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Lubomir and Prashant, Math has almost, if not the same, number of definitions and subfields as design. I find myself stiting in between some of these viewpoints. I agree with Ken in that the type of mathematics introduced to students should be tailored to the type of design education. As an engineering design student and former engineering design professor, I have found that, though I do not use tools like Calculus and Differential Equations everyday, indeed these are rare events, the approach to solving problems using these tools as well as the intuition gained from understanding how these principles apply to physical systems is something I use constantly. I must diagree with Lubomir on the waning need for mathematics education in engineering especially. I have seen countless students surrender their critical thinking ability to the calculator or computer, seeking the anser and assuming, often incorrectly, that the answer provided is correct. I have seen high school textbooks written around particular calculators, instructing students on which keys to press instead of what principles to learn. The late Prof Rolf Faste was under constant bombardment by his Product Design students at Stanford begging to remove the math and engineering course requirements from the undergraduate program. "We don't need math, we're going to be designers!" Rold argued that because they were going to be designers they had a critical need for the skills and approaches garnered by exposure to these topics. Rolf was one of the few register professional engineers in the Mechanical Engineering Department at Stanford. He praticed what he advocated, encouraging design students to gather as much skill and experience from as many domains as possible. These skills many not be something you use everyday. Imagine the intelligence a designer brings to their work if they can not only architect the product, ensure compelling aesthetic qualities are present, confirm that their vision is indeed manufacturable, can calculate the forces it can withstand from normal use, and has the downstream visibility of how components could be reused. Rolf's approach to developing the design curriculum at Stanford falls inline with Buckminster Fuller's notion of a Comprehensive Designer. There is a growing awareness that we have been overproducing rigorously disciplined, game-playing specialists who, through hard work and suppressed imagination, earn their academic union cards, only to have their specialized field become obsolete or by-passed by evolutionary events of altered techniques and exploratory strategies. We need the philosopher-scientist-artist - the comprehensivist, not merely more deluxe-quality-technician-mechanics. - R. Buckminster Fuller I believe to define design curriculums by what to exclude is to deprive our students of the skills and empathy so critical to being an effective designer. The other domains within academia are growing more specialized in their pursuits, alienating opportunities that come from other domains. A few opened minded academic are reaching across the ivory towers to pursue interdisciplinary collaborations. What should not be surprising are the incredible breakthroughs being generated by their more inclsuive and comprehensive efforts. We owe it to our students not to be seduced by the temptations of overspecialization. All the fish seem big in these smaller ponds or specialized subdomains. The scope of your awareness and therefore the problems you can help solve are limited by the size of the pond you swim in. I would much rather swim in the ocean, even as a small fish. John On Fri, 1 Oct 2004, Lubomir S. Popov wrote: > Dear Colleagues, > > Some engineering profession are using mathematics because the natural > processes that they have to consider can be described with mathematical > formulas. These descriptions are not perfect, but they work satisfactorily. > In the social sciences, social processes are much more unpredictable and > mathematical descriptions can be used mostly in the realm of mass process. > However, even there the formulas do not reflect well the process. I > personally have a lot of reservations about mathematical description in the > social realm. > > Some engineering professions engage heavily in mathematical studies for > these reasons. Evidently mathematics help, particularly in situations > pursuing innovations. Mathematical models are used for predicting the > behavior of nuclear devices and ballistic missiles. Such modeling drives > the need for supper computers. Our word processors are improved a lot as a > by-product of developing new technologies for such "inhuman" needs. > > In the age of computers and computer programs, you might ask, is there a > need that engineers study mathematics. I would not provide a definite > answer. While rank-and-file engineers may not need much of math and may not > use it at all (like me) developers of new calculation methods, mathematical > descriptions, and in general inventors, need it for sure. The issue is that > if all engineers are not taught math, than how can we fill the "inventive" > positions? The general level of engineers will drop substantially, plus the > pool of qualified professionals will be very small. > > This is a very important issue for theory of design. The solution of this > problem will allow us to better understand a number of design and > engineering phenomena. > > More materials about this topic can be found in philosophy of science. > > Best, > > Lubomir >