國立虎尾科技大學 |

Mathematics in Computing = An Accessible Guide to Historical, Foundational and Application Contexts /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mathematics in Computing/ by Gerard O’Regan.
其他題名:	An Accessible Guide to Historical, Foundational and Application Contexts /
作者:	O’Regan, Gerard.
面頁冊數:	XXVI, 458 p. 206 illus., 73 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	History of Mathematical Sciences. -
電子資源:	https://doi.org/10.1007/978-3-030-34209-8
ISBN:	9783030342098

Mathematics in Computing = An Accessible Guide to Historical, Foundational and Application Contexts /
O’Regan, Gerard.

Mathematics in ComputingAn Accessible Guide to Historical, Foundational and Application Contexts /[electronic resource] :by Gerard O’Regan. - 2nd ed. 2020. - XXVI, 458 p. 206 illus., 73 illus. in color.online resource. - Undergraduate Topics in Computer Science,1863-7310. - Undergraduate Topics in Computer Science,.

What 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.

This 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.

ISBN: 9783030342098

Standard No.: 10.1007/978-3-030-34209-8doiSubjects--Topical Terms:

785417
History of Mathematical Sciences.

LC Class. No.: QA76.9.M35

Dewey Class. No.: 004.0151

Mathematics in Computing = An Accessible Guide to Historical, Foundational and Application Contexts /
LDR:04094nam a22004095i 4500 001 1025058
003 DE-He213
005 20200701025529.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030342098 $9 978-3-030-34209-8
024 7 $a 10.1007/978-3-030-34209-8 $2 doi
035 $a 978-3-030-34209-8
050 4 $a QA76.9.M35
072 7 $a UYAM $2 bicssc
072 7 $a COM018000 $2 bisacsh
072 7 $a UYAM $2 thema
072 7 $a UFM $2 thema
082 0 4 $a 004.0151 $2 23
100 1 $a O’Regan, Gerard. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1278920
245 1 0 $a Mathematics in Computing $h [electronic resource] : $b An Accessible Guide to Historical, Foundational and Application Contexts / $c by Gerard O’Regan.
250 $a 2nd ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XXVI, 458 p. 206 illus., 73 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Undergraduate Topics in Computer Science, $x 1863-7310
505 0 $a What 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.
520 $a This 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.
650 2 4 $a History of Mathematical Sciences. $3 785417
650 2 4 $a Coding and Information Theory. $3 669784
650 2 4 $a Mathematical Logic and Formal Languages. $3 670059
650 2 4 $a Mathematical Applications in Computer Science. $3 815331
650 1 4 $a Math Applications in Computer Science. $3 669887
650 0 $a History. $3 669538
650 0 $a Mathematics. $3 527692
650 0 $a Information theory. $3 595305
650 0 $a Coding theory. $3 561460
650 0 $a Mathematical logic. $2 bicssc $3 810627
650 0 $a Computer mathematics. $3 1199796
650 0 $a Computer science—Mathematics. $3 1253519
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030342081
776 0 8 $i Printed edition: $z 9783030342104
830 0 $a Undergraduate Topics in Computer Science, $x 1863-7310 $3 1254738
856 4 0 $u https://doi.org/10.1007/978-3-030-34209-8
912 $a ZDB-2-SCS
912 $a ZDB-2-SXCS
950 $a Computer Science (SpringerNature-11645)
950 $a Computer Science (R0) (SpringerNature-43710)