Bøger af Stephen Abbott

Outlines an elementary, one semester course, which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. This book focuses on questions which give analysis its inherent fascination.

"When the Europeans came to this continent at the end of the fifteenth century they found it already inhabited by races of men very different from themselves. These people, whom they took to calling 'Indians, ' were spread out, though very thinly, from one end of the continent to the other. Who were these nations, and how was their presence to be accounted for? To the first discoverers of America, or rather to the discoverers of the fifteenth and sixteenth centuries (Columbus and his successors), the origin of the Indians presented no difficulty. To them America was supposed to be simply an outlying part of Eastern Asia, which had been known by repute and by tradition for centuries past. Finding, therefore, the tropical islands of the Caribbean sea with a climate and plants and animals such as they imagined those of Asia and the Indian ocean to be, and inhabited by men of dusky colour and strange speech, they naturally thought the place to be part of Asia, or the Indies. The name 'Indians, ' given to the aborigines of North America, records for us this historical misunderstanding. But a new view became necessary after Balboa had crossed the isthmus of Panama and looked out upon the endless waters of the Pacific, and after Magellan and his Spanish comrades had sailed round the foot of the continent, and then pressed on across the Pacific to the real Indies. It was now clear that America was a different region from Asia." - The Antiquity of Man in North America - The Descendants of Paleolithic Man in American - Traces of a Pre-Indian People - Man in America .

"How playwrights from Alfred Jarry and Samuel Beckett to Tom Stoppard and Simon McBurney brought the power of abstract mathematics to the human stage. The discovery of alternate geometries, paradoxes of the infinite, incompleteness, and chaos theory revealed that, despite its reputation for certainty, mathematical truth is not immutable, perfect, or even perfectible. Beginning in the last century, a handful of adventurous playwrights took inspiration from the fractures of modern mathematics to expand their own artistic boundaries. Originating in the early avant-garde, mathematics-infused theater reached a popular apex in Tom Stoppard's 1993 play Arcadia. In The Proof Stage, mathematician Stephen Abbott explores this unlikely collaboration of theater and mathematics. He probes the impact of mathematics on such influential writers as Alfred Jarry, Samuel Beckett, Berthold Brecht, and Stoppard, and delves into the life and mathematics of Alan Turing as they are rendered onstage. The result is an unexpected story about the mutually illuminating relationship between proofs and plays-from Euclid and Euripides to Gèodel and Godot.Theater is uniquely poised to discover the soulful, human truths embedded in the austere theorems of mathematics, but this is a difficult feat. It took Stoppard twenty-five years of experimenting with the creative possibilities of mathematics before he succeeded in making fractal geometry and chaos theory integral to Arcadia's emotional arc. In addition to charting Stoppard's journey, Abbott examines the post-Arcadia wave of ambitious works by Michael Frayn, David Auburn, Simon McBurney, Snoo Wilson, John Mighton, and others. Collectively, these gifted playwrights transform the great philosophical upheavals of mathematics into profound and sometimes poignant revelations about the human journey"--