Intuition – Based Teaching Mathematics for Engineers

It is suggested to teach Mathematics for engineers based on development of mathematical intuition, thus, combining conceptual and operational approaches. It is proposed to teach main mathematical concepts based on discussion of carefully selected case studies following solving of algorithmically generated problems to help mastering appropriate mathematical tools. The former component helps development of mathematical intuition; the latter applies means of adaptive instructional technology to improvement of operational skills. Proposed approach is applied to teaching uniform convergence and to knowledge generation using Computer Science object-oriented methodology.