The Importance of Being Fuzzy (eBook)

And Other Insights from the Border between Math and Computers

Arturo Sangalli (Autor)

eBook Download: PDF

2018
200 Seiten
Princeton University Press (Verlag)
978-0-691-18735-8 (ISBN)

Infos

How has computer science changed mathematical thinking? In this first ever comprehensive survey of the subject for popular science readers, Arturo Sangalli explains how computers have brought a new practicality to mathematics and mathematical applications. By using fuzzy logic and related concepts, programmers have been able to sidestep the traditional and often cumbersome search for perfect mathematical solutions to embrace instead solutions that are "e;good enough."e; If mathematicians want their work to be relevant to the problems of the modern world, Sangalli shows, they must increasingly recognize "e;the importance of being fuzzy."e; As Sangalli explains, fuzzy logic is a technique that allows computers to work with imprecise terms--to answer questions with "e;maybe"e; rather than just "e;yes"e; and "e;no."e; The practical implications of this flexible type of mathematical thinking are remarkable. Japanese programmers have used fuzzy logic to develop the city of Sendai's unusually energy-efficient and smooth-running subway system--one that does not even require drivers. Similar techniques have been used in fields as diverse as medical diagnosis, image understanding by robots, the engineering of automatic transmissions, and the forecasting of currency exchange rates. Sangalli also explores in his characteristically clear and engaging manner the limits of classical computing, reviewing many of the central ideas of Turing and Godel. He shows us how "e;genetic algorithms"e; can solve problems by an evolutionary process in which chance plays a fundamental role. He introduces us to "e;neural networks,"e; which recognize ill-defined patterns without an explicit set of rules--much as a dog can be trained to scent drugs without ever having an exact definition of "e;drug."e; Sangalli argues that even though "e;fuzziness"e; and related concepts are often compared to human thinking, they can be understood only through mathematics--but the math he uses in the book is straightforward and easy to grasp. Of equal appeal to specialists and the general reader, The Importance of Being Fuzzy reveals how computer science is changing both the nature of mathematical practice and the shape of the world around us.

Autor

Arturo Sangalli is Professor of Mathematics at Champlain Regional College in Lennoxville, Québec.

Produkt-Details

• Erscheint lt. Verlag: 5.6.2018
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Naturwissenschaften
• Schlagworte: absurdity • Accuracy and precision • adaptive strategies • Addition • algorithm • Ambiguity • Analogy • analysis of algorithms • Artificial Neural Network • Artificial neuron • Axiom • axiomatic system • backpropagation • Best, worst and average case • binary data • Binary function • Bit • boolean satisfiability problem • Byte • Calculation • chaos theory • combination • complex adaptive system • Complexity • Computability • computable function • Computable number • Computation • Computer • Computer Program • computing • conjecture • Contradiction • Decision problem • Decision rule • Deductive Reasoning • defection • Derivative • detection • dialectical materialism • difference engine • Doctrine • Drawback • Entscheidungsproblem • error • estimation • Eulerian path • Expert System • exponentiation • fallacy • False positive rate • Finitary • Fuzzy concept • Fuzzy control system • Fuzzy Logic • fuzzy rule • Fuzzy Set • Genetic Algorithm • Gödel's Incompleteness Theorems • Goldbach's conjecture • Granular material • Group call • Halting Problem • Handle System • Heuristic • Ideology • Implicit parallelism • inference • Information Overload • Ingenuity • Instance (computer science) • Instruction set • Integrator • interdependence • irrational number • Kenneth Appel • lamarckism • learning rule • Linear Programming • Logic • Logical disjunction • logic gate • margin of error • Mathematical problem • mathematician • Mathematics • Michael Garey • Monotonic Function • Natural number • Negation • Nondeterministic algorithm • np-completeness • NP (complexity) • optimization problem • Partial function • Phenotype • Polemic • polynomial • Practical reason • Prerogative • Prime number • Prisoner's dilemma • Probabilistic Logic • Probability • Problem Solving • propagation delay • P versus NP problem • Quantity • Random-access memory • Random element • Ranking (information retrieval) • Reality • Reductio ad absurdum • Requirement • result • Rule of inference • Scientist • self-organizing map • self-replication • Simulated annealing • Soft Computing • Special case • Subset • Substring • subtraction • Summation • Term logic • Theorem • theory • Thought • time complexity • Train of Thought • transposable element • travelling salesman problem • Trial and Error • Turing Machine • Type I and type II errors • Uncertainty • vagueness • Variable (computer science) • Variable (mathematics)
• ISBN-10: 0-691-18735-5 / 0691187355
• ISBN-13: 978-0-691-18735-8 / 9780691187358