LEADER 04875nam 22006735 450 001 9910373923603321 005 20230810132339.0 010 $a3-030-34209-3 024 7 $a10.1007/978-3-030-34209-8 035 $a(CKB)4900000000505158 035 $a(DE-He213)978-3-030-34209-8 035 $a(MiAaPQ)EBC6113499 035 $a(PPN)242845614 035 $a(EXLCZ)994900000000505158 100 $a20200110d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematics in Computing $eAn Accessible Guide to Historical, Foundational and Application Contexts /$fby Gerard O?Regan 205 $a2nd ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XXVI, 458 p. 206 illus., 73 illus. in color.) 225 1 $aUndergraduate Topics in Computer Science,$x2197-1781 311 $a3-030-34208-5 327 $aWhat is a Computer? -- Foundations of Computing -- Overview of Mathematics in Computing -- Introduction to Algorithms -- Number Theory -- Algebra -- Sequences, Series, and Permutations and Combinations -- Mathematical Induction and Recursion -- Graph Theory -- Cryptography -- Coding Theory -- Language Theory and Semantics -- Computability and Decidability -- Matrix Theory -- A Short History of Logic -- Propositional and Predicate Logic -- Advanced Topics in Logic -- The Nature of Theorem Proving -- Software Engineering Mathematics -- Software Reliability and Dependability -- Overview of Formal Methods -- Z Formal Specification Language -- Automata Theory -- Model Checking -- Probability and Statistics -- Complex Numbers and Quaternions -- Calculus -- Epilogue. 330 $aThis illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. Topics and features: Includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary Describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann Introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices Explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory Reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking Covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving Presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader. 410 0$aUndergraduate Topics in Computer Science,$x2197-1781 606 $aComputer science$xMathematics 606 $aMachine theory 606 $aCoding theory 606 $aInformation theory 606 $aMathematics 606 $aHistory 606 $aMathematical Applications in Computer Science 606 $aFormal Languages and Automata Theory 606 $aCoding and Information Theory 606 $aHistory of Mathematical Sciences 615 0$aComputer science$xMathematics. 615 0$aMachine theory. 615 0$aCoding theory. 615 0$aInformation theory. 615 0$aMathematics. 615 0$aHistory. 615 14$aMathematical Applications in Computer Science. 615 24$aFormal Languages and Automata Theory. 615 24$aCoding and Information Theory. 615 24$aHistory of Mathematical Sciences. 676 $a004.0151 676 $a511.1 700 $aO?Regan$b Gerard$4aut$4http://id.loc.gov/vocabulary/relators/aut$0921504 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910373923603321 996 $aMathematics in Computing$92282119 997 $aUNINA