Set Theory

A First Course

AvDaniel W. Cunningham

Inbunden, Engelska, 2016

Del i serien Cambridge Mathematical Textbooks

630 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-07-18
Mått:157 x 235 x 20 mm
Vikt:510 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Mathematical Textbooks
Antal sidor:262
Förlag:Cambridge University Press
ISBN:9781107120327

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik

Mer om författaren

Daniel W. Cunningham is a Professor of Mathematics at State University of New York, Buffalo, specializing in set theory and mathematical logic. He is a member of the Association for Symbolic Logic, the American Mathematical Society, and the Mathematical Association of America. Cunningham's previous work includes A Logical Introduction to Proof, which was published in 2013.

Recensioner i media

'… 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

Innehållsförteckning

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.