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So I'm doing calculus at this moment in my first year, but I think I'm lacking in terms of mathematical notation, logic, etc.

After some research I found that Set Theory is sort of mandatory for any mathematics major and I decided to start learning it on my own. I got the book "Naive Set Theory" by Halmos and have just started reading. However,I'm finding it time consuming.

Is the book good for starters? And is high school mathematics background enough to learn Set Theory on my own while doing calculus(currently doing functions, limits, etc) at university?

Thanks

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  • $\begingroup$ I am not professional enough to answer this, and I am not familiar with the book you mention. Based on my own experience I can only say that Set Theory does not (or hardly) require you to have other mathematical stuff at your disposal. A high school background was enough for me. Success. $\endgroup$ – drhab Mar 19 '14 at 20:23
  • $\begingroup$ For a more interactive approach, may I humbly suggest my proof-checking software with accompanying tutorial. It may be more directly applicable to your situation than a textbook devoted to set theory. Visit my website for a video demo and free download at dcproof.com Write to me if you have any problems at all. $\endgroup$ – Dan Christensen Mar 19 '14 at 21:02
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In my opinion if you have some idea of what a $proof$ is then $Naive$ $Set$ $Theory$ does not need any particular prerequisites (atleast for first $10$ or $12$ chapters). However sometime it seems very dry due to the fact that a particular statement may look obvious to you (though it may not be!) but you'll find a proof for that in the book. The best strategy to read it (in my opinion) is to form a study group of $3-4$ people and discuss among each other.

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  • $\begingroup$ Ah, I got problems with proofs as well. I'm actually reading the book "How to read and do proofs" By Solow, since I don't have any prior experience with proofs. It's pretty hectic at this time since I'm trying to cope with functions(which is tougher than high school functions), trying to learn proofs and set theory on my own. What other books would you suggest? $\endgroup$ – Sab ಠ_ಠ Mar 19 '14 at 20:19
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    $\begingroup$ Although I first learned set theory in a course, I am familiar with Halmos’s book, and as I recall, it’s as good as you can get. What you need above all, as @wanderer suggests, is mathematical maturity, and you get that just with experience. $\endgroup$ – Lubin Mar 19 '14 at 20:21
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    $\begingroup$ that is where study groups can help...learn through discussion and seek the help of an instructor when needed. also have patience...you'll learn things with experience...Halmos' book is the best one for introduction simply because he is Halmos :) $\endgroup$ – wanderer Mar 19 '14 at 20:24
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    $\begingroup$ Thanks guys. Looks like it will take some great deal of understanding, practice and patience to reach the mathematical maturity. I'll be asking loads of questions around here very soon. $\endgroup$ – Sab ಠ_ಠ Mar 19 '14 at 20:28
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If you're looking for a good beginning that incorporates both set theory and logic, I'd really recommend 'How to Prove it - A structured approach by Velleman as only the most basic of high school mathematics is assumed. While Halmos is good as a reference, it is not a good way to begin set theory. Velleman will provide you with all the rudiments you need to tackle proofs and proofs involving sets. Hope this helps!

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