PhD Curriculum for Symbolic Computation / Mathematics for Computer Science / The "Thinking, Speaking, Writing" Course / The White-Box - Black-Box Principle

Special Didactic Activities/The "Thinking, Speaking, Writing" Course:

My main teaching activity in recent years concentrated on the "Thinking, Speaking, Writing" course. This is a unique course that aims at training the basic five activities of math and computer science students, researchers, and teachers:

• reading
  
• listening
  
• thinking
  
• speaking
  
• writing

and their interplay in

• cooperating.

This corresponds to the basic model of intelligent behavior in in research and development communities: We have to absorb input information (reading, listening), to process it (thinking), and to present the result of our thinking to the outside (speaking, writing). Progress is obtained only by the interaction of intelligent, well-trained individuals in the community (cooperating).

In practical terms, in this course, the students (in particular the international PhD students and the diploma students of RISC) are trained professionally to

• work with the literature and math and computer science knowledge bases
  
• interact in discussions for clarifying problems and solutions
  
• formalize real-world problems in mathematical terms, invent new
• math and computer science knowledge, and, in particular, find and formally carry through mathematical proofs,
  
• prepare and present talks and courses,
  
• prepare and work out papers, documentation, manuals etc.
  
• work together in R&D groups and direct such groups.

Particular emphasis is laid on mastering the formal aspects of math and computer science, i.e. on mastering all technical details of math and computer science languages and becoming professional in the various proof techniques. My experience in teaching the formal thinking and presentation techniques of mathematics is also one of the main sources for my research project "Theorema", which basically can also be viewed as bringing these technqiues onto the computer for making them available, in the future, as sophisticated computer-support to the "masses" of math and computer science students, teachers, researchers and engineers.

My teaching in this course is mainly done by examples and case studies and detailed discussions of all aspects of the examples in terms of "reading, listening, thinking, speaking, writing, and cooperating".

Over the years, dozens of students from all over the world took part in this course. These students, hopefully, contribute to the development of refined working techniques at the places where they are working now.