elimination

4. Operational research
   • Linear programming
   • Simplex method
   • Production process optimization
   • Transportation problems
   • Optimal allocation of investment

5. 1. Interest rates
      • Simple interest
      • Compound interest
      • Debts
      • Continuous compounding

Knowledge and understanding:
By the end of this course students will be able to:
-do operations with matrices
-calculate determinants
-solve linear systems
-find the eigenvalues and eigenvectors of a matrix
-solve problems with vectors, lines and planes in the space
-solve problems regarding linear programming

• G. Tomšič, B.Orel, N. Mramor Kosta, Matematika I, Založba FE in FRI, Ljubljana, 2000 (3.izdaja).
• M. Zeljko, Matematične metode. E-version
• S. Boyd, L. Vandenberghe, Introduction to applied linear algebra, Cambridge University Press 2018. Catalogue E-version
• J. Usenik, Izbrana poglavja iz matematike, Novo Mesto 2020. E-version
• Linearno programiranje. E-version

Seminar work and homeworks. Written exam. 30%/ 70%

dr. Irina Elena Cristea
Habilitation: Assoc. Prof. in the field of Mathematics
Principal education and research areas: Mathematics, algebraic hyperstructures and connections with fuzzy sets and their generalizations.
Professional career: Prof. Irina Elena Cristea received the PhD in Mathematics, with specialization in Algebra, in 2007, from the University of Constanta, Romania. She started the research career in 2003 at the University of Iasi, Romania, where she worked as Teaching Assistant for 4 years. After a postdoctoral position at Udine University, Italy, in January 2012, she was employed at the University of Nova Gorica, as Assistant Professor in Mathematics, conducting research in Algebraic Hyperstructure Theory. Since 2017, she is Associate Professor in Mathematics, being affiliated with the Centre for Information Technologies and Applied Mathematics. She is currently teaching Mathematics at the School of Engineering and Management, School of Environmental Sciences and School of Sciences at the University of Nova Gorica.

Selected bibliography:

1. SONEA, Andromeda Cristina, CRISTEA, Irina Elena. Eulerʹs totient function applied to complete hypergroups. AIMS mathematics. 2023, vol. 8, iss. 4, str. 7731-7746. ISSN 2473-6988. [COBISS.SI-ID 138561795]

2. LINZI, Alessandro, CRISTEA, Irina Elena. Dependence relations and grade fuzzy set. Symmetry. 2023, vol. 15, iss. 2, 311, str. 1-18, ilustr. ISSN 2073-8994. [COBISS.SI-ID 138966275]

3. BORDBAR, Hashem, JANČIĆ-RAŠOVIĆ, Sanja, CRISTEA, Irina Elena. Regular local hyperrings and hyperdomains. AIMS mathematics. 2022, vol. 7, iss. 12, str. 20767-20780. ISSN 2473-6988. [COBISS.SI-ID 123160323]

4. CRISTEA, Irina Elena, NOVAK, Michal, ONASANYA, Babatunde Oluwaseun. Links between HX-groups and hypergroups. Algebra colloquium. [Print ed.]. 2021, vol. 28, iss. 3, str. 441-452. ISSN 1005-3867. [COBISS.SI-ID 65771011]

5. CRISTEA, Irina Elena, KANKARAS, Milica. The reducibility concept in general hyperrings. Mathematics. 2021, vol. 9, iss. 17, str. 1-14, ilustr. ISSN 2227-7390. [COBISS.SI-ID 73968899]

6. DAVVAZ, Bijan, CRISTEA, Irina Elena. Fuzzy algebraic hyperstructures : an introduction, (Studies in fuzziness and soft computing, vol. 321). Cham: Springer, cop. 2015. X, 242 str., ilustr. ISBN 978-3-319-14761-1 [COBISS.SI-ID 3704571]