LEADER 00727nam0-2200253 --450 001 9910890501103321 005 20241010153035.0 010 $a9780826488749 100 $a20241010d2009----kmuy0itay5050 ba 101 0 $aeng 102 $aGB 105 $a 001yy 200 1 $a<< A >>critical introduction to phonetics$fKen Lodge 210 $aLondon$cContinuum$d2009 215 $a244 p.$cill.$d23 cm 225 1 $aContinuum critical introductions to linguistics 700 1$aLodge,$bKen$0330420 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a9910890501103321 952 $a414 SILV 01$b2024/11562$fFLFBC 959 $aFLFBC 996 $aCritical introduction to phonetics$94244079 997 $aUNINA LEADER 05130nam 22006135 450 001 9910300255203321 005 20200706162336.0 010 $a1-4939-3223-3 024 7 $a10.1007/978-1-4939-3223-8 035 $a(CKB)3710000000521679 035 $a(SSID)ssj0001585274 035 $a(PQKBManifestationID)16264910 035 $a(PQKBTitleCode)TC0001585274 035 $a(PQKBWorkID)14863995 035 $a(PQKB)11296400 035 $a(DE-He213)978-1-4939-3223-8 035 $a(MiAaPQ)EBC5576253 035 $a(PPN)190520728 035 $a(EXLCZ)993710000000521679 100 $a20151013d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLogic, Mathematics, and Computer Science $eModern Foundations with Practical Applications /$fby Yves Nievergelt 205 $a2nd ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (XII, 391 p. 9 illus., 4 illus. in color.) 300 $a"Adapted from Foundations of Logic and Mathematics : Applications to Computer Science and Cryptography"--Preface. 311 $a1-4939-3222-5 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis 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 Birkh?user, 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  . 606 $aLogic, Symbolic and mathematical 606 $aNumber theory 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aMathematical Logic and Formal Languages$3https://scigraph.springernature.com/ontologies/product-market-codes/I16048 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aLogic, Symbolic and mathematical. 615 0$aNumber theory. 615 14$aMathematical Logic and Foundations. 615 24$aMathematical Logic and Formal Languages. 615 24$aNumber Theory. 676 $a511.3 700 $aNievergelt$b Yves$4aut$4http://id.loc.gov/vocabulary/relators/aut$022951 701 $aNievergelt$b Yves$022951 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300255203321 996 $aLogic, mathematics, and computer science$91522468 997 $aUNINA