An introduction to the language of mathematics / Frédéric Mynard.

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An introduction to the language of mathematics / Frédéric Mynard.

9783030006419 (electronic book)
3030006417 (electronic book)
9783030006402

Cham, Switzerland : Springer, 2018.

English

1 online resource (xii, 185 pages) : illustrations

10.1007/978-3-030-00641-9 doi

QA9.54

511.3/6

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.-- Provided by publisher.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed December 5, 2018).

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