國立虎尾科技大學 |

Logic, Mathematics, and Computer Science = Modern Foundations with Practical Applications /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Logic, Mathematics, and Computer Science/ by Yves Nievergelt.
Reminder of title:	Modern Foundations with Practical Applications /
Author:	Nievergelt, Yves.
Description:	XII, 391 p. 9 illus., 4 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical logic. -
Online resource:	https://doi.org/10.1007/978-1-4939-3223-8
ISBN:	9781493932238

Logic, Mathematics, and Computer Science = Modern Foundations with Practical Applications /
Nievergelt, Yves.

Logic, Mathematics, and Computer ScienceModern Foundations with Practical Applications /[electronic resource] :by Yves Nievergelt. - 2nd ed. 2015. - XII, 391 p. 9 illus., 4 illus. in color.online resource.

Preface -- 1. Propositional Logic: Proofs from Axioms and Inference Rules -- 2. First Order Logic: Proofs with Quantifiers -- 3. Set Theory: Proofs by Detachment, Contraposition, and Contradiction -- 4. Mathematical Induction: Definitions and Proofs by Induction -- 5. Well-Formed Sets: Proofs by Transfinite Induction with Already Well-Ordered Sets -- 6. The Axiom of Choice: Proofs by Transfinite Induction -- 7. Applications: Nobel-Prize Winning Applications of Sets, Functions, and Relations -- 8. Solutions to Some Odd-Numbered Exercises -- References -- Index.

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory. The focus is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so unintuitive? Why are there no recipes to design proofs? Where do these numerous mathematical rules come from? What issues in logic, mathematics, and computer science still remain unresolved? And the perennial question: In what ways are we going to use this material? Additionally, the selection of topics presented reflects many major accomplishments from the twentieth century and includes applications in game theory and Nash's e quilibrium, Gale and Shapley's match making algorithms, Arrow's Impossibility Theorem in voting, to name a few. From the reviews of the first edition: "...All the results are proved in full detail from first principles...remarkably, the arithmetic laws on the rational numbers are proved, step after step, starting from the very definitions!...This is a valuable reference text and a useful companion for anybody wondering how basic mathematical concepts can be rigorously developed within set theory." —MATHEMATICAL REVIEWS "Rigorous and modern in its theoretical aspect, attractive as a detective novel in its applied aspects, this paper book deserves the attention of both beginners and advanced students in mathematics, logic and computer sciences as well as in social sciences." —Zentralblatt MATH .

ISBN: 9781493932238

Standard No.: 10.1007/978-1-4939-3223-8doiSubjects--Topical Terms:

810627
Mathematical logic.

LC Class. No.: QA8.9-10.3

Dewey Class. No.: 511.3

Logic, Mathematics, and Computer Science = Modern Foundations with Practical Applications /
LDR:04252nam a22004095i 4500 001 966772
003 DE-He213
005 20200706162336.0
007 cr nn 008mamaa
008 201211s2015 xxu| s |||| 0|eng d
020 $a 9781493932238 $9 978-1-4939-3223-8
024 7 $a 10.1007/978-1-4939-3223-8 $2 doi
035 $a 978-1-4939-3223-8
050 4 $a QA8.9-10.3
072 7 $a PBC $2 bicssc
072 7 $a MAT018000 $2 bisacsh
072 7 $a PBC $2 thema
072 7 $a PBCD $2 thema
082 0 4 $a 511.3 $2 23
100 1 $a Nievergelt, Yves. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1069787
245 1 0 $a Logic, Mathematics, and Computer Science $h [electronic resource] : $b Modern Foundations with Practical Applications / $c by Yves Nievergelt.
250 $a 2nd ed. 2015.
264 1 $a New York, NY : $b Springer New York : $b Imprint: Springer, $c 2015.
300 $a XII, 391 p. 9 illus., 4 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
505 0 $a Preface -- 1. Propositional Logic: Proofs from Axioms and Inference Rules -- 2. First Order Logic: Proofs with Quantifiers -- 3. Set Theory: Proofs by Detachment, Contraposition, and Contradiction -- 4. Mathematical Induction: Definitions and Proofs by Induction -- 5. Well-Formed Sets: Proofs by Transfinite Induction with Already Well-Ordered Sets -- 6. The Axiom of Choice: Proofs by Transfinite Induction -- 7. Applications: Nobel-Prize Winning Applications of Sets, Functions, and Relations -- 8. Solutions to Some Odd-Numbered Exercises -- References -- Index.
520 $a This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory. The focus is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so unintuitive? Why are there no recipes to design proofs? Where do these numerous mathematical rules come from? What issues in logic, mathematics, and computer science still remain unresolved? And the perennial question: In what ways are we going to use this material? Additionally, the selection of topics presented reflects many major accomplishments from the twentieth century and includes applications in game theory and Nash's e quilibrium, Gale and Shapley's match making algorithms, Arrow's Impossibility Theorem in voting, to name a few. From the reviews of the first edition: "...All the results are proved in full detail from first principles...remarkably, the arithmetic laws on the rational numbers are proved, step after step, starting from the very definitions!...This is a valuable reference text and a useful companion for anybody wondering how basic mathematical concepts can be rigorously developed within set theory." —MATHEMATICAL REVIEWS "Rigorous and modern in its theoretical aspect, attractive as a detective novel in its applied aspects, this paper book deserves the attention of both beginners and advanced students in mathematics, logic and computer sciences as well as in social sciences." —Zentralblatt MATH .
650 0 $a Mathematical logic. $2 bicssc $3 810627
650 0 $a Number theory. $3 527883
650 1 4 $a Mathematical Logic and Foundations. $3 669393
650 2 4 $a Mathematical Logic and Formal Languages. $3 670059
650 2 4 $a Number Theory. $3 672023
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9781493932221
776 0 8 $i Printed edition: $z 9781493932245
776 0 8 $i Printed edition: $z 9781493937134
856 4 0 $u https://doi.org/10.1007/978-1-4939-3223-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)