Ricerche sui fondamenti della matematica

Paolo Casalegno, Mauro Mariani
Carocci editore

La teoria degli insiemi, le cui nozioni sono alla base del linguaggio matematico corrente, è di grande importanza non solo per ragioni tecniche, ma anche da un punto di vista filosofico, per il suo innovativo approccio al problema dell'infinito. La gamma dei lettori potenzialmente interessati a un libro sull'argomento è vasta: studenti di filosofia, studenti di matematica, insegnanti curiosi di sapere sul conto degli insiemi qualcosa di più del poco contemplato dagli attuali programmi scolastici. Il volume è un'introduzione ai capitoli fondamentali della disciplina, non presuppone alcuna conoscenza matematica preliminare ed è organizzato in modo da consentire due diversi percorsi di lettura, uno rapido e un altro maggiormente approfondito.

Seymour Lipschutz
Etas libri

Martin Davis
Edizioni Abete

J. Donald Monk
Boringhieri

Gabriele Lolli
Boringhieri

Stefano Donati
Firenze Atheneum

La filosofia della matematica di Bertrand Russell nella sua fase matura e definitiva: la fase logicista, in cui egli sostenne che tutta la matematica pura deriva da premesse puramente logiche e utilizza solo concetti logici, o definibili in termini puramente logici.

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.

F. W. Lawvere, S. H. Schanuel
Franco Muzzio Editore

Alfred North Whitehead
Lampugnani Nigri Editore

Yu. L. Ershov, E. A. Palyutin
Mir Publisher

René Thom
Giulio Einaudi Editore

Krishnaji Shankara Patwardhan, S. A. Naimpally , Shyam Lal Singh
Motilal Banarsidass publishers

In 1150 AD, Bhaskaracarya (b. 1114 AD), renowned mathematician and astronomer of Vedic tradition composed Lilavati as the first part of his larger work called Siddhanta Siromani, a comprehensive exposition of arithmetic, algebra, geometry, mensuration, number theory and related topics. Lilavati has been used as a standard textbook for about 800 years. This lucid, scholarly and literary presentation has been translated into several languages of the world. Bhaskaracarya himself never gave any derivations of his formulae. N.H. Phadke (1902-1973) worked hard to construct proofs of several mathematical methods and formulae given in original Lilavati. The present work is an enlargement of his Marathi work and attempts a thorough mathematical explanation of definitions, formulae, short cuts and methodology as intended by Bhaskara. Stitches are followed by literal translations so that the reader can enjoy and appreciate the beauty of accurate and musical presentation in Lilavati. The book is useful to school going children, sophomores, teachers, scholars, historians and those working for cause of mathematics.