03175nam 2200601 450 991081990300332120230807213537.00-19-870644-80-19-101647-0(CKB)3710000000355060(EBL)1961795(OCoLC)903858749(SSID)ssj0001468442(PQKBManifestationID)11884037(PQKBTitleCode)TC0001468442(PQKBWorkID)11521499(PQKB)10166442(MiAaPQ)EBC1961795(Au-PeEL)EBL1961795(CaPaEBR)ebr11019693(CaONFJC)MIL728833(EXLCZ)99371000000035506020150302h20152015 uy 0engur|n|---|||||txtccrThe foundations of mathematics /Ian Stewart and David TallSecond edition.New York, New York :Oxford University Press,2015.©20151 online resource (409 p.)Description based upon print version of record.1-322-97551-5 0-19-870643-X Includes bibliographical references and index.Cover -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Part I The Intuitive Background -- 1 Mathematical Thinking -- 2 Number Systems -- Part II The Beginnings of Formalisation -- 3 Sets -- 4 Relations -- 5 Functions -- 6 Mathematical Logic -- 7 Mathematical Proof -- Part III The Development of Axiomatic Systems -- 8 Natural Numbers and Proof by Induction -- 9 Real Numbers -- 10 Real Numbers as a Complete Ordered Field -- 11 Complex Numbers and Beyond -- Part IV Using Axiomatic Systems -- 12 Axiomatic Systems, Structure Theorems, and Flexible Thinking -- 13 Permutations and Groups -- 14 Cardinal Numbers -- 15 Infinitesimals -- Part V Strengthening the Foundations -- 16 Axioms for Set Theory -- Appendix: How to Read Proofs: The 'Self-Explanation' Strategy -- References and Further Reading -- Index.The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on studeMathematicsLogic, Symbolic and mathematicalMathematics.Logic, Symbolic and mathematical.510Stewart Ian1945-447732Tall David OrmeMiAaPQMiAaPQMiAaPQBOOK9910819903003321The foundations of mathematics4093911UNINA