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Name: harvey s reall
Status: N/A
Age: N/A
Location: N/A
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Date: Around 1995

As a first year math undergraduate I have done a lot of work on vector spaces, groups and the like. Why do I need to study them? Is it just because so many mathematical sets have theses structures so studying the abstract structure, gives information on many different subjects? If so, why do the lecturers not point this out?

It seems to me that your suggested reason is a major one. When an efficient set of properties describes a lot of different ideas in a lot of different contexts then there is real value in studying these structures abstractly. A general language is then valuable for communication and for focusing thought. It is true that lecturers do not try hard enough to communicate this to the students. They are probably discouraged by a feeling that the attempt would not be productive since it is so much easier to understand after "having been there."


Your question is a very good one and illustrates one of the deficiencies of math education in this country. The math teachers (as opposed to the mathematicians) have isolated themselves from the other disciplines and impart gibberish to their students without providing any context.

The language of vector spaces is extremely useful in quantum mechanics and classical mechanics and heaven only knows where else. There are many beautiful mathematical structures, and many are only dimly understood. Go and talk to your nearest friendly physics or electrical engineering profes- sor for more information.


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