Transdisciplinary Courses

Transdisciplinary courses are probably among the most difficult to plan, implement and teach. A first natural question is whether one needs such courses at all? Modern science, and complex global life, pose challenges that may be difficult to address with classical techniques from just one particular field. Indeed, if individual fields would be enough, there would be a lot less (open) problems. The need to branch out, combine, connect and intertwine as a problem solving-strategy has already produced tremendous results, e.g., modern medicine would be impossible without heavy input via tools and approaches from chemistry and physics. It seems quite likely that the next generations of students could benefit from learning how to bridge disciplines. A key question is when students should branch out: immediately when starting at university, in the intermediate part of their studies, or just when needed in doctoral studies or even via continuing education? This question is already a tricky one. The standard answer is: it depends! However, it seems that a balanced approach is to be called for, i.e., starting far too early, might mean that the basics suffer while starting too late, or never, could lead to missing out on a potentially promising approach. It seems reasonable to roughly spend six semesters really focusing mostly on technical groundwork. it should be noted that this does not necessarily mean to just take courses from one particular area. Many classical established combinations of subjects have been proven to be successful roads. From my personal experience, this has been the interface between mathematics and physics as well as to computer science. Learning fundamental mathematical tools is necessary for physics and computer science. Being able to program and to understand algorithms is a key skill for mathematics and physics, while basic physical intuition and core problems motivate many parts of mathematical thinking and computing. Hence, there is literally no reason why, say a mathematics major, should not aim to maybe take a minor in physics, computer science or a related discipline. Once major technical skills have been acquired during the first few years, there is opportunity in the curriculum to expand horizons if students continue at university; if not, training on-the-job in an industrial setup is a suitable broadening of horizons anyhow. On the university level, continuing to a master-level or doctoral degree should give students at least some flexibility. In this situation expanding to new areas can easily be accomplished. Students are now prepared with a toolkit from their core discipline, which allows them to start out on firm ground. Practical issues are mostly sorted as having a first degree usually implies familiarity with studying and learning principles at university. Even though there may be no real consensus on the timing, let us suppose now that one wants to offer a few transdisciplinary courses around the time of semesters 7-10 to supplement master-level or beginning doctoral studies. Then one has to decide how to practically implement a course. Administrative hurdles do arise: which department is responsible, what amount of credit to give, and whether the course should be co-taught by two faculty members, are just the tip of the iceberg of questions. In fact, the ‘underwater’ part of the iceberg might be even more dangerous as we all known. I would argue that the university should just provide a broad skeleton and leave the precise decisions to individual departments. On the departmental level, a simple rule could be to implement an equal contribution principle. This means that each department contributes equally in all regards: faculty support, credit points, topical contributions, and so on. This would ensure that not too much additional strain is placed on the existing curricula. To guarantee flexibility, the courses should be oriented towards challenges that are recent and of general interest. For example, it is clearly a mathematical challenge how to analyze the dynamical processes of and on complex networks while the impetus and implications for this class of problems can easily be found in the stability of financial markets or in the sustainability of ecological diversity. An advantage in this context is that students would adapt and learn new methods from distant subjects on the fly. To pick up the last example, agent-based and game-theoretic models from economics or foodweb modeling and structure could be picked up in a course on economic or ecological network dynamics. These tools are also important from theoretical standpoint in mathematics per se. They are frequently not part of the undergraduate curriculum so a transdisciplinary course is an excellent opportunity to introduce them. Overall, I would argue that if a transdisciplinary course is well-prepared, it can open up new horizons for students after some technical groundwork. After all, leading students to the edge of knowledge and new research horizons is also one of the goals of university education.

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