文档介绍：INTERD ISCIPL IN ARY MATHEMATICS
VOLUME VI I I
LINEAR SYSTEMS THEORY AND INTRODUCTORY
ALGEBRA IC GE0~1ETRY
ROBERT HERMANN
MATH SCI PRESS
53 JORDAN ROAD
BROOKLI tiE, HA 02146
INTERDISCIPLINARY MATHEMATICS, VOLUME VIII
LINEAR SYSTEMS THEORY AND INTRODUCTORY
ALGEBRAIC GEOMETRY
Copyright C 1974 by Robert Hermann
All rights reserved
ISBN 0-915692-07-4
MATH SCI PRESS
Printed ln the United States of Ameri ca
PR EFACE
Systems Theory is a good contemporary example of the
sort of to science that I call Interdisciplinary
Mathematics. It arose in the 1940's and 1950's from work
in Electrical and Mechanical En~ineering , particularly
circuit, communication and, opt1mal control theory. It
offers a unified mathematical framework to look at (and
solve) problems in a wide variety of fields. Further,
this mathematics is not of the traditional sort involved
in engineering education, but involves virtually every
field of modern mathematics. The attract ion for me in
this subject is that one sees her e an interplay of intuition
suggested by interesting and important··applications and the
full for ce and beauty of mode rn mathematics, as one used to
see in the c lassical period of mathematical physics.
It would be interesting historical question to ask
why mathematical physics no longer plays this vanguard role.
I suspect it is not intrinsic to the subject (as I have
tried to show in my earlier books, physics, particularly
elementary particle physics, is still extremely rich in
generating ideas and intuition) , but is due to
certain perverse features of the discipline. Nany leading
physicists are smug; a manifestation of this is the poor
education of physics students in mathematics, as contrasted
say with that of the best engineering students. Not that
physicists don't learn mathematics - my criticism is that
mainly learn outdated or overly "pragmatic" mathe•