Mathematical Problems
Mathematical Problems

Author: David Hilbert

Publisher: Good Press

Published: 2021-04-11

Total Pages: 60

ISBN-13:

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'Mathematical Problems' is a book derived from a lecture given by David Hilbert, a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert's address begins with the following: "Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?"

Algebraic Theories
Algebraic Theories

Author: Leonard Dickson

Publisher: Courier Corporation

Published: 2014-03-05

Total Pages: 241

ISBN-13: 048615520X

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This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significant concepts, including matrices, invariants, and groups. Algebraic Theories studies all of the important theories; its extensive offerings range from the foundations of higher algebra and the Galois theory of algebraic equations to finite linear groups (including Klein's "icosahedron" and the theory of equations of the fifth degree) and algebraic invariants. The full treatment includes matrices, linear transformations, elementary divisors and invariant factors, and quadratic, bilinear, and Hermitian forms, both singly and in pairs. The results are classical, with due attention to issues of rationality. Elementary divisors and invariant factors receive simple, natural introductions in connection with the classical form and a rational, canonical form of linear transformations. All topics are developed with a remarkable lucidity and discussed in close connection with their most frequent mathematical applications.

Philosophy and Foundations of Mathematics
Philosophy and Foundations of Mathematics

Author: A. Heyting

Publisher: Elsevier

Published: 2014-05-12

Total Pages: 645

ISBN-13: 1483278158

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L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

The Eightfold Way
The Eightfold Way

Author: Silvio Levy

Publisher: Cambridge University Press

Published: 2001-05-28

Total Pages: 350

ISBN-13: 9780521004190

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Expository and research articles by renowned mathematicians on the myriad properties of the Klein quartic.

Mathematical Knowledge and the Interplay of Practices
Mathematical Knowledge and the Interplay of Practices

Author: José Ferreirós

Publisher: Princeton University Press

Published: 2015-12-22

Total Pages: 357

ISBN-13: 0691167516

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This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.