Elements of Mathematics

From Euclid to Gödel
Author: John Stillwell
Publisher: Princeton University Press
ISBN: 1400880564
Category: Mathematics
Page: 440
View: 3480

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Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

Mathematische Modellierung bei Platon zwischen Thales und Euklid

Author: Claas Lattmann
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110615002
Category: History
Page: 504
View: 6754

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Wissenschaftliche Mathematik ist eine der wichtigsten Kulturleistungen des antiken Griechenland. Doch wann und wo genau hatte sie ihren Ursprung? Die Einschätzung der Antike, zwischen Thales und Euklid habe Platon eine maßgebliche Rolle gespielt, gilt als Fiktion. Diese Studie wirft einen neuen, modelltheoretischen Blick auf die Zeugnisse und erweist im Gegenteil, dass in der Tat Platon als Schöpfer von axiomatisch-deduktiver Mathematik gelten muss. Grundlage der Analyse ist eine Neubewertung des Diagramms als zentralen Charakteristikums griechischer Mathematik aus modelltheoretischer Perspektive. Eine Untersuchung der Quadratverdopplung im Menon und zur Würfelverdopplung (Delisches Problem) zeigt, dass eine theoretische Mathematik erstmals für Platon bezeugt ist. Dass weiter auch nur Platon ein Motiv hatte, sie zu erfinden, ergibt sich aus der Explikation von Platons Theorie der mathematischen Modellierung anhand des Liniengleichnisses in Verbindung mit dem Nachweis, dass der Timaios als deren praktische Umsetzung fungiert. Die Studie bietet wissenschaftshistorisch neue Einsichten zur Entstehung von Mathematik, philosophiehistorisch zu Platons Ontologie und Epistemologie und modelltheoretisch zu Theorie und Praxis von Modellierung.

Bibliotheca mathematica

Verz. d. Bücher über d. gesammten Zweige d. Mathematik, als: Arithmetik, höhere Analysis, construirende u. analyt. Geometrie, Mechanik, Astronomie u. Geodäsie, welche in Deutschland u.d. Auslande vom J. 1830 bis Mitte d. J. 1854 ersch. sind ; mit e. vollst. Materienreg
Author: Ludwig Adolph Sohncke
Publisher: N.A
Category: Astronomy
Page: 388
View: 5727

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There's Something About Gödel

The Complete Guide to the Incompleteness Theorem
Author: Francesco Berto
Publisher: John Wiley & Sons
ISBN: 1444357611
Category: Philosophy
Page: 256
View: 6854

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Berto’s highly readable and lucid guide introduces students and the interested reader to Gödel’s celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters Discusses interpretations of the Theorem made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel’s theories Written in an accessible, non-technical style

A Mathematical History of the Golden Number

Author: Roger Herz-Fischler
Publisher: Courier Corporation
ISBN: 0486152324
Category: Mathematics
Page: 224
View: 7163

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This comprehensive study traces the historic development of division in extreme and mean ratio ("the golden number") from its first appearance in Euclid's Elements through the 18th century. Features numerous illustrations.

Elements of Mathematics Functions of a Real Variable

Elementary Theory
Author: N. Bourbaki
Publisher: Springer Science & Business Media
ISBN: 9783540653400
Category: Mathematics
Page: 338
View: 2246

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This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

Writing the History of Mathematics: Its Historical Development

Author: Joseph W. Dauben,Christoph J. Scriba
Publisher: Springer Science & Business Media
ISBN: 9783764361679
Category: Mathematics
Page: 689
View: 1591

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As an historiographic monograph, this book offers a detailed survey of the professional evolution and significance of an entire discipline devoted to the history of science. It provides both an intellectual and a social history of the development of the subject from the first such effort written by the ancient Greek author Eudemus in the Fourth Century BC, to the founding of the international journal, Historia Mathematica, by Kenneth O. May in the early 1970s.

Kurt Gödel: Collected Works:

Author: Kurt Gödel,Solomon Feferman,John W. Dawson,Warren Goldfarb,Charles Parsons,Wilfried Sieg
Publisher: Oxford University Press on Demand
ISBN: 019968961X
Category: Computers
Page: 686
View: 2247

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Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. The final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV, published for the first time in paperback, covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

A New Mathematical and Philosophical Dictionary

Comprising an Explanation of Terms and Principles of Pure and Mixed Mathematics, and Such Branches of Natural Philosophy as are Susceptible of Mathematical Investigation. With Historical Sketches of the Rise, Progress and Present State of the Several Departments of These Sciences, and an Account of the Discoveries and Writings of the Most Celebrated Authors, Both Ancient and Modern
Author: Peter Barlow
Publisher: N.A
Category: Mathematics
Page: 772
View: 7522

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An Essay on the Foundations of Geometry

Author: Bertrand Russell
Publisher: Psychology Press
ISBN: 9780415141451
Category: Mathematics
Page: 197
View: 4886

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This text was first published in 1897, and is based on Russell's Cambridge dissertation as well as lectures given during a journey through the USA. It provides both an insight into the foundations of Russell's philosophical thinking and an introduction to the philosophy of mathematics and logic. As such it should be a useful resource not only for students of philosophy, but also for those interested in Russell's philosophical development. The text consists of four chapters, which explore the various concepts of geometry and their philosophical implications, including an historical overview of the development of geometrical theory.

Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics
Author: S. Gandon
Publisher: Springer
ISBN: 1137024658
Category: Mathematics
Page: 263
View: 2239

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In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.