Il libro A] la naturale continuazione di 'Introduzione alla complessitA computazionale'. Il libro inizia affrontando il problema della primalitA e della difficile identificazione della sua precisa complessitA computazionale, per portarci all'analisi delle relazioni tra determinismo e casualitA . Vengono poi presentati modelli di calcolo. Essempi ed esercizi aiutano il lettore ad impadronirsi degli strumenti matematici che vengono introdotti. Il testo puA essere utilizzato per corsi universitari avanzati (in particolare del corso di laurea in Informatica) e per corsi di dottorato. Inoltre si propone come riferimento per i ricercatori del settore e di aree affini.

Quantum physicist Etienne Klein and astrophysicist Marc Lachieze-Rey present and comment on the successive unifications that have marked the fundamental advances in physics. A good deal of modern theoretical physics is lightly and gracefully explained, rooted in a philosophical examination of the motivations that drive physicists and physics. The book is a discourse on the nature of elegance and beauty in physics, seeking to explain how and why beauty is a reliable guide in the ongoing search for Truth in physics.

From a review of the second edition:

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it 's accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Social revolutions--critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. The publication of Kuhn's The Structure of Scientific Revolutions in 1962 led to an exciting discussion of revolutions in the natural sciences; an off-shoot of this was a debate in the United States in the mid-1970's as to whether the concept of revolution could be applied to mathematics as well as science. This book is the first comprehensive examination of the question. It reprints the original papers of leading supporters and opponents, together with additional chapters giving their current views. To this are added new contributions from nine other experts in the history of mathematics, who each discuss an important episode and consider whether it was a revolution. The whole question of mathematical revolutions is thus examined comprehensively and from a variety of perspectives, and will interest mathematicians, philosophers, and historians alike.

Fur 1994 wurde Zurich die Durchfuhrung des Internationalen Mathematiker Kongresses anvertraut. Zurich ist damit der bisher einzige Ort, an dem diese Veranstaltung nach 1897 und 1932 bereits zum dritten Mal stattfinden kann. Dies ist kaum zufallig, denn das Fachgebiet Mathematik in Zurich war seit der Grundung der Universitat und der Eidgenoessischen Technischen Hochschule um die Mitte des 19. Jahrhunderts immer durch bedeutende Persoenlichkeiten vertreten. Das vorliegende Buch gibt einen UEberblick uber die Entwicklung der Mathematik an den beiden Zurcher Hochschulen bis in die sechziger Jahre dieses Jahrhunderts hinein, wobei die personellen Aspekte im Vordergrund stehen. Der Text wird von vielen Abbildungen, darunter Portrats der meisten Mathematiker, die in Zurich tatig gewesen sind, illustriert.

Die allgemeine Relativitastheorie lasst sich nur mit Hilfe des Tensorkalkuls formulieren. Diesen lernte Einstein 1912 in Form des absoluten Differentialkalkuls kennen. Dessen Schopfer war Gregorio Ricci, dem zusammen mit Sophus Lie und anderen der Ausbau der Theorie der Differentialinvarianten gelang. Der absolute Differentialkalkul passte zur allgemeinen Relativitatstheorie wie ein Schlussel zum Schloss: der in den Jahren 1884-92 von Ricci entwickelte Kalkul erfullte in der Tat genau das physikalische Konzept der allgemeinen Relativitatstheorie, das Einstein 1907-15 ausarbeitete. Ein derartiges Zusammenpassen war nur dadurch moglich, weil sowohl Ricci innerhalb der Mathematik als auch Einstein innerhalb der Physik vergleichbare Fragen stellten, namlich Fragen nach Invarianten bei speziellen Transformationen. Es wird versucht, den historischen Weg so genau wie moglich anhand der Quellen nachzuzeichnen. Neu ist die Herausarbeitung des invariantentheoretischen Aspekts, dem gegenuber die Bedeutung der Differentialgeometrie fur die Entwicklung des Tensorkalkuls in den Hintergrund treten muss."

This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.