
PhD Curriculum for
Symbolic Computation / Mathematics
for Computer Science / The
"Thinking, Speaking, Writing" Course / The
WhiteBox  BlackBox 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
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,
welltrained 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 realworld 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
computersupport 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.

