What is an appropriate sequence of math courses to take if your goal
is to achieve a firm grasp both of mathematical logic and of
differential geometry/topology.  More specifically with respect to
differential geometry/topology, the desired endstate is a level of
proficiency more than adequate to fully appreciate the math used in
Thorne, Misner & Wheeler's textbook, "Gravitation".  Assume a
background already of 2 semesters of differential & integral calculus,
one semester differential equations, and one semester linear algebra
and matrices.

---

Clarification of Question by johndavid-ga on 21 Dec 2005 19:48 PST

Thanks berkeleychocolate-ga, that was exactly the type of feedback I
was looking for.  Seems like I should just find myself a graduate
student tutor and work my way through MTW.

It obviously is dependant on your university and what courses they
offer, at my univeristy I would probably take something similar to the
following:
MATH 483            MATHEMATICAL WAVES  PROPAGATION THEORY 
MATH 463            COMPLEX VARIABLES 
MATH 459/659        PARTIAL DIFFERENTIAL EQUATIONS
MATH 458/658        APPLIED MATHEMATICAL ANALYSIS I 
MATH 431/631        TOPOLOGY
PHYSCS 320          ELECTRICITY AND MAGNETISM I          
PHYSCS 322          ELECTRICITY AND MAGNETISM II        
PHYSCS 410/610      MODERN PHYSICS
PHYSCS 412/612      MODERN PHYSICS II
a description of these courses can be found at the following site:
http://www.uww.edu/Catalog/02%2D04/index4.html
(just use the legend on the right to select Mathematics and Physics obviously)
Also, if you are unfamiliar with mathematical notation I would suggest
a course in numerical analysis or abstract algebra.  I would also
check out reviews at online book stores such as amazons:
http://www.amazon.com/gp/product/0716703440/qid=1133928062/sr=2-1/ref=pd_bbs_b_2_1/002-8423265-8991249?s=books&v=glance&n=283155
Pick a review that many people have found helpful read and see what
the book deals with then ask an advisor for courses offered dealing
with those areas, also asking an advior may save you $20 ;o)

You are ready now for a course in mathematical logic. It only requires
some mathematical maturity, not really any specific mathematics
courses.

A warning about studying differential geometry or topology: It won't
prepare you for Misner, Thorne, Wheeler. I have looked around for
material to prepare me for that book and have come to the conclusion
that it is one of the best books on the subject. The explanations are
as lucid as any and better than most. Of course general knowledge of
physics is helpful. You will progress in this book if you don't get
bogged down (as I have) in places. You can spend endless time trying
to confirm or prove what they say. It's better to spend a little time
on questions that bother you and then move on. The best prerequisite
for MTW is MTW.