LEADER 02615nam 22004575 450 001 9910300114003321 005 20200704215126.0 010 $a3-030-00641-7 024 7 $a10.1007/978-3-030-00641-9 035 $a(CKB)4100000007158811 035 $a(DE-He213)978-3-030-00641-9 035 $a(MiAaPQ)EBC6312029 035 $a(PPN)232474265 035 $a(EXLCZ)994100000007158811 100 $a20181124d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to the Language of Mathematics /$fby Frédéric Mynard 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XII, 185 p. 34 illus., 16 illus. in color.) 311 $a3-030-00640-9 327 $aChapter 1- The language of logic and set-theory -- Chapter 2- On proofs and writing mathematics -- Chapter 3- Relations -- Chapter 4- Cardinality -- Appendix A- Complements -- Appendix B- Solutions to exercises in the text -- Index -- Bibliography. 330 $aThis is a textbook for an undergraduate mathematics major transition course from technique-based mathematics (such as Algebra and Calculus) to proof-based mathematics. It motivates the introduction of the formal language of logic and set theory and develops the basics with examples, exercises with solutions and exercises without. It then moves to a discussion of proof structure and basic proof techniques, including proofs by induction with extensive examples. An in-depth treatment of relations, particularly equivalence and order relations completes the exposition of the basic language of mathematics. The last chapter treats infinite cardinalities. An appendix gives some complement on induction and order, and another provides full solutions of the in-text exercises. The primary audience is undergraduate mathematics major, but independent readers interested in mathematics can also use the book for self-study. 606 $aProof theory 606 $aStructures and Proofs$3https://scigraph.springernature.com/ontologies/product-market-codes/M24010 615 0$aProof theory. 615 14$aStructures and Proofs. 676 $a511.3 676 $a511.36 700 $aMynard$b Frédéric$4aut$4http://id.loc.gov/vocabulary/relators/aut$0732154 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300114003321 996 $aIntroduction to the Language of Mathematics$91564654 997 $aUNINA