Set Theory: A First Course (Cambridge Mathematical Textbooks)

I’m only in the first chapter but have skimmed the entire book. This is the kind of book that is ideal for self study: (1) it covers a sufficiently narrow topic so as not to get bogged down, (2) the material requires thought but no special intellectual athletic prowess like differential geometry or Hilbert spaces do, (3) it’s very well laid out with an index just for special symbols and operators, worth the price of the book in itself, and (4) it’s a slim volume, easy to carry around and hold, like the “Student’s Guide to …” series (most by Daniel Fleisch) (which I also highly recommend for the same reasons). This book is manufactured as print on demand, so the “hardcover” version is basically two boards glued to a glued-bound POD cheap paperback book. I always find cheap binding using generic printer paper to manufacture a reference book to be sad. But I guess I’d rather be sadly reading good content in a real book than reading a technical/reference book on the screen of a kindle app (where would I attach my post-its?).

Using the text as a reference in refreshing my skills in Set Theory. Accomplishing my goal!

Cunningham writes carefully and clearly. The book begins with a short introduction to logic notation and its meaning. The ZF axioms are listed together on page 24 of chapter one before used to develop the theory axiomatically, beginning in chapter two. A likely comparison to this book is Herbert Enderton's Elements of Set Theory (1977). Cunningham's book is a cleaner presentation. One difference is that Cunningham does not give a construction of the real numbers, as Enderton does. In his References, Cunningham lists 14 books. Set theory textbooks listed are Enderton's Elements, Halmos' Naive ST, Kunen's The Foundations of Mathematics, Levy's Basic ST, and Moschovakis' Notes on ST. Also listed, among others, are Potter's ST and Its Philosophy, and Enderton's A Mathematical Introduction to Logic. To my mind, Cunningham's Set Theory : A First Course is the best introduction to set theory in the English language.

The content is good but the author introduces symbols without defining them explicitly, expecting you to understand from context. The symbol notation is also sometimes inconsistent. The equations also appear very small on the ipad but PC is fine.

I just got this book for Christmas and started reading. Cunningham wrote another book: A LOGICAL INTRODUCTION TO PROOFS. i like the guy. I feel with other people--and still remember the pain of students, when they were exposed to MATHEMATICAL ANALYSIS right after the usual calculus courses. I JUST DO NOT GET IT: WHY TORTURE THEM? There should be two tracks for math students; An ABSTRACT and an APPLIED one. The two tracks should be cleanly separated. LOGIC, SET THEORY, MEASURE THEORY, ABSTRACT ALGEBRA, ANALYSIS,...is the abstract one. CALCULUS, MATHEMATICS FOR PHYSICS AND ENGINEERING, interwoven with PYTHON,...the applied one. Both have different cultures. In ABSTRACT TRACK, you are extremely careful. In THE APPLIED, you play and experiment, and accept stuff without using an electronic microscope. Cunningham's logic is a little stilted. There is another more natural approach (KALISH & MONTAGUE: LOGIC--TECHNIQUES OF FORMAL REASONING), which mirrors more how mathematicians think. But all in all, he is so right with his suggestion that students need the preparation he is offering with his two books to start their abstract journey.

I graduated in mathematics many, many years ago but I always worked on other things, never in Math. I read this book and did almost all the exercises in about 6 months of self-study. The book is simply excellent, very well written, I recommend it 100%. I even wrote to the author several times and he always responded promptly with kindness. The best book at its level on the market.

Achei esse livro um prato cheio para todos aficcionados pelos fundamentos da matemática.Gostei muito da prova do lema de Zorn etc. O produto chegou dentro do prazo,em perfeito estado e o conteúdo é melhor do que eu esperava. Super indico

Been reading this to help understand the notation for some of the literature relevant to my research project whilst enjoyably learning about Set Theory itself. Full of great exercises and examples, but not the repetitive kind that bored you at school. Very well written, makes one feel very clever. I'm reading as a post graduate zoologist with no mathematical training since A Level and it is satisfyingly challenging but doesn't force you to scour the internet to understand what the hell it's talking about like some books I've encountered.

I love this book. It starts with the basics although presented more as a reminder of Naive set theory. It advances steadily into axiomatic set theory providing a firm grounding in the subject. Not as a first book in the topic but mightily useful to move on with once the basics are assimilated. The text would support any decent course on the topic but is very informative for the more mathematically mature enquirer.