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020 _a9781461466369
_9978-1-4614-6636-9
024 7 _a10.1007/978-1-4614-6636-9
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
082 0 4 _a510
_223
100 1 _aBajnok, Béla.
_eauthor.
245 1 3 _aAn Invitation to Abstract Mathematics
_h[electronic resource] /
_cby Béla Bajnok.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXIV, 406 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUndergraduate Texts in Mathematics,
_x0172-6056
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aHistory.
650 0 _aMathematical logic.
650 1 4 _aMathematics.
650 2 4 _aMathematics, general.
650 2 4 _aHistory of Mathematical Sciences.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461466352
830 0 _aUndergraduate Texts in Mathematics,
_x0172-6056
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-6636-9
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c44678
_d44678