Logic, mathematics, and computer science: modern foundations with practical applications
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
[2015]
|
| Ausgabe: | Second edition |
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online Ressource (XII, 391 Seiten, 9 illus., 4 illus. in color) |
| ISBN: | 9781493932238 |
| DOI: | 10.1007/978-1-4939-3223-8 |
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Datensatz im Suchindex
| _version_ | 1804175707393228800 |
|---|---|
| adam_text | LOGIC, MATHEMATICS, AND COMPUTER SCIENCE
/ NIEVERGELT, YVES
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
LOGIC, MATHEMATICS, AND COMPUTER SCIENCE
/ NIEVERGELT, YVES
: 2015
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| spelling | Nievergelt, Yves 1954- Verfasser (DE-588)121171108 aut Foundations of logic and mathematics Logic, mathematics, and computer science modern foundations with practical applications Yves Nievergelt Second edition New York, NY Springer [2015] © 2015 1 Online Ressource (XII, 391 Seiten, 9 illus., 4 illus. in color) txt rdacontent c rdamedia cr rdacarrier Mathematics Mathematical logic Number theory Mathematical Logic and Foundations Mathematical Logic and Formal Languages Number Theory Mathematik Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Mengenlehre (DE-588)4074715-3 s 1\p DE-604 Erscheint auch als Druckausgabe 978-1-4939-3222-1 https://doi.org/10.1007/978-1-4939-3223-8 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632206&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632206&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nievergelt, Yves 1954- Logic, mathematics, and computer science modern foundations with practical applications Mathematics Mathematical logic Number theory Mathematical Logic and Foundations Mathematical Logic and Formal Languages Number Theory Mathematik Mathematische Logik (DE-588)4037951-6 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4074715-3 |
| title | Logic, mathematics, and computer science modern foundations with practical applications |
| title_alt | Foundations of logic and mathematics |
| title_auth | Logic, mathematics, and computer science modern foundations with practical applications |
| title_exact_search | Logic, mathematics, and computer science modern foundations with practical applications |
| title_full | Logic, mathematics, and computer science modern foundations with practical applications Yves Nievergelt |
| title_fullStr | Logic, mathematics, and computer science modern foundations with practical applications Yves Nievergelt |
| title_full_unstemmed | Logic, mathematics, and computer science modern foundations with practical applications Yves Nievergelt |
| title_short | Logic, mathematics, and computer science |
| title_sort | logic mathematics and computer science modern foundations with practical applications |
| title_sub | modern foundations with practical applications |
| topic | Mathematics Mathematical logic Number theory Mathematical Logic and Foundations Mathematical Logic and Formal Languages Number Theory Mathematik Mathematische Logik (DE-588)4037951-6 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Mathematics Mathematical logic Number theory Mathematical Logic and Foundations Mathematical Logic and Formal Languages Number Theory Mathematik Mathematische Logik Mengenlehre |
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