Mathematical Formalism and learning

This blog entry results from my successive attempts to learn mathematics. Without going much into philosophical discussions on what constitutes "learning", I will merely mention the obstacles and my comments. My basic degree is in engineering from a Regional College of Engineering, electrical to be specific "EE" as it is fondly known. 

Anyways, what has always bothered me and perhaps hampered my learning is the sudden jump in formalism from the undergraduate mathematics which is taught in most colleges in India, never mind their claims to be "premier institutes" to the graduate level mathematics needed for decent research work. Worse, there are very few courses for spanning this bridge. The engineering professors teach the subject from application point of view while the mathematics people look down upon "applications". This is another pet peeve of mine. When mathematicians get hoity-toity about their "abstractness" and sneer down upon applications, I think they should be made to attend a compulsory course on history of their branch of maths. It will be seen that immediately some practical application has stimulated their field. This is not to say that theorists should not be encouraged but acting hoity-toity is not going to help. Most great mathematicians have helped, in form of books/notes/lectures to bring understanding to, if not actually thrill the engineering audience. Point is, maths guys should run some "pep up" course in India and people who cannot make such course should perhaps look reconsider their PhD aspirations.

Let us come back to the point on the gap between mathematical formalism in graduate level and the lack of rigour in undergraduate levels. From personal experience, I think some amount of rigour is needed to build one's confidence, especially if it has taken a beating in the morass of UG maths. The newer approach to learning mathematics should revive interest in mathematics and help in the newer and more mature perspective in mathematics. The crucial point here is the emphasis on formalism. In my humble opinion, mathematical formalism has come to dominate the proceedings to badly that an ordinary engineer is rattled by the formalism which has come to dominate simply things. Talking to most people in mathematics, it gives the impression that they revel in formalism. I do not for one moment doubt the necessity and importance of formalism. To some, building formalism may also be interesting and their life-goal. However, one cannot expect an engineering background student to build his theory, from his point of view to make it ("the theory") useful for his dealings with the practical world. Any recourse to some commonsensical explanations are now classified as "classical" and mumbo-jumbo formalism, almost like legalese is used for proofs.  I was and still am hesitant to air these views in a general audience. However, I recently found another person who also has similar views.  He has made his displeasure known in trigonometry. I quote "Set notation and set language have pervaded all discussion, with the result that a relatively simple subject became obscured in meaningless formalism." He attributes this to the sarcastically titled(in my humble opinion), "New Maths" which was imposed on America by Americans in response to the Soviet launch of satellite to space.

Now, I do not know much nor care about USA. They seem to be doing great, New Maths or otherwise. We in India need to look into our system, at least for the graduate level if we are to produce people of any intrinsic value to themselves and society. For this, a major reform is needed in the teaching and presentation of mathematics at a graduate level. This is the summary of the blog entry!