The rapid integration of large language models into higher education creates opportunities for mathematics instruction, but also raises the need for structured interaction strategies that support reflective learning rather than passive answer consumption. This study, conducted within the Erasmus+ MAESTRO-AI project, examines how selected AI prompt patterns can be implemented in concrete university mathematics activities and how students evaluate these AI-supported experiences. Two experimental modules were compared: complex numbers for first-semester Applied Mathematics students in Poland ($n=100$) and conditional probability for second-year Computer Science students in Romania ($n=213$). After completing AI-assisted learning activities with ChatGPT and/or Gemini, students completed a common evaluation questionnaire assessing engagement, perceived usefulness, and reflections on AI as a tutor. Group comparisons and experience-based analyses were performed using the Mann–Whitney test. Results indicate that students who reported regular prior use of AI tools evaluated AI-supported learning significantly more positively than those with occasional or no prior experience. They gave higher ratings across most questionnaire items as well as for the overall score. The findings suggest that prompt-pattern-based designs can support engaging AI-assisted mathematics activities. They also indicate that such designs can provide a structured learning experience, while introductory guidance may be important to ensure comparable benefits for less experienced students.

This study presents necessary conditions for the existence and sufficient conditions for the stability or instability of the static meniscus (liquid bridge) appearing in the ribbon single crystal growth from the melt, of predetermined sizes, by using the edge-defined-film- fed (EFG) growth method. The cases when the contact angle and the growth angle verify the inequality 0<αc<π2 -αg or π2>αc>π2 -αg are treated separately. Experimentally, only static meniscus (liquid bridges) which verifies the necessary condition of existence and the sufficient conditions of stability can be created; static meniscus (liquid bridges) which does not verify both of these conditions, exist only in theory because in reality they collapses. The results of this study is significant for thin ribbon single crystal growth from melt, with prior given macroscopic dimensions, using prior given specific equipment. That is because the obtained inequalities represent limits for what can and cannot be achieved experimentally.