R
esearch in theoretical physics often
proceeds in two stages.
The first
sharpens a vague idea into a specific
question whose answer can be found
by solving a specific mathematical
problem.
The second, much easier
stage is to solve that problem.
The balance of courses in the undergraduate physics curriculum re
flects the dichotomy of physics research.
Most courses are con
cerned primarily with fundamental theoretical concepts, their
mathematical expression, and relation to the material world.
These
courses
involve
solving problems, of course, but they are
about
the
natural phenomena we observe and how we describe them mathe
matically.
The present course, in contrast, is
about
solving problems.
Mathematics is a tool for a physicist, a means to an end.
It is not an
end in itself.
The objective is not to prove mathematical theorems,
important though they may be.
Rather, the first goal for a physicist is
to learn
how
to use those theorems and associated mathe
matical structures to
calculate
results.
A second goal, which
often becomes more important as one matures scientifically,
is to see
why
the definitions of mathematical structures are
as they are.
Mathematical definitions often have roots in models of physical phenom
ena, and understanding they are interesting often yields insight both into how the mathematics
works and into the conceptual content of the associated physical models.
Course Objectives
The first objective of this course is to develop students’ facility with certain mathematical tech
niques.
By its end, each student should be familiar enough with these that he or she can waste
little time wondering how to proceed when solving problems in future courses.
It may some
times be difficult in practice to get a numerical result, but it should be clear in principle how to
go about it.
The primary responsibility for this objective is the students’.
As with any tool,
there is no substitute for practice when learning to use the mathematical methods we discuss.
Students should therefore commit to devoting substantial time to the assigned problems.
The second objective is to highlight applications of mathematical methods to physical systems.
As discussed above, such applications shed light on both the mathematics and the logic under
pinning physical models.
This allows students to develop valuable intuition for subsequent
courses where these same methods will be applied.
We will accomplish this objective primarily
in the lectures.
These will tend to focus in roughly equal parts on
what
the mathematical struc
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 Fall '10
 STAFF
 Physics, course web site, undergraduate physics curriculum

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