Set Theory
Set Theory
$68.99
USDSet 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.
- Accessible to students without a background in logic and logical notation
- Clear, detailed proofs written for students who are still learning how to compose a proof
- Usable by instructors who are not experts in axiomatic set theory
Reviews & endorsements
'… Cunningham neglects no opportunity to make the subject as accessible as possible. The mathematical development is rigorous, as it should be, but not excessively so. Although he starts from zero, that is not to say the book is easy, but any difficulty that arises is in the nature of the subject, and is no fault of the author's. Throughout the book, he offers many appropriate examples (or non-examples), and provides numerous and diverse exercises, which often prove results that are later used in the body of the text, drawing the reader into the subject.' Frederic Green, ACM SIGACT News
'This book fulfills its stated goals: 'The textbook is suitable for a broad range of readers, from undergraduate to graduate students, who desire a better understanding of the fundamental topics in set theory that may have been, or will be, overlooked in their other mathematics courses'.' Shoshana Friedman, MathSciNet
Product details
July 2016Adobe eBook Reader
9781316682401
0 pages
0kg
13 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 1. Introduction
- 2. Basic set building axioms and operations
- 3. Relations and functions
- 4. The natural numbers
- 5. On the size of sets
- 6. Transfinite recursion
- 7. The axiom of choice (revisited)
- 8. Ordinals
- 9. Cardinals.
