Craig Smorynski

History of Mathematics (eBook, PDF)

A Supplement

• Format: PDF

Produktbeschreibung

General textbooks, attempting to cover three thousand or so years of mathematical history, must necessarily oversimplify almost everything, which can scarcely promote a critical approach to the subject. History of Mathematics offers deeper coverage of key select topics, providing students with material that could encourage more critical thinking. It also includes proofs of important results typically neglected in the modern history of mathematics curriculum.

Coverage includes:

• A new approach to the historical development of the natural numbers, which was only settled in the 19th century



• Construction problems of antiquity, with a proof that the angle cannot be trisected nor the cube duplicated by ruler and compass alone



• A modern recounting of a Chinese word problem from the 13th century, illustrating the need for consulting multiple sources

Lighter material, including historically interesting (and hard to find) poems and humorous song lyrics with mathematical themes.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 274
• Erscheinungstermin: 3. Dezember 2007
• Englisch
• ISBN-13: 9780387754819
• Artikelnr.: 43732709

Inhaltsangabe

Annotated Bibliography.- Foundations of Geometry.- The Construction Problems of Antiquity.- A Chinese Problem.- The Cubic Equation.- Horner's Method.- Some Lighter Material.

Rezensionen

From the reviews:

"This is very personal book, full of personal asides and footnotes that reveal the author's thought process. It's also an argumentative book ... which made me want to argue back. I kept reading. ... this is an interesting book. ... I do think anyone who teaches history of mathematics can find useful things here." (Fernando Q. Gouvêa, MathDL, December, 2007)

"This volume ... aims to discuss just a few topics from pre-20th-century mathematics, but to address them in some mathematical and historical detail. ... The book includes an appendix offering a dozen historical/mathematical projects. Overall, an interesting volume. Summing Up: Recommended. Upper-division undergraduates through researchers/faculty." (S. J. Colley, CHOICE, Vol. 45 (11), August, 2008)

Aus den Rezensionen: "... Craig Smorynski hat ein 'Supplement' zu einer Vorlesung über die Geschichte der Mathematik vorgelegt, mit dem er sowohl das kritische Verständnis seiner Hörer schulen möchte, wie auch an ... ausgewählten Beispielen die Mathematik im Detail beschreiben will. ... Mir gefällt der Stil des Autors und seine Auswahl der Inhalte ganz außerordentlich. ... Man findet hier tatsächlich das Material, dass man in einem Überblickskurs verwenden kann, um partiell etwas tiefer zu bohren. ... Insgesamt ist Smorynskis Buch ein wertvolles und lesbares Addendum ... zur mathematikhistorischen Literatur ..." (Thomas Sonar, in: Mathematische Semesterberichte, 31. Jan. 2009, Vol. 156, S. 134 f.)