Five Golden Rules - Great Theories of 20th-Century Mathematics - and Why They Matter

John L. Casti demonstriert an fünf mathematische Theoremen die weitreichenden Folgen für dieses Jahrhundert - für den mathematisch interessierten Leser anschaulich erklärt:
Der Minimax-Satz brachte die Spieltheorie erst richtig zur Entfaltung, eine Theorie, die von enormer Bedeutung für die Ökonomie geworden ist.
Der Brouwersche Fixpunktsatz ermöglicht das Lösen von Gleichungen unter sehr allgemeinen Bedingungen, was für die Vorbereitung der Mondlandung ebenso wichtig war wie für ökonomische Berechnungen.
Das Theorem von Morse führte zur Katastrophentheorie, die eine wichtige Grundlage für die mathematische Modellierung natürlicher Abläufe darstellt.
Der Anhalte-Satz und die Theorie der Berechenbarkeit können als theoretische Grundlage der Computerrevolution gelten.
Und die Simplexmethode machte die lineare Optimierung zum Werkzeug aller Effizienzbestrebungen.Probing the frontiers of modern mathematics, Casti examines the origins of some of the most important findings of this century. This is a tale of mystery and logic, eleganceand reason; it is the story of five monumental mathematical breakthroughs and how they shape our lives. All those intrigued by the mathematical process, nonacademics and professionals alike, will find this an enlightening, eye-opening, and entertaining work. High school algebra or geometry-and enthusiasm-are the only prerequisites.From the theorem that provided the impetus for modern computers to the calculations that sent the first men to the Moon, these breakthroughs have transformed our lives. Casti illustrates each theorem with a dazzling array of real-world problems it has helped solve-how to calculate the shape of space, optimize investment returns, even chart the course of the development of organisms.Along the way, we meet the leading thinkers of the day: John von Neumann, L. E. J. Brouwer, Marston Morse, and Alan Turing, among others. And we come to understand the combination of circumstances that led each to such revolutionary discoveries as the Minimax Theorem, which spawned the exciting field of game theory, and the Simplex Method, which underpins the powerful tools of optimization theory.It has been estimated that about 200,000 theorems are published each year. How, then, does an author go about selecting a precious few as the most significant of the century? At the beginning of his search, Casti set forth five criteria: Significance: Did the theorem break a major logjam in the development of mathematics? Beauty and Scope: Is the theorem elegant and does it shed light on questions over a wide range of areas? Applications: Do applications extend outside of pure mathematics and provide a more complete understanding of the workings of the world? Proof Method: Were new techniques or modes of logic required in the proof and did these methods provide insight into other important problems? Philosophical Implications: Does the theorem provide opportunities to obtain deeper knowledge of ourselves and the universe?One of the first books to focus exclusively on the mathematical breakthroughs of the 20th century, Five Golden Rules is wonderfully accessible, informative, and incisive.

Inhaltsverzeichnis

The Minimax Theorem (Game Theory).The Brouwer Fixed-Point Theorem (Topology).Morse's Theorem (Singularity Theory).The Halting Theorem (Theory of Computation).The Simplex Method (Optimization Theory).Bibliography.Index.

Über den Autor / die Autorin

John L. Casti, Ph.D., is a professor at the Santa Fe Institute and the Technical University of Vienna and the author of Would-Be Worlds and Five Golden Rules (both published by Wiley) as well as The Cambridge Quintet.

Produktdetails

• Autoren: John L. Casti
• Verlag: Wiley & Sons
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 01.01.1996
• EAN: 9780471002611
• ISBN: 978-0-471-00261-1
• Seiten: 235
• Gewicht: 572 g
• Illustration: w. figs.
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Allgemeines, Lexika