An Introduction to the Language of Mathematics. 1st ed. 2018

種類:

電子ブック

責任表示:

by Frédéric Mynard

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Mynard, Frédéric.
• SpringerLink (Online service)

ISBN:

9783030006419 [3030006417]    

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.

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