03869nam a22005535i 4500 978-3-031-30488-0 DE-He213 20251030110909.0 cr nn 008mamaa 240103s2024 sz | s |||| 0|eng d 9783031304880 978-3-031-30488-0 10.1007/978-3-031-30488-0 doi QA297.4 PBD bicssc MAT008000 bisacsh PBD thema Tourlakis, George. author. aut http://id.loc.gov/vocabulary/relators/aut 68948 Discrete Mathematics [electronic resource] : A Concise Introduction / by George Tourlakis. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XVIII, 253 p. 24 illus., 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Synthesis Lectures on Mathematics & Statistics, 1938-1751 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. 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. Discrete mathematics. Computer science Mathematics. 64041 Set theory. 68949 Mathematical logic. 66195 Discrete Mathematics. Discrete Mathematics in Computer Science. Applications of Discrete Mathematics. 67427 Set Theory. 68950 General Logic. 68951 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031304873 Printed edition: 9783031304897 Printed edition: 9783031304903 Synthesis Lectures on Mathematics & Statistics, 1938-1751 https://doi.org/10.1007/978-3-031-30488-0 ZDB-2-SXSC 57016 57016