Q: Should a *mathematics*
graduate
student take Math 5101-5102 ?

A: That depends on the student's objective. The *purpose*
of this
sequence is (obviously) to offer the best and most important
results which
linear algebra (finite and infinite dimensional) has to offer. A
person
taking this sequence will find that the offered topics constitute
the conceptual
foundations found in a large part of mathematics and that
their applications
lie at the base of modern science and technology. The *point of
view*
of this sequence is to highlight, when appropriate, the synergetic
relation
between theory and applications. For Math603 this becomes
particularly
evident by scanning the introductory
overview.

Q: Should a *physics* graduate
student
take Math 5101-5102 ?

A: The two fields of physics that revolutionized twentieth
century physics
are relativity and quantum theory, and both of them rely on the
concepts
of linearity in a fundamental way. The student will find
that linear
algebra results in an enourmous increase in the effficiency with
which
concepts will be grasped. This is in particular also true for
those students
who are stydying classical electrodynamics using the books of,
say, Jackson
or Schwinger. They will find that Math 603.02 is particularly
valuable
in that it gives them *precisely* the kind of mathematics
necessary.
For example,

by looking at the introductory
overview, the cognescenti will note, among others, the
theory of special
functions is developed implicitly from the principles of group
theory.

Q: Should an *engineering*
graduate
student take Math 5101-5102?

A: Yes.

Q: Should an *engineering*
graduate
student take Math 5102 ?

A: Yes, if your interests/inclinations coincide with one of the following.

Q: Should an *undergraduate*
student
take Math 5101-5102 ?

A: As the answers to the previous questions indicate, the earlier you have digested the material in this course sequence, the easier a time you will have in graduate school or in business. However, most undergraduates take this sequence not until their senior year.