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Mathematical Masterpieces: Further Chronicles by the Explorers: Undergraduate Texts in Mathematics

Autor Art Knoebel, Reinhard Laubenbacher, Jerry Lodder, David Pengelley
en Limba Engleză Paperback – 14 aug 2007
In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J. Gould writes: [W]e acquire a surprising source of rich and apparently limitless novelty from the primary documents of great thinkers throughout our history. But why should any nuggets, or even ?akes, be left for int- lectual miners in such terrain? Hasn’t the Origin of Species been read untold millions of times? Hasn’t every paragraph been subjected to overt scholarly scrutiny and exegesis? Letmeshareasecretrootedingeneralhumanfoibles. . . . Veryfew people, including authors willing to commit to paper, ever really read primary sources—certainly not in necessary depth and completion, and often not at all. . . . I can attest that all major documents of science remain cho- full of distinctive and illuminating novelty, if only people will study them—in full and in the original editions. Why would anyone not yearn to read these works; not hunger for the opportunity? [99, p. 6f] It is in the spirit of Gould’s insights on an approach to science based on p- mary texts that we o?er the present book of annotated mathematical sources, from which our undergraduate students have been learning for more than a decade. Although teaching and learning with primary historical sources require a commitment of study, the investment yields the rewards of a deeper understanding of the subject, an appreciation of its details, and a glimpse into the direction research has taken. Our students read sequences of primary sources.
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Specificații

ISBN-13: 9780387330617
ISBN-10: 0387330615
Pagini: 333
Ilustrații: XII, 340 p.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.51 kg
Ediția:2007
Editura: Springer
Colecția Springer
Seriile Undergraduate Texts in Mathematics, Readings in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Lower undergraduate

Cuprins

The Bridge Between Continuous and Discrete.- Solving Equations Numerically: Finding Our Roots.- Curvature and the Notion of Space.- Patterns in Prime Numbers: The Quadratic Reciprocity Law.

Recenzii

From the reviews:
"This book is closely related to courses of mathematics held for students at New Mexico State University … . An important aspect of the book is the numerous exercises, which should help students to gain a deeper insight into the presented material. Numerous references and well-organized indices make the book easy to use. It can be recommended for university libraries and students with an interest in the history of mathematics presented from a modern point of view." (EMS Newsletter, September, 2008)
"This book consists of four chapters, each of which presents a ‘sequence of selected primary sources’ leading up to a ‘masterpiece of mathematical achievement’. … Each chapter contains … lots of historical comments sketching the further development of the topic. There are also a lot of exercises. … This is a well written and entertaining book that can (and should) be used in seminars or reading courses." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1140, 2008)

Textul de pe ultima copertă

Experience the discovery of mathematics by reading the original work of some of the greatest minds throughout history. Here are the stories of four mathematical adventures, including the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry,  perspective to proposed conceptual solutions, and a glimpse into the direction research has taken. The text is ideal for an undergraduate seminar, independent reading, or a capstone course, and offers a wealth of student exercises with a prerequisite of at most multivariable calculus.

Caracteristici

This text has been developed and class tested for over 15 years Uses original sources to teach the history of mathematics Heavily illustrated with line drawings and half-tones, and each chapter is accompanied by exercises Each chapter is self-contained and could be used independently Includes supplementary material: sn.pub/extras