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From Kant to Hilbert Volume 1 A Source Book in the Foundations of Mathematics 1st Edition by William Bragg Ewald 9780198505358 0198505353

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Author(s): William Bragg Ewald
ISBN(s): 9780198505358, 0198505353
Edition: Reprint
File Details: PDF, 38.32 MB
Year: 2007
Language: english
SKU: EB-975584 Category: Tag:

From Kant to Hilbert Volume 1 A Source Book in the Foundations of Mathematics 1st Edition by William Bragg Ewald – Ebook PDF Instant Download/Delivery: 9780198505358, 0198505353

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Product details:

ISBN 10: 0198505353

ISBN 13: 9780198505358

Author: William Bragg Ewald

Immanuel Kant’s Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics–algebra, geometry, number theory, analysis, logic and set theory–with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics.

Table of contents:

Chapter 1: George Berkeley 
A. From the Philosophical Commentaries
B. Of Infinites
C. Letter to Samuel Molyneux
D. From A Treatise concerning the Principles of Human Knowledge, Part One
E. De Motu
F. From Alciphron
G. From Newton’s Principia Mathematica
H. The Analyst

Chapter 2: Colin Maclaurin 
A. From A Treatise of Fluxions

Chapter 3: Jean Lerond d’Alembert
A. Differential
B. Infinite
C. Limit

Chapter 4: Immanuel Kant 
A. From Thoughts on the True Estimation of Active Forces
B. From the Transcendental Aesthetic
C. From the Discipline of Pure Reason
D. Frege on Kant

Chapter 5: Johann Heinrich Lambert 
A. From the Theory of Parallel Lines

Chapter 6: Bernard Bolzano 
A. Preface to Considerations on Some Objects of Elementary Geometry
B. Contributions to a Better-grounded Presentation of Mathematics
C. Purely Analytic Proof of the Theorem that between any Two Values which give Results of Opposite Signs…
D. From Paradoxes of the Infinite

Chapter 7: Carl Friedrich Gauss
A. On the Metaphysics of Mathematics
B. Gauss on Non-Euclidean Geometry
C. Notice on the Theory of Biquadratic Residues

Chapter 8: Duncan Gregory 
A. On the Real Nature of Symbolical Algebra

Chapter 9: Augustus De Morgan 
A. On the Foundation of Algebra
B. Trigonometry and Double Algebra

Chapter 10: William Rowan Hamilton 
A. From the Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay
B. Preface to the Lectures on Quaternions
C. From the Correspondence of Hamilton with De Morgan

Chapter 11: George Boole 
A. The Mathematical Analysis of Logic, being an Essay towards a Calculus of Deductive Reasoning

Chapter 12: James Joseph Sylvester 
A. Presidential Address to Section “A” of the British Association

Chapter 13: William Kingdon Clifford 
A. On the Space Theory of Matter
B. On the Aims and Instruments of Scientific Thought

Chapter 14: Arthur Cayley
A. Presidential Address to the British Association, September 1883

Chapter 15: Charles Sanders Peirce 
A. From Linear Associative Algebra
B. Notes on Benjamin Peirce’s Linear Associative Algebra
C. On the Logic of Number
D. On the Algebra of Logic: A Contribution to the Philosophy of Notation
E. The Logic of Mathematics in Relation to Education
F. From The Simplest Mathematics

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Tags: William Bragg Ewald, Kant, Hilbert, Foundations