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Topology books

  1. Dec 9, 2013 #1
    Hello :) I am looking for some books for an intro to topology and what other books I need to supplement my readings not quite sure the prereqs for topology but I am willing to learn the stuff needed thank you!

    P.S Physical textbooks are what I am looking for but if thats not available then online stuff is fine.
     
  2. jcsd
  3. Dec 9, 2013 #2
    What is your math background?
     
  4. Dec 9, 2013 #3
    Grade 12 university stream math (Canadian system) U math is the equivalent to AP in America I think.
    Pre-calc, some calc knowledge and that's it.

    Will I need to know abstract algebra and stuff like that?
     
  5. Dec 9, 2013 #4
    In principle, no (and in practice no to abstract algebra) but topology might be hopelessly abstract if you have not encountered other abstract math and proofs before. Some exposure to metric spaces and proofs would be very useful.

    What do you need topology for?

    In any event, a very light, intuitive introduction to topology is Janich, Topology and the standard undergraduate topology textbook is Munkres, Topology.
     
  6. Dec 9, 2013 #5
    Just a curious cat if you will and since my semester coming up is going to be easy (some tech classes and Chemistry) it means I will have plenty of time to learn new stuff and satisfy a curious mind. I will check out those books I probably will only look at the Undergrad text books not much more.

    Too kind of fit into this though no reason to open another thread but any good abstract algebra textbooks to supplement my readings?
     
    Last edited: Dec 9, 2013
  7. Dec 9, 2013 #6
    Study analysis first. Topological spaces are abstractions of metric spaces. If you don't get metric spaces, topological spaces will be meaningless.

    If you understand continuity in metric spaces with the idea of "distance", then the idea of mapping open sets to open sets and closed sets to closed sets is a completely natural extension.
     
  8. Dec 9, 2013 #7
    Alrighty and analysis is just an extension of calculus right? Aren't those related.
     
  9. Dec 10, 2013 #8

    jgens

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    Gold Member

    I second the opinion that you should study elementary analysis before point-set topology. Doing so motivates the definitions to come and also gives you a nice class of topological spaces to use for intuition. In any case, whenever you decide the learn some point-set topology, you can pick pretty much any book. Most people will not need much more point-set topology than is covered in a first course, and when additional material is needed, most textbooks will introduce the relevant topological notions at that time.

    As for recommended algebra books:
    1. Abstract Algebra by Dummit and Foote is decent but uninspiring.
    2. Algebra by Artin is supposed to be great. I've never skimmed through it, but I hear good things.
    3. Algebra by Lang is a fantastic book. Probably not ideal for a first run through the material, but it has great perspective.
    Hopefully this all helps!
     
  10. Dec 10, 2013 #9
    Pinter is a very light introduction to abstract algebra. Nicholson, Introduction to Abstract Algebra is a more mature text but still undergraduate level (He covers basic proof techniques which may be useful to you).
     
  11. Dec 10, 2013 #10
    Youre still in high school and have had no exposure to undergrad Maths by the looks of it, I would not recommend jumping straight into real analysis or abstract algebra. Get "Numbers and Proofs" by Allenby, this is a gem of a book written to help people transition from school/informal to undergrad Maths. After you have thoroughly completed that, get Spivak's book on Calculus. And then after that, look into analysis/topology and abstract algebra.
     
  12. Dec 10, 2013 #11

    WannabeNewton

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    Science Advisor

    Woah you gotta back it up a bit there :wink:

    There are basically no pedagogically good texts on point-set topology. If you don't have a good teacher then self-studying it isn't going to be all that fruitful to be quite honest. It's easy to get a grasp of topology at a surface level using the various point-set topology texts but getting to know the tricks, techniques, subtleties, and mode of thinking that one requires for topology really takes a competent teacher. If you are already well experienced with pure math (e.g. you've mastered real analysis at the level of baby Rudin) then you could probably pick up just about any standard point-set topology text, self-study it, and find it very fruitful. But given that you only know pre-calc and calc, you're stepping way out of the zone of pragmatism here if you don't have a friend or mentor who can help you with problem sets and questions as you work through a topology text.

    In other words, I'm agreeing with the poster directly above. If you can get access to Spivak somehow, peruse through it and see how accessible it is to you.
     
  13. Dec 10, 2013 #12
    Or check Calculus by Lax. It seems like it could be serious competition for spivak:
    https://www.amazon.com/Calculus-Applications-Undergraduate-Texts-Mathematics/dp/1461479452
     
    Last edited by a moderator: May 6, 2017
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