Mathematical Masterpieces: Further Chronicles by the Explorers [Paperback]

Intended for juniors and seniors majoring in mathematics, as well as anyone pursuing independent study, this book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Each chapter showcases a masterpiece of mathematical achievement, anchored to a sequence of selected primary sources. The authors examine the interplay between the discrete and continuous, with a focus on sums of powers. They then delineate the development of algorithms by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, and finally they look at the properties of prime numbers. The book includes exercises, numerous photographs, and an annotated bibliography.

Advanced undergraduates will find here an introduction to the excitement of mathematical discovery, through close examination of original historical sources. Each chapter is anchored by a different story sequence of selected primary sources showcasing a masterpiece of mathematical achievement, illustrated by mathematical exercises and historical photographs.

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? Hasnt the Origin of Species been read untold millions of times? Hasnt every paragraph been subjected to overt scholarly scrutiny and exegesis? Letmeshareasecretrootedingeneralhumanfoibles. . . . Veryfew people, including authors willing to commit to paper, ever really read primary sourcescertainly 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 themin full alƒ%