Here are a few observations based on my undergraduate days as a math major. Engineers, mathematicians, and anyone in the sciences together took a 3 term calcul

Here are a few observations based on my undergraduate days as a math major. Engineers, mathematicians, and anyone in the sciences together took a 3 term calculus sequence and ordinary differential equations. After ODE in our second year, disciplines started to split apart. The calculus courses were taught by math professors and their TA's. Calculus was presented through exercises with a small tribute to proofs. Right here is I think where things went wrong. The engineers really didn't care about proofs and, as important, the exercises were learning by rote. At no time were engineers given anything practical to do with calculus. They would have been better served by exercises that led to building something: a model bridge, a model circuit, anything that makes the use of calculus more concrete. The mathematicians were concerned with why calculus works but weren't given a good grounding in proofs. Consequently, I was not prepared for the sudden jump in proof maturity when I took real analysis during my fifth term. Abstract algebra equally boggled my mind the following term. Rather than study calculus with engineers, I would have been better served by learning calculus through historical development with emphasis on the reasoning process the great mathematicians went through in developing calculus. Engineers and mathematicians had diametrically opposed purposes for learning math yet were forced through the same curriculum that was a compromise between the two disciplines. Most likely the compromise was due to resources, but it did nothing to make math more interesting to either student engineers or mathematicians. As an aside, my math adviser asked me about continuing to graduate school. I replied that I had no confidence in my ability to understand higher math. His reply, "Oh, as an undergraduate we largely leave you to figure things out for yourself. Once you're a graduate student we start showing you how math really works." This is not a good policy for attracting potential mathematicians. I too have been practicing martial arts for close to 20 years. You see the same difference in purpose there as well. There are people who practice martial arts and then there are martial artists. Martial arts schools have the luxury of letting the 2 groups grow apart over time. Universities have 4 years to get the 2 groups developed for different purposes. They need to become more aware of the time limitation.