Mathematician's Approach to Teaching. Pedagogy in Higher Education

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Focusing on teaching methodologies in higher education, the article examines the common structure shared by all subjects, including mathematics, which consists of assumptions, properties, and applications. It proposes an idealistic method for research-oriented students and a realistic inductive method as effective approaches for graduate and postgraduate learners. The discussion highlights the absence of a universally best teaching method while emphasizing the importance of adapting techniques to suit different educational levels, concluding with suggestions for further research in the field.