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Proven Impossible

Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More
TaschenbuchKartoniert, Paperback
Englisch
Cambridge University Pr.erschienen am18.01.2024
In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand.mehr
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BuchGebunden
EUR76,50
TaschenbuchKartoniert, Paperback
EUR36,00
E-BookPDFDRM AdobeE-Book
EUR34,99

Produkt

KlappentextIn mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs. This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic - and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training - all you need is the discipline to follow logical arguments and a pen in your hand.
Details
ISBN/GTIN978-1-009-34949-9
ProduktartTaschenbuch
EinbandartKartoniert, Paperback
Erscheinungsjahr2024
Erscheinungsdatum18.01.2024
SpracheEnglisch
MasseBreite 154 mm, Höhe 228 mm, Dicke 22 mm
Gewicht441 g
IllustrationenWorked examples or Exercises
Artikel-Nr.60594810

Inhalt/Kritik

Inhaltsverzeichnis
Preface; 1. Yes you can prove a negative!; 2. Bell's impossibility theorem(s); 3. Enjoying Bell magic; 4. Arrow's (and friends') impossibility theorems; 5. Clustering and impossibility; 6. Gödel-ish impossibility; 7. Turing undecidability and incompleteness; 8. Chaitin's theorem: More devastating; 9. Gödel (for real, this time).mehr

Autor

Dan Gusfield is Distinguished Professor emeritus, and former department chair, in the Computer Science Department at University of California, Davis. He is a Fellow of the ACM, the IEEE, and the ISCB. His previous books are 'The Stable Marriage Problem' (1989, co-authored with Rob Irving); 'Strings, Trees and Sequences' (1997); 'ReCombinatorics' (2014); and 'Integer Linear Programming in Computational and Systems Biology' (2019). As this book reflects, his teaching emphasized mathematical rigor as well as accessibility and clarity. He produced over 100 hours of video lectures on a wide range of topics, now viewed over a million times on the web.