An Introduction to the Language of Mathema...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Frédéric Mynard is currently a professor of mathematics at New Jersey City University. Originally from France where he obtained his PhD in 1999, he has been teaching at various universities in the US since 2001, teaching a wide spectrum of mathematics courses, from entry level to graduate courses. A topologist, he has published 35 peer-reviewed research papers, and the book Convergence Foundations of Topology, revisiting classical General Topology from the point of view of his area of research: convergence spaces.

Zusammenfassung

Includes both solved and unsolved exercises

Includes informal discussions of aspects of philosophy of mathematics, and of the relation between certain mathematical notions and thought processes

Helps engage students in a reflexion on the nature of mathematics and periodically breaks away from technicalities

Provides a more extensive treatment of relations, including equivalence relations and order relations, than most comparable books

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Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Grundlagen
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xii 185 S. 18 s/w Illustr. 16 farbige Illustr. 185 p. 34 illus. 16 illus. in color.
ISBN-13:	9783030006402
ISBN-10:	3030006409
Sprache:	Englisch
Herstellernummer:	978-3-030-00640-2
Einband:	Gebunden
Autor:	Mynard, Frédéric
Auflage:	1st edition 2018
Hersteller:	Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 17 mm
Von/Mit:	Frédéric Mynard
Erscheinungsdatum:	10.12.2018
Gewicht:	0,471 kg