Basic language of mathematics

by Schaffer, Juan Jorge

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Title Statements

Full title :Basic language of mathematics / Juan Jorge Schäffer, Carnegie Mellon University, USA.

Summary

"This book originates as an essential underlying component of a modern, imaginative three-semester honor program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable. The book is intended to provide a comprehensive and rigorous account of the concepts of set, mapping, family, order, number (both natural and real), as well as such distinct procedures as proof by induction and recursive definition, and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and information on alternative presentations. The work ends with an excursion on infinite sets, principally a discussion of the mathematics of Axiom of Choice and often very useful equivalent statements."--Back cover.

Edition Statements

Publication Date:©2014

Publication Statements

Publisher(s):World Scientific
Place of Publication:New Jersey
Language:eng
Publication Date:©2014

Notes

Includes indexes.

The Physical Object

Description:x, 310 pages ; : 26 cm

Edition Identifiers

ISBN:9789814596091, 9814596094
oclc:ocn871789758
LC Classification:QA37.3
Dewey Decimal:510

Preface -- Sets -- Mappings -- Properties of mappings -- Families -- Relations -- Ordered sets -- Completely ordered sets -- Induction and recursion -- The natural numbers -- Finite sets -- Finite sums -- Countable sets -- Some algebraic structures -- The real numbers: complete ordered fields -- The real-number system -- The real numbers: existence -- Infinite sets -- Indexes.