In today’s fast-paced, time-constrained educational environment, motivating students to engage with abstract concepts and acquire the skills essential for their future professions presents a significant challenge. First-year mathematics courses at applied science universities are just as crucial as more practical subjects. These courses emphasize algorithmic reasoning, logical thinking, and pattern recognition—skills that are transformative not only in professional settings but in everyday life.

As educators, we fulfil multiple critical roles—one of the most important being the creation of a bridge between the curriculum and students’ intrinsic motivation to understand it at a deep, conceptual level. Active learning and critical thinking are key to achieving this goal.

In this paper, we present a method that has shown great success in sparking student interest and helping them appreciate the relevance of mathematical tools and models within their fields of interest. Each semester, 4–6 students are selected based on their academic success and offered the opportunity to participate in a group seminar project (in groups of two or three) as an extra-credit activity. The project must involve the application of previously taught mathematical tools to an area of personal interest. This independent research assignment engages students in exploring topics they are passionate about—at an academic level and from a scientific perspective. Once an appropriately challenging subject is chosen, students are required to study relevant literature and articles, considering both the mathematical and applied aspects.

Over the past three academic years, student projects have explored topics such as the application of matrices in digital photography and search algorithms, the use of matrices and vectors in video game development, and the role of vectors in robotics. These contemporary and relatable subjects resonate with today’s students, helping them discover the meaning and purpose of mathematics in technologies and systems they interact with daily. In this paper, from both the educator and the student points of view, we present several of the most compelling examples, with explanations that are accessible to all educators and students, while clearly highlighting the underlying mathematical concepts.

This approach has proven invaluable in fostering students’ passion for continued study and in building a solid foundation in the mathematical models they will rely on in their professional careers.

Keywords: Higher education, mathematics application, student motivation, bridging theory and practice, active learning.