Which Path Should I Take for Self-Directed Studies: Topology or Analysis?

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SUMMARY

The discussion centers on the decision between two self-directed study paths in mathematics: Path (a) focuses on completing Part II of "Topology" by James Munkres and then progressing to "Elements of Algebraic Topology" and "Abstract Algebra" by Dummit and Foote. Path (b) suggests a similar route but substitutes "Elements of Algebraic Topology" with basic Analysis textbooks. The contributor expresses a preference for Path (a) based on personal interest, while acknowledging the importance of adequate preparation, which Path (b) may provide. Additionally, there is a critique of Munkres' algebraic topology book, suggesting that alternative resources may be more effective.

PREREQUISITES
  • Familiarity with "Topology" by James Munkres
  • Understanding of "Abstract Algebra" by Dummit and Foote
  • Basic knowledge of Algebraic Topology
  • Awareness of foundational Analysis textbooks
NEXT STEPS
  • Research alternative resources for Algebraic Topology beyond Munkres
  • Explore foundational Analysis textbooks suitable for self-study
  • Investigate study techniques for effective self-directed learning
  • Consider joining online forums or study groups focused on topology and analysis
USEFUL FOR

Mathematics students, self-learners in topology and analysis, and anyone preparing for graduate studies in mathematics will benefit from this discussion.

jmjlt88
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This year I prepared graduate school applications, and they were all ready to be sent out. Unfortunately, my father passed away shortly before Christmas. This, as you can imagine, placed me in circumstances (for the time being) where it is longer possible to leave my job and head off to graduate school late this summer. However, my intention is to try again next year. (By “try again,” I mean to actually get a chance to send them out.) That being said, I am currently engaged in self-directed studies, and I could use a little advice on which path to take.

Path (a): I could finish up Part II of Topology by Munkres (which I already started), and I could then begin working through “Elements of Algebraic Topology” by the same author. Sometime this summer I would also begin working through Abstract Algebra by Dummit and Foote. Hence, by next summer (2014), I would have a good handle on general Topology, Algebraic Topology, and Algebra.

Part (b): Part (b) is the same as Path (a) except replace “Elements of Algebraic Topology” with a few basic Analysis textbooks.

My interest leads me down Path (a). My desire for adequate preparation suggests Path (b).

And, of course, please note that any other suggestions are more than welcome! I value any input greatly!
 
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In self-directed studies - follow the path of your interests.
 
Simon Bridge said:
In self-directed studies - follow the path of your interests.

Absolutely! Self-study works best when you study something that interests you the most. See George Jones his signature: https://www.physicsforums.com/showpost.php?p=4259735&postcount=21

That said, I don't think that Munkres his algebraic topology book is very good. There are better books out there.
 

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