Intro to Set Theory

[Two Espressos]

Hello all,

 

I'm planning on doing a lot of reading this summer before I start my Ph.D. this fall, and one of the things I'd like to learn about is set theory.  Could any of you suggest an intro-level book on set theory that doesn't presuppose a lot of mathematical knowledge? There appear to be a lot of ostensibly "intro-level" set theory books; I'm having trouble finding one that fits my needs.  I'm in the humanities, so obviously my mathematics background is rather paltry, mostly limited to propositional and predicate logic, but I think I could handle a book with some rigor so long as the theorems, proofs, etc. are introduced slowly and only after having been given the requisite information needed to understand them.  I tried reading this book, but I quickly found it to be too difficult, as it began using notation without prior explanation.  What's worse, the book had no solutions to its exercises, which is terrible.

 

I was thinking about trying this book instead.  Is this a good choice?  Would you suggest something else instead?  My ideal text would have at least a handful of exercises--with solutions!-- and would be self-contained, i.e., providing all the knowledge necessary in the early sections to understand the later, more difficult sections.

 

Thanks! 

Edited April 28, 2013 by Two Espressos

[clurp]

What's your motivation for wanting to learn more about set theory? That makes a difference.

 

I just skimmed through the Halmos book online and it looks to me like it would take a lot of work for someone without much of a mathematics background to get much out of it. (Mathematicians have a habit of naming things which seems to downplay the difficulty involved in the subject. So "naive" set theory is not really so naive and you'll see graduate students walking around with books titled "algebra".) 

[Two Espressos]

What's your motivation for wanting to learn more about set theory? That makes a difference.

 

I just skimmed through the Halmos book online and it looks to me like it would take a lot of work for someone without much of a mathematics background to get much out of it. (Mathematicians have a habit of naming things which seems to downplay the difficulty involved in the subject. So "naive" set theory is not really so naive and you'll see graduate students walking around with books titled "algebra".) 

 

Thanks for responding, clurp.  I'm very interested in interdisciplinary work between the sciences and the humanities, especially as regards language, so I've begun exploring formal logic, which is intimately related to natural language.  I'd like gain a working knowledge of set theory as well--more than just a passing familiarity, but obviously much less than what graduate level maths students need-- because set theory is in some sense fundamental to mathematics, which also bears some relationship to natural language.

 

In short, I'd like to have a background in set theory that would enable me to use those ideas in my humanistic research.  Ideally, I'll be able to study set theory formally at my Ph.D. institution, but I wonder if I'll be able to find a course that will suit my needs, seeing as my maths background is minimal at best.

 

One other bit of relevant info: I've read and own this book, which very briefly treats set theory, and while I think it's a great text, I want to find a book that's more in-depth while still remaining accessible.

Edited April 30, 2013 by Two Espressos

[Guest dot.matrix]

While it's not a textbook, you might enjoy David Foster Wallace's book Everything and More. Not everyone likes his writing style with the excessive footnoting (I find it a bit annoying), but he is enthusiastic about the subject and provides some interesting historical details. I would advise looking at the reviews. At the very least there are some good references in the bibliography (which you can view in the preview). 

[ALeafOnTheWind]

One problem you'll run into is that basic set theory is a fundamental component of other fields of math, but courses on set theory itself tend to be for the more advanced, and will usually pre-suppose some base knowledge, especially notation.

 

To that end, you might be better off looking at an Analysis book to start (Since they often have a chapter on basic set theory and topology), and then once you get a handle on the basics and notation, switch to a set theory book. It is still possible that some notation will be pre-supposed in them, though... But if you're able to describe any notation that you're having trouble with, I know I, and I'm sure others here, would be willing to help you out.

 

I happened to have a couple of my old Analysis books on hand, so I checked them out. This one book looks pretty good for the very basics. It's called "An Introduction to Analysis" by James R. Kirkwood. The first chapter has a section on sets. It's only a few pages, but it introduces (Pretty standard) notation. Should help you out

Edited May 1, 2013 by ALeafOnTheWind

[Two Espressos]

dot.matrix and ALeafOnTheWind, thank you for your suggestions.  I remember seeing the DFW book on infinity in my university library; I'll have to check it out.  And per your advice, ALeafOnTheWind, I'll look into an Analysis book for the set theory basics.

[ANDS!]

There is no way I would spend money on Kirkwood if you're only interested in Set Theory from a non-mathemagician stand point.  YOu should be able to Google "Basic Set Theory" lecture notes and be able to find an instructors course materials on the topic.  Hell most ANY math book (even probability books) would have the basics of set theory if that is your goal.

 

If you are dead set on a "formal" text book, http://www.scribd.com/doc/5655796/Halmos-Naive-Set-Theory'>Naive Set Theory linked in your original posts seems to read like a good introduction to the topic.

[Two Espressos]

There is no way I would spend money on Kirkwood if you're only interested in Set Theory from a non-mathemagician stand point.

 

This might be the best typo on the internet.

[PompousPilots]

I like Discrete Mathematics by Rosen as an introduction to basic concepts and to mathematical thinking in general. It's a giant textbook, but don't be intimidated. You might only want to read the first couple chapters.

 

I'm sure your university library has it.

[Agradatudent]

I agree with others. Do not buy a set theory book and expect to learn anything out of it. If I were you, I'd look for an "introduction to mathematical proofs" book or a Schaum's outline on set theory. Otherwise, there won't be worked examples.

[notafrequentist]

http://www.jirka.org/ra/realanal.pdf

 

Here's a free Real Analysis book that covers set theory.

[Two Espressos]

http://www.jirka.org/ra/realanal.pdf

 

Here's a free Real Analysis book that covers set theory.

 

Cool, thanks for the link!  I appreciate the helpful advice and recommendations all of you have provided in this thread.

[gnufoo]

I would begin with a book on introductory discrete math from Dover, it should surely cover basic set theory. http://www.amazon.com/Discrete-Mathematics-Elementary-Beyond-Undergraduate/dp/0387955852/ref=sr_1_4?ie=UTF8&qid=1372121834&sr=8-4&keywords=discrete+math From there, I would suggest reading Smullyan's book on set theory. http://www.amazon.com/Theory-Continuum-Problem-Dover-Mathematics/dp/B00B55AVPI/ref=sr_1_9?s=books&ie=UTF8&qid=1372121959&sr=1-9&keywords=smullyan