Applied mathematics has always evolved together with the challenges of society. Over the past decades, mathematical modelling, scientific computing, uncertainty quantification and optimisation have become indispensable tools in engineering, finance and the natural sciences. Today, however, a new transformation is underway. Artificial intelligence, data science, digital finance and quantum technologies are reshaping the landscape in which applied mathematicians work. For universities educating the next generation of applied mathematicians, this raises an important question: how can we preserve the rigorous mathematical foundations that define our discipline while ensuring that graduates are prepared for emerging industrial and scientific challenges?
At the Faculty of Sciences of the University of Novi Sad, this question motivated a comprehensive redesign of our undergraduate Applied Mathematics programme, a three-year programme (180 ECTS) that started in 2020/21. Rather than replacing traditional mathematical content, our goal was to strengthen its relevance by integrating contemporary topics that increasingly influence industrial practice and applied research. The revised programme that will start in 2027/28 retains a strong mathematical core based on analysis, linear algebra, discrete mathematics, probability, statistics, differential equations, optimisation, numerical methods and programming courses. Around this core of ca. 110 ECTS, students can specialise through three complementary modules: Data Analytics and Statistics, Financial Mathematics, and Artificial Intelligence and Systems Modelling, each of ca. 30 ECTS module specific courses, leaving ca. 40 ECTS for elective courses.
Several new courses were introduced in response to developments observed across industry and academia. These include Blockchain Technologies, Quantum Computing, Physics Informed Neural Networks for Modelling, etc. Together, they expose students to emerging application areas while emphasising the underlying mathematical principles. The Data Analytics and Statistics module was among the first bachelor-level programmes in Europe to embrace data science, featuring courses in machine learning, neural networks, advanced statistical methods, and project-based learning, which we kept as good practice. At the same time, the Financial Mathematics module has been enriched with selected courses originating from the data science track, exposing students to machine learning techniques increasingly employed in the financial sector, particularly in credit risk analysis, fraud detection, and insurance risk modelling. Perhaps the most visible transformation concerns the former Technomathematics module that was oriented towards physics, mechanics and classical engineering topics. While mathematical modelling of physical systems remains central, the module has been reimagined as Artificial Intelligence and Systems Modelling. The new concept reflects the growing importance of combining classical modelling approaches with machine learning, data-driven methods and artificial intelligence including PINNs and basic quantum technologies. Students continue to study dynamical systems, mechanics and mathematical modelling, but they are also introduced to modern approaches for analysing and modelling complex systems in science and industry.
In this way, the new Applied Mathematics bachelor programme seeks to build a bridge between classical industrial mathematics and the rapidly expanding world of AI-enabled modelling. Rather than viewing artificial intelligence as a separate discipline, we present it as a new mathematical toolset that complements traditional modelling methodologies.
Dora Seleši
Head of studies for Applied Mathematics
Faculty of Sciences, University of Novi Sad
