Paolo Freguglia's Books

The Early Period of the Calculus of Variations

By: Paolo Freguglia,Mariano Giaquinta

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The Early Period of the Calculus of Variations

By: Paolo Freguglia,Mariano Giaquinta

This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s δ-calculus, including: • The isoperimetrical problems • Shortest lines and geodesics • Euler’s Methodus Inveniendi and the two Additamenta Finally, the authors give the readers a sense of how vast the calculus of variations has become in centuries hence, providing some idea of what lies outside the scope of the book as well as the current state of affairs in the field. This book will be of interest to anyone studying the calculus of variations who wants a deeper intuition for the techniques and ideas that are used, as well as historians of science and mathematics interested in the development and evolution of modern calculus and analysis.

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Page Count

297

Publisher

Birkhäuser

Published Date

ISBN 10

3319389459

ISBN 13

9783319389455

Abstraction and Infinity

By: Paolo Mancosu

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Abstraction and Infinity

By: Paolo Mancosu

Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism.

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Page Count

240

Publisher

Oxford University Press

Published Date

ISBN 10

0191063800

ISBN 13

9780191063800

The Adventure of Reason

Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

By: Paolo Mancosu

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The Adventure of Reason

Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

By: Paolo Mancosu

Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

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Page Count

631

Publisher

OUP Oxford

Published Date

ISBN 10

0191021997

ISBN 13

9780191021992

The Early Period of the Calculus of Variations

By: Paolo Freguglia,Mariano Giaquinta

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The Early Period of the Calculus of Variations

By: Paolo Freguglia,Mariano Giaquinta

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

297

Publisher

Birkhäuser

Published Date

ISBN 10

3319389459

ISBN 13

9783319389455

Book's by Paolo Freguglia

The Early Period of the Calculus of Variations

The Early Period of the Calculus of Variations

Abstraction and Infinity

Abstraction and Infinity

The Adventure of Reason

The Adventure of Reason

The Early Period of the Calculus of Variations

The Early Period of the Calculus of Variations

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