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Discrete Mathematics A Concise Introduction
Author
Title
Discrete Mathematics [electronic resource] : A Concise Introduction / by George Tourlakis.
ISBN
9783031304880
Edition
1st ed. 2024.
Publication
Cham : Springer International Publishing : Imprint: Springer, 2024.
Physical Description
1 online resource (XVIII, 253 p.) 24 illus., 2 illus. in color.
Local Notes
Access is available to the Yale community.
Access and use
Access restricted by licensing agreement.
Summary
This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. "Safe" - that is, paradox-free - informal set theory is introduced following on the heels of Russell's Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor's diagonalisation technique. Predicate logic "for the user" is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics. In addition, this book: Provides a concise but mathematically rigorous and correct approach with examples and exercises to help readers understand key definitions and theorems; Features careful attention to current mathematical terminology, mathematical techniques, and results; Presents coverage of equivalence and order relations, minimal condition, and inductive definitions of functions and sets.
Variant and related titles
Springer Nature Synthesis Collection of Technology.
Other formats
Printed edition:
Printed edition:
Printed edition:
Format
Books / Online
Language
English
Added to Catalog
January 17, 2024
Series
Synthesis Lectures on Mathematics & Statistics,
Contents
Elementary Informal Set Theory
Safe Set Theory
Relations and Functions
A Tiny Bit of Informal Logic
Inductively Defined Sets and Structural Induction
Recurrence Equations
Trees and Graphs.
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