02615nam 22004575 450 991030011400332120200704215126.03-030-00641-710.1007/978-3-030-00641-9(CKB)4100000007158811(DE-He213)978-3-030-00641-9(MiAaPQ)EBC6312029(PPN)232474265(EXLCZ)99410000000715881120181124d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierAn Introduction to the Language of Mathematics /by Frédéric Mynard1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XII, 185 p. 34 illus., 16 illus. in color.) 3-030-00640-9 Chapter 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.This 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.Proof theoryStructures and Proofshttps://scigraph.springernature.com/ontologies/product-market-codes/M24010Proof theory.Structures and Proofs.511.3511.36Mynard Frédéricauthttp://id.loc.gov/vocabulary/relators/aut732154MiAaPQMiAaPQMiAaPQBOOK9910300114003321Introduction to the Language of Mathematics1564654UNINA