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＜電子ブック＞
An Introduction to the Language of Mathematics / by Frédéric Mynard

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	XII, 185 p. 34 illus., 16 illus. in color : online resource
著者標目	*Mynard, Frédéric author SpringerLink (Online service)
件　名	LCSH:Proof theory FREE:Proof Theory and Constructive Mathematics
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-00641-9

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