Università Roma Tre, 1995-2005 Architecture and Mathematics

Andrea Pagano and Laura Tedeschini Lalli present a brief note on what has to be considered a teaching success story. They tell of ten years of teaching mathematics at the Faculty of Architecture of the Università di Roma Tre, describing some new course content that has been introduced, the methods used and, above all, the spirit that has driven the ideas about teaching mathematics to future architects. The experience covers the full curriculum of the student: from first year courses to individual projects. We began with a very precise idea: that the mathematics being taught is antiquated, it isn't obsolete. Mathematics is a living subject, and it transforms itself, something that few non-mathematicians are aware of. Further, it doesn't grow through falsification of previous theories, which, happily, we continue to use in all of their rigour, but through amplification of theories or by changes in the themes being dealt with, often through the influence of other fields, of the surrounding culture, and the "spirit of the times", of which mathematics has always been an integral part. We sought, therefore, to update the topics, the methods, and the themes, noting how in each case we continued to use the mathematics that came before as well, which typically over time acquired a kind of nimbleness, and with that a rigour and elegance which architecture students were as sensitive to as the math students were. From the beginning, buoyed by teaching experience gained in the United States, and from our Italian background, we had some clear ideas. The first thing to be taught is a working method: the first of the tools that have to be offered to the students is the ability to read a mathematical text. We therefore tried to furnish, within the context of a typical calculus program, adequate skills for becoming aware that the ideas that were not discussed in the course exist in the literature and are accessible at various levels, even for beginners. Even during a mathematics course an ordinary student should be able to go into a scientific library and find the texts that he or she needs. This is obvious for students of the humanities, but much less so for students of so-called "service" mathematics courses. This is not even an objective of graduate courses in mathematics, and many warned us that we would be unable to achieve our goal. As it turned out, however, we were not only able to achieve our goal but came up with a sure way to overcome "math anxiety", by addressing that very subject on a personal level, and making choices that were individual as well based on available texts and interests