#5 in Mathematical logic books
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Reddit mentions of Naive Set Theory (Undergraduate Texts in Mathematics)
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Reddit mentions: 12
We found 12 Reddit mentions of Naive Set Theory (Undergraduate Texts in Mathematics). Here are the top ones.
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I was once a teacher's aide for an autistic teen. He seemed very bored with the 3rd grade arithmetic the teacher thought was his limit. One day, we had some extra time. I asked him if he wanted to read my set theory book. It's difficult to assess consent and comprehension, but we have our ways. I figured out that not only did he like this book, but he could follow along. It took about 3 months, but he was able to learn basics of sets. What makes me sad is the hard truth that people who know about this kind of math, generally don't find themselves being an educator for special needs students. His higher math education ended when I left. That's not right.
You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me.
Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good.
Basically, don't limit yourself to the track you see before you. Explore and enjoy.
In response to the same question, my Logic professor suggested:
There are a few options. Firstly, if you are more familiar using infinity in the context of Calculus, then you might want to look into Real Analysis. These subjects view infinity in the context of limits on the real line and this is probably the treatment you are probably most familiar with. For an introductory book on the subject, check out Baby Rudin (Warning: Proofs! But who doesn't like proofs, that's what math is!)
Secondly, you might want to look at Projective Geometry. This is essentially the type of geometry you get when you add a single point "at infinity". Many things benefit from a projective treatment, the most obvious being Complex Analysis, one of its main objects of study is the Riemann Sphere, which is just the Projective Complex Plane. This treatment is related to the treatment given in Real Analysis, but with a different flavor. I don't have any particular introductory book to recommend, but searching "Introductory Projective Geometry" in Amazon will give you some books, but I have no idea if they're good. Also, look in your university library. Again: Many Proofs!
The previous two treatments of infinity give a geometric treatment of the thing, it's nothing but a point that seems far away when we are looking at things locally, but globally it changes the geometry of an object (it turns the real line into a circle, or a closed line depending on what you're doing, and the complex plane into a sphere, it gets more complicated after that). But you could also look at infinity as a quantitative thing, look at how many things it takes to get an infinite number of things. This is the treatment of it in Set Theory. Here things get really wild, so wild Set Theory is mostly just the study of infinite sets. For example, there is more than one type of infinity. Intuitively we have countable infinity (like the integers) and we have uncountable infinity (like the reals), but there are even more than that. In fact, there are more types of infinities than any of the infinities can count! The collection of all infinities is "too big" to even be a set! For an introduction into this treatment I recommend Suppes and Halmos. Set Theory, when you actually study it, is a very abstract subject, so there will be more proofs here than in the previous ones and it may be over your head if you haven't taken any proof-based courses (I don't know your background, so I'm just assuming you've taken Calc 1-3, Diff Eq and maybe some kind of Matrix Algebra course), so patience will be a major virtue if you wish to tackle Set Theory. Maybe ask some professors for help!
I haven't read it myself, but I have heard Naive Set Theory recommended here several times before.
Two great introductions are:
both are short and very well written. Some books particularly close to my heart are:
Naive Set Theory if you want a more textbook approach, the book mentioned in my other response if you're looking for something more like a story with proofs.
Still the best math book cover ever
Halmos's Naive Set Theory is a classic.
http://www.amazon.com/Naive-Theory-Undergraduate-Texts-Mathematics/dp/0387900926/ref=sr_1_1?ie=UTF8&qid=1320969231&sr=8-1
Naive Set Theory , by Halmos
http://www.amazon.ca/Naive-Set-Theory-P-Halmos/dp/0387900926/ref=sr_1_2?ie=UTF8&qid=1348249606&sr=8-2
Concepts of Modern Mathematics by Ian Stewart is an excellent book about modern math. As is Foundations and Fundamental Concepts of Mathematics by Howard Eves I would recommend these two along with the far more expensive Naive Set Theory by Halmos
IMHO if you don't understand AC and its equivalents, then Jech is not the book you should be reading. That book is pretty heavy and is used (as far as I know - I have a handful of friends who work in set theory) as a research reference. Maybe read Naive Set Theory first. Despite its name, it's reasonably advanced but way more readable.