Mathematics in industry

There are no prerequisites.

The student becomes familiar with solving mathematical problems in practice in collaboration with companies, offices, or research institutions. The implementation takes place in the form of project work, from the agreement to the completion of the project. The content of the project work must be in the field of mathematics or computational mathematics and must include at least some of the following elements: creating a model solution for a specific real-world mathematical problem, numerical modeling, application to real data, comparison of the model solution with a real-world task, preparation and implementation of a comprehensive mathematical or computational workshop on a selected topic, development of various computational tools. Upon completion, the student prepares a report and presents the results in the form of a seminar lecture.

1. C. L. Dym: Principles of mathematical modeling, 2nd ed., Amsterdam : Elsevier Academic Press, cop. 2004.
2. S. Howison: Practical applied mathematics : modelling, analysis, approximation, Cambridge : Cambridge University Press, 2005.
3. M. S. Klamkin, ed.: Mathematical modelling : classroom notes in applied mathematics, Philadelphia : Society for Industrial and Applied Mathematics, 1995, cop. 1987.
4. E. Zakrajšek: Matematično modeliranje, Ljubljana : DMFA - založništvo, 2004.

The aim of the course is to foster collaboration between mathematiciants and non-mathematiciants by solving problems from real world. The competences are: to promote communication with possible users of mathematical methods, to promote team work, to extend academic examples to a real world problems, to acquire some knowledge of mathematical software, summarazing, to educate Industrial Mathematicians to meet the growing demand for such experts.

Knowledge and understanding:
Knowledge how to communicate with users of mathematical methods, ability to rationally formulate problems, knowledge of mathematical modeling.
Application:
Solving real word problems. Cross breeding with users of mathematical methods.
Reflection:
Reflection of own understanding of mathematical knowledge by solving problems from a real world. Critical assesment of differences between theoretical and practical principles.
Transferable skills:
How to use knowledge bases, how to collect and interpret data, collaboration with experts from different areas, team work, how to present results, how to write reports.

Project working, field work, consultations, individual study, presentations.

Project
Project presentation
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

George Mejak:
MEJAK, George. On extension of functions with zero trace on a part of boundary. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 1993, let. 175, str. 305-314. [COBISS-SI-ID 5828441]
MEJAK, George. Finite element solution of a model free surface problem by the optimal shape design approach. International journal for numerical methods in engineering, ISSN 0029-5981. [Print ed.], 1997, vol. 40, str. 1525-1550. [COBISS-SI-ID 9983833]
MEJAK, George. Eshebly tensors for a finite spherical domain with an axisymmetric inclusion. European journal of mechanics. A, Solids, ISSN 0997-7538. [Print ed.], 2011, vol. 30, iss. 4, str. 477-490. [COBISS-SI-ID 16025177]

Marjetka Knez:
KURALT, Marko, CMOK KUČIČ, Alja, GAŠPERŠIČ, Rok, GROŠELJ, Jan, KNEZ, Marjetka, FIDLER, Aleš. Gingival shape analysis using surface curvature estimation of the intraoral scans. BMC oral health. 2022, vol. 22, str. 1-11. DOI: 10.1186/s12903-022-02322-y. [COBISS-SI-ID 116774659]
GROŠELJ, Jan, KNEZ, Marjetka. Generalized C1 Clough-Tocher splines for CAGD and FEM. Computer methods in applied mechanics and engineering. May 2022, vol. 395, art. 114983 (22 str.) DOI: 10.1016/j.cma.2022.114983. [COBISS-SI-ID 125760515]
KNEZ, Marjetka, PELOSI, Francesca, SAMPOLI, Maria Lucia. Construction of G2 spatial interpolants with prescribed arc lengths. Journal of computational and applied mathematics. May 2024, vol. 441, [article no.] 115684 (14 str.) DOI: 10.1016/j.cam.2023.115684. [COBISS-SI-ID 179837955]