Sets, Functions, and Logic

An Introduction to Abstract Mathematics

Keith Devlin

143 pages, parution le 05/01/2004

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Résumé

Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students.

Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead.

Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read…and enjoy…and learn from.

L'auteur - Keith Devlin

Directeur du Centre d'étude du langage et de l'information de l'université de Stanford où il enseigne également les mathématiques, Keith Devlin est l'auteur de nombreux ouvrages, notamment de vulgarisation qui ont rencontré un large succès, comme, au Pommier, Les Énigmes mathématiques du 3e millénaire.

Sommaire

Students start here
What is mathematics and what does it do for us?
- It's Not Just Numbers
- Mathematical Notation
- Making the Invisible Visible
- This is Where You Come In
- The Study of Modern Mathematics
Math speak
- The Language of Mathematics: Part 1
- Properties of the Language
- The Language of Mathematics: Part 2
- Properties of Quantification
- Proofs in Mathematics
- The Integers
- Mathematical Truth
Set theory
- Sets
- Operations on Sets
- Real Intervals
- Absolute Values
- Inequalities
- Arbitrary Unions and Intersections
- Cartesian Products
- The Historical Development of Set Theory
Functions
- The Function Concept
- Examples of Functions
- History of the Modern Function Concept
- One-One and onto Functions
- Composition and Inverse Functions
- Denumerability
- Uncountability
Relations
- Binary Relations
- Properties of Relations
- Relations as Sets of Ordered Pairs
- Relations as Graphs
- Equivalence Relations
- Functions as Relations
- An Example: the Reals
- Upper Bounds. Completeness
- Sequences
- No Answers to the Exercises
- List of Symbols
- Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Keith Devlin
Parution	05/01/2004
Nb. de pages	143
Format	16 x 24
Couverture	Relié
Poids	360g
Intérieur	Noir et Blanc
EAN13	9781584884491
ISBN13	978-1-58488-449-1