LEADER 04635nam 22007095 450 001 9910438159603321 005 20200705031518.0 010 $a1-4614-6636-9 024 7 $a10.1007/978-1-4614-6636-9 035 $a(CKB)3390000000037140 035 $a(EBL)1316884 035 $a(OCoLC)870244191 035 $a(SSID)ssj0000904258 035 $a(PQKBManifestationID)11479089 035 $a(PQKBTitleCode)TC0000904258 035 $a(PQKBWorkID)10919669 035 $a(PQKB)10155087 035 $a(DE-He213)978-1-4614-6636-9 035 $a(MiAaPQ)EBC6312822 035 $a(MiAaPQ)EBC1316884 035 $a(Au-PeEL)EBL1316884 035 $a(CaPaEBR)ebr10970547 035 $a(PPN)170487733 035 $a(EXLCZ)993390000000037140 100 $a20130510d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn Invitation to Abstract Mathematics /$fby Béla Bajnok 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (406 p.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aDescription based upon print version of record. 311 $a1-4899-9560-9 311 $a1-4614-6635-0 327 $aPreface to Instructors -- Preface to Students -- Acknowledgments -- I What's Mathematics -- 1 Let's Play a Game! -- 2 What's the Name of the Game? -- 3 How to Make a Statement?- 4 What's True in Mathematics? -- 5 Famous Classical Theorems -- 6 Recent Progress in Mathematics -- II How to Solve It? -- 7 Let's be Logical! -- 8 Setting Examples -- 9 Quantifier Mechanics -- 10 Mathematical Structures -- 11 Working in the Fields (and Other Structures) -- 12 Universal Proofs -- 13 The Domino Effect -- 14 More Domino Games -- 15 Existential Proofs -- 16 A Cornucopia of Famous Problems -- III Advanced Math for Beginners -- 17 Good Relations -- 18 Order, Please! -- 19 Let's be Functional! -- 20 Now That's the Limit! -- 21 Sizing It Up -- 22 Infinite Delights -- 23 Number Systems Systematically -- 24 Games Are Valuable! -- IV. Appendices -- A. Famous Conjectures in Mathematics -- B The Foundations of Set Theory -- C All Games Considered -- D Top 40 List of Math Theorems. - Index. 330 $aThis undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind.  The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to enthuse.  The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader.  With a unified approach to a diverse collection of topics, this text points out connections, similarities, and differences among subjects whenever possible.  This book shows students that mathematics is a vibrant and dynamic human enterprise by including historical perspectives and notes on the giants of mathematics, by mentioning current activity in the mathematical community, and by discussing many famous and less well-known questions that remain open for future mathematicians. Ideally, this text should be used for a two semester course, where the first course has no prerequisites and the second is a more challenging course for math majors; yet, the flexible structure of the book allows it to be used in a variety of settings, including as a source of various independent-study and research projects. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aMathematics 606 $aHistory 606 $aLogic, Symbolic and mathematical 606 $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 615 0$aMathematics. 615 0$aHistory. 615 0$aLogic, Symbolic and mathematical. 615 14$aMathematics, general. 615 24$aHistory of Mathematical Sciences. 615 24$aMathematical Logic and Foundations. 676 $a153.43 700 $aBajnok$b Béla$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521435 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438159603321 996 $aInvitation to abstract mathematics$9836867 997 $aUNINA