Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Vector spaces and groups
Name: harvey s reall
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:
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?


Replies:
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."

chaffer


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.

jlu



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory