Discrete Mathematics

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.

Provides a concise approach with examples and exercises to help readers understand key definitions and theorems Features careful attention to current and updated terminology, mathematical techniques, and results Presents coverage of equivalence, order relations, minimal condition, and inductive definitions of functions

Auteur

George Tourlakis, Ph.D., is a Professor in the Department of Electrical Engineering and Computer Science at York University, Toronto, Canada. He obtained his B.Sc. in mechanical and electrical engineering from the National Technical University of Athens and his M.Sc. and Ph.D. in computer science from the University of Toronto. Dr. Tourlakis has authored eight books in computability, logic, and axiomatic set theory and has also authored several journal articles in computability and modal logic. His research interests include calculational logic, modal logic, proof theory, computability with partial oracles, and complexity theory.

Texte du rabat

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.

Contenu
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.