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Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (Dover Books on Mathematics) - Softcover
Synopsis
This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or examples of applications, readers will encounter a coherent presentation of mathematical ideas that begins with the natural numbers and basic laws of arithmetic and progresses to the problems of the real-number continuum and concepts of the calculus.
Contents include examinations of the various types of numbers and a criticism of the extension of numbers; arithmetic, geometry, and the rigorous construction of the theory of integers; the rational numbers, the foundation of the arithmetic of natural numbers, and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers.
In issues of mathematical philosophy, the author explores basic theoretical differences that have been a source of debate among the most prominent scholars and on which contemporary mathematicians remain divided. "With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics." — Carl B. Boyer, Brooklyn College. 27 figures. Index.
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About the Author
Brian McGuinness is now Professor of the History of Philosophy at Siena. Past publications include the translation of Wittgenstein's "Tractatus Logico-Philosophicus" (with David Pears) and "A Life of Wittegenstein" (Volume 1, "Young Ludwig," 1988). George Henrik von Wright was a pupil and friend of Wittgenstein and succeeded him as Professor of Philosophy at Cambridge. He has since been President of the National Academy in his native Finland. He is one of the trustees to the Wittgenstein estate, and responsible for many of the posthumous publications of Wittgensteins writings.
Language Notes
Text: English (translation)
Original Language: German
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Introduction to Mathematical Thinking : The Formation of Concepts in Modern Mathematics
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Dover Publications, Incorporated, 2003
ISBN 10: 0486428044
ISBN 13: 9780486428048
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Introduction to Mathematical Thinking
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Condition: Bueno. : Introducción al Pensamiento Matemático: La Formación de Conceptos en la Matemática Moderna es un estudio esclarecedor de la formación de conceptos matemáticos, atractivo para lectores con inclinaciones filosóficas. No se requiere formación matemática formal para apreciar su clara exposición de los fundamentos matemáticos. Más que un sistema de teoremas con pruebas completamente desarrolladas o ejemplos de aplicaciones, presenta una exposición coherente de ideas matemáticas que comienza con los números naturales y las leyes básicas de la aritmética, y avanza hacia los problemas del continuo de los números reales y los conceptos del cálculo. Incluye exámenes de varios tipos de números y una crítica de la extensión de los números, aritmética, geometría y la construcción rigurosa de la teoría de los enteros, los números racionales, la base de la aritmética de los números naturales y la construcción rigurosa de la aritmética elemental. Los temas avanzados abarcan el principio de inducción completa, el límite y el punto de acumulación, la operación con secuencias y el cociente diferencial, curvas notables, números reales y ultrarrealistas, y números complejos e hipercomplejos. EAN: 9780486428048 Tipo: Libros Categoría: Filosofía Título: Introduction to Mathematical Thinking Autor: Friedrich Waismann Editorial: Dover Publications Idioma: en Páginas: 272 Formato: tapa blanda. Seller Inventory # Happ-2025-08-08-c76c131f
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Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (Dover Books on Mathematics)
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Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (Dover Books on Mathematics)
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