Turning Points in the History of Mathematics

Inhaltsverzeichnis

Axiomatics - Euclid's and Hilbert's: From Material to Formal.- Solution by Radicals of the Cubic: From Equations to Groups and from Real to Complex Numbers.- Analytic Geometry: From the Marriage of Two Fields to the Birth of a Third.- Probability: From Games of Chance to an Abstract Theory.- Calculus: From Tangents and Areas to Derivatives and Integrals.- Gaussian Integers: From Arithmetic to Arithmetics.- Non-Euclidean Geometry: From One Geometry to Many.- Hypercomplex Numbers: From Algebra to Algebras.- The Infinite: From Potential to Actual.- Philosophy of Mathematics: From Hilbert to Gödel.- Some Further Turning Points.- Index.

Turning Points in the History of Mathematics

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Turning Points in the History of Mathematics

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Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

16.04.2016

Verlag

Springer Us

Seitenzahl

109

Maße (L/B/H)

23,5/15,5/0,7 cm

Beschreibung

Rezension

“This slim volume will be especially helpful to those teaching high school and junior college students the rudiments of selected ‘major turning points’ in the history of mathematics. It offers compact vignettes divided into ten basic topics: axiomatization, solutions of cubic equations, analytical geometry, probability, calculus, Gaussian integers, non-Euclidean geometries, hyper complex numbers, the infinite, and philosophy of mathematics from Hilbert to Gödel. … Thumbnail portraits and photographs of major mathematicians are also included.” (Joseph W. Dauben, Mathematical Reviews,May, 2017)

“Turning Points does provide a useful summary and outline of at least a portion of the subject, and also functions nicely as a way of helping to mentally organize the material. It contains a number of good quotes, and a decent selection of bibliographic references at the end of each chapter. There are also problems at the end of each chapter, generally calling for essay-type answers that should require the student to do further reading.” (Mark Hunacek, MAA Reviews, maa.org, June, 2016)

“Each chapter contains some problems and projects (they extend and increase the understanding of the material) as well as references and suggestions of further readings. A comprehensive index has been supplemented. The book can serve everyone interested in the historical development of mathematics – some mathematical background is of course required. It can serve teachers and students, can be used in courses in the history of mathematics as well as in courses in particular domains of mathematics … .” (Roman Murawski, zbMATH 1342.01005, 2016)

Details

Einband

Taschenbuch

Erscheinungsdatum

16.04.2016

Verlag

Springer Us

Seitenzahl

109

Maße (L/B/H)

23,5/15,5/0,7 cm

Gewicht

1942 g

Auflage

1st ed. 2015

Sprache

Englisch

ISBN

978-1-4939-3263-4

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  • Turning Points in the History of Mathematics
  • Axiomatics - Euclid's and Hilbert's: From Material to Formal.- Solution by Radicals of the Cubic: From Equations to Groups and from Real to Complex Numbers.- Analytic Geometry: From the Marriage of Two Fields to the Birth of a Third.- Probability: From Games of Chance to an Abstract Theory.- Calculus: From Tangents and Areas to Derivatives and Integrals.- Gaussian Integers: From Arithmetic to Arithmetics.- Non-Euclidean Geometry: From One Geometry to Many.- Hypercomplex Numbers: From Algebra to Algebras.- The Infinite: From Potential to Actual.- Philosophy of Mathematics: From Hilbert to Gödel.- Some Further Turning Points.- Index.