000 a
999 _c33749
_d33749
008 250227b xxu||||| |||| 00| 0 eng d
020 _a9783031304873
_c(hbk)
082 _a511.1
_bTOU
100 _aTourlakis, George
245 _aDiscrete mathematics : a concise introduction
260 _bSpringer,
_c2024
_aCham :
300 _axviii, 253 p. ;
_bill.,
_c25 cm
365 _b39.99
_c
_d93.20
490 _aSynthesis Lectures on Mathematics & Statistics
504 _aIncludes bibliographical references and index.
520 _aThis 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.
650 _aDiscrete mathematics
650 _aTransitive closure
650 _aAxiomatic set theory
650 _aDeduction theorem
650 _aEquivalence relation
650 _aRussell's paradox
942 _2ddc
_cBK