Fall 2010 Course Schedule Planning

[sutupidmath]

Hi all,

Since the pre-registration time for the Fall semester is approaching i need to make plans as what to take next semester.

Specifically, i am planning on taking one or two reading courses since they are not offered via regular curriculum. While it is not for sure that i might be able to do so, since i need the consent of my instructors, i still want to know which of the following would be a better option.

1. One option is to cover completely the first part of General Topology by Munkres; that is the remaining chapters.
2. Cover only the essential remaining parts from General Topology and move on to Algebraic Topology (Second part of Topology by Munkres)
3. A second part of Real Analysis using Rudin's book, Principles of Mathematical Analysis and cover as much as possible.
4. A second portion of Abstract Algebra (> Polynomial Rings etc.)

Since, at best, i will be able to do only two of the above, i was wondering what would you recommend that i insist for?

Option 1 or 2 are the most likely to happen, since the professor i am taking Point-Set topology with, is more of a Topologist rather than Analyst or Algebraist.

But anyways, what would you guys suggest me do?

Thanks in advance.

 

[sutupidmath]

I need to meet with my advisor in three days. Any suggestion?

 

[some_dude]

I'd personally do option 2. I used Hatcher's algebraic topology and the topology background I'd gotten from analysis was more than enough. You'll of course be able to use Munkres as reference while studying algebraic topology, so can lookup things as needed.

EDIT:
Oh, I just saw you can do two of the above. How much topology is in PMA? If there's a lot, then use that and do the analysis and alg top, they'll compliment each other well and there won't be much redundancy. Otherwise maybe (if possible) try your analysis course with a book containing more topology than PMA (Real Analysis by Folland has a chapter on topology that is pretty in depth, but careful, it's very terse).