LEADER 03175nam 2200601 450 001 9910819903003321 005 20230807213537.0 010 $a0-19-870644-8 010 $a0-19-101647-0 035 $a(CKB)3710000000355060 035 $a(EBL)1961795 035 $a(OCoLC)903858749 035 $a(SSID)ssj0001468442 035 $a(PQKBManifestationID)11884037 035 $a(PQKBTitleCode)TC0001468442 035 $a(PQKBWorkID)11521499 035 $a(PQKB)10166442 035 $a(MiAaPQ)EBC1961795 035 $a(Au-PeEL)EBL1961795 035 $a(CaPaEBR)ebr11019693 035 $a(CaONFJC)MIL728833 035 $a(EXLCZ)993710000000355060 100 $a20150302h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe foundations of mathematics /$fIan Stewart and David Tall 205 $aSecond edition. 210 1$aNew York, New York :$cOxford University Press,$d2015. 210 4$dİ2015 215 $a1 online resource (409 p.) 300 $aDescription based upon print version of record. 311 $a1-322-97551-5 311 $a0-19-870643-X 320 $aIncludes bibliographical references and index. 327 $aCover -- 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. 330 $aThe 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 stude 606 $aMathematics 606 $aLogic, Symbolic and mathematical 615 0$aMathematics. 615 0$aLogic, Symbolic and mathematical. 676 $a510 700 $aStewart$b Ian$f1945-$0447732 702 $aTall$b David Orme 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819903003321 996 $aThe foundations of mathematics$94093911 997 $aUNINA