Set Theory: A First Course (Cambridge Mathematical Textbooks) 1st Edition by Daniel W. Cunningham (PDF)

Description

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐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.

⭐This book is an amazing too for learning about Set theory. Full of exercises for you to do.However there are no solutions to the exercises which is a huge annoyance.You can’t find them online either.

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