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An introduction to the language of mathematics

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An introduction to the language of mathematics/ by Frederic Mynard.
作者:	Mynard, Frederic.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xii, 185 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Proof theory. -
電子資源:	https://doi.org/10.1007/978-3-030-00641-9
ISBN:	9783030006419

An introduction to the language of mathematics
Mynard, Frederic.

An introduction to the language of mathematics[electronic resource] /by Frederic Mynard. - Cham :Springer International Publishing :2018. - xii, 185 p. :ill. (some col.), digital ;24 cm.

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.

ISBN: 9783030006419

Standard No.: 10.1007/978-3-030-00641-9doiSubjects--Topical Terms:

579943
Proof theory.

LC Class. No.: QA9.54 / .M963 2018

Dewey Class. No.: 511.36

An introduction to the language of mathematics
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505 0 $a 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.
520 $a 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.
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