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Some background about me.

I study on my own and I am not a math major but I am interested in math. I am not even sure if I am mathematically mature enough to handle the 2 topics but I have read a few books.

Books I have read and finished: *Kiselev's Geometry *Gelfands Algebra and Trigononetry *Tasarov's Calculus: Basic Concept for High School

I have read the "foundation" part of the 3 Calculus book by Spivak, Courant, or Apostol. Although, I did not continue reading the rest of the book, I do know about the techiques of differentiation and integration. Honestly, I don't have any goal in mind in learning math but for now I am just doing it for self fulfillment of sorts.

Which of the topic is easier to read?

tighten
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  • Instead of easier, I'd go for interesting, and then abstract algebra wins. – lhf Aug 16 '17 at 13:45
  • @lhf Does abstract algebra require a thorough knowledge on sets to understand it? – tighten Aug 16 '17 at 14:13
  • Not really. But it does require the ability to read set notation and to reason with symbols. All the set theory you needed more is contained in the first chapter of Topology by Munkres. – lhf Aug 16 '17 at 14:17
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    Most of the set theory you would need for the level you're talking about is basically trivial. It could be picked up from the internet, most of the books like Apostol Calculus Vol 1. Would have shown you enough. You could look at How to Prove it, by Velleman which has a pretty decent coverage of logic and set theory. Due to what you say you've seen, I would second the "interesting." – smokeypeat Aug 16 '17 at 20:15
  • @user221227 I think what you have suggested is a good read. I will try to pi ck that up first and probably go to abstract algebra after. While reading the books I always thought to myself if I am thinking "correctly". My only guide was myself and two after certain amount of reading I made a rule that as long as I can break down all my proofs and it follows from the rules/axiom set by the author then I am fine. After finishing both I planned to pick up Apostol again. – tighten Aug 17 '17 at 07:45

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