Società Edison 1884-1934 Milano

Giuseppe Peano
Edizioni Cremonese

Stewart Shapiro
North-Holland

''Platonism and intuitionism are rival philosophies of Mathematics, the former holding that the subject matter of mathematics consists of abstract objects whose existence is independent of the mathematician, the latter that the subject matter consists of mental construction... both views are implicitly opposed to materialistic accounts of mathematics which take the subject matter of mathematics to consist (in a direct way) of material objects...'' FROM THE INTRODUCTION Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.

Piero Ginori Conti
Tip. Giuseppe Cencetti

Georges Hacault
Librairie J.B. Baillère et fils

Boris A. Dubrovin, Sergej P. Novikov, Anatolij T. Fomenko
Editori Riuniti University Press

Antonio Bordoni
Paolo Emilio Giusti

Vasilij Sergeevic Vladimirov
Edizioni Mir

Michail L. Krasnov, Grigorij I. Makarenko, Aleksandr I. Kiselev
Edizioni Mir

Gheorghij Evghenievic Silov
Edizioni Mir

Kurt Gödel
Bollati Boringhieri

Laurence Sigler
Springer-Verlag

First published in 1202, Fibonacci's Liber abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. Its author, Leonardo Pisano, known today as Fibonacci, was a citizen of Pisa, an active maritime power, with trading outposts on the Barbary Coast and other points in the Muslim Empire. As a youth, Fibonacci was instructed in mathematics in one of these outposts; he continued his study of mathematics while traveling extensively on business and developed contacts with scientists throughout the Mediterranean world. A member of the academic court around the Emperor Frederick II, Leonardo saw clearly the advantages for both commerce and scholarship of the Hindu positional number system and the algebraic methods developed by al-Khwarizmi and other Muslim scientists. Though it is known as an introduction to the Hindu number system and the algorithms of arithmetic that children now learn in grade school, "Liber abaci" is much more: an encyclopaedia of thirteenth-century mathematics, both theoretical and practical. It develops the tools rigorously, establishing them with Euclidean geometric proofs, and then shows how to apply them to all kinds of situations in business and trade - conversion of measures and currency, allocations of profit, computation of interest, alloying of currencies, and so forth. It is rigorous mathematics, well applied, and vividly described. As the first translation into a modern language of the "Liber abaci", this book will be of interest not only to historians of science, but to all mathematicians and mathematics teachers interested in the origins of their methods.

G. Vitali, G. Sansone
Zanichelli