Intro to Topology Recommended Texts

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Discussion Overview

The discussion revolves around recommendations for introductory topology texts suitable for a high school student with limited mathematical background. Participants explore various texts, their accessibility, and the availability of solutions manuals, focusing on resources that do not require advanced knowledge of real or complex analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks a topology text that is thorough and does not require higher-level analysis knowledge.
  • Another participant recommends Munkres as a suitable text, noting it starts from basic set theory but may lack motivation without real analysis.
  • There is a request for sources to download a solutions manual for Munkres, with concerns about the availability of such resources without payment.
  • Some participants acknowledge the absence of an official solutions manual for Munkres and discuss incomplete solutions found online.
  • A suggestion is made for an alternative resource, a problem course that offers a free version online but requires payment for a complete text with proofs and solutions.
  • Another participant mentions Schaum's outline series as a potential supplement, highlighting its many examples and solved problems.

Areas of Agreement / Disagreement

Participants generally agree on the recommendation of Munkres as a primary text, but there is no consensus on the availability of a solutions manual, with some expressing doubt about finding one without payment. Multiple suggestions for supplementary texts are presented, indicating a variety of perspectives on the best approach to learning topology.

Contextual Notes

Limitations include the participant's current level of mathematical education and the specific requirement for a solutions manual, which may restrict the choice of texts. The discussion also reflects varying opinions on the necessity of supplementary materials.

Who May Find This Useful

This discussion may be useful for high school students or beginners in topology seeking accessible texts and resources, as well as educators looking for supplemental materials for directed study.

STEM2012
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I know there are some threads out there already, but none really help me (see my description below).

I am a high school student. My highest level of math education is Calculus I. I am currently taking Calculus II (although I already know the integration portion of this course).

I have no education in topology besides some simple knowledge from discrete math texts.

I need a topology text that is thorough, ideally has a solutions manual, and does NOT require knowledge of higher-level real/complex analysis.

Thanks in advance
 
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Munkres will be your best bet. It starts from the very basics of set theory and it goes quite deep.
However, a lot of motivation for the things we do actually comes from real analysis. So it may very well happen that you find topology to be ill-motivated. But other than that, Munkres should be ideal for you.
 
Thanks micromass. Although its a bit pricy, my school is paying for it so I think I'll purchase it.

By the way, could you give me a good source for downloading the solutions manual. I've done some looking into that already, but everything I've found is incomplete and requires logging in through subscribing w/ pay (which I'd like to avoid).
 
STEM2012 said:
Thanks micromass. Although its a bit pricy, my school is paying for it so I think I'll purchase it.

By the way, could you give me a good source for downloading the solutions manual. I've done some looking into that already, but everything I've found is incomplete and requires logging in through subscribing w/ pay (which I'd like to avoid).

I'm not aware that a solution manual even exists :frown: And I doubt you will find one without paying...
 
You're right about a nonexistent official solutions manual. I was looking at some solutions posted by other users, which I guess is the reason they were incomplete.

With that said, do you know of some other text that matches what I'm looking for AND has a solutions manual (either for free or for purchase, I guess it doesn't matter)? The reason why I really would prefer a solutions manual is because I'm using this text for an directed study and my high school teacher is not really familiar with topology.

Thanks a lot in advance
 
STEM2012 said:
You're right about a nonexistent official solutions manual. I was looking at some solutions posted by other users, which I guess is the reason they were incomplete.

With that said, do you know of some other text that matches what I'm looking for AND has a solutions manual (either for free or for purchase, I guess it doesn't matter)? The reason why I really would prefer a solutions manual is because I'm using this text for an directed study and my high school teacher is not really familiar with topology.

Thanks a lot in advance

What about this one?

http://www.pdmi.ras.ru/~olegviro/topoman/index.html

It's not really a textbook, but rather a problem course. That is, you learn the material by solving problems. You can find a free version of the text on the website above. However, if you want a text that contains the proofs and solutions, then you'll have to pay for it.

To my (limited) knowledge, this is the only text with a solution manual.
 
You should consider https://www.amazon.com/dp/0070379882/?tag=pfamazon01-20. Schaum books contain many examples and solved problems (plus other problems without solutions). It probably will work best as a supplement to another text. You can preview parts of the book in the Amazon link. You also might be able to find a copy in a local bookstore and browse through it.
 
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@micromass. Thanks for the problem course link. I'll use it as a supplement to the Munkres text which I just ordered.

@Petek. Thanks for the idea. Like you said, it seems ideal as a supplement to another text since it is only an "outline."
 

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