A Treatise on Universal Algebra: With Applications

A Treatise on Universal Algebra: With Applications

by Alfred North Whitehead
     
 

ISBN-10: 1108001688

ISBN-13: 9781108001687

Pub. Date: 07/20/2009

Publisher: Cambridge University Press

Alfred North Whitehead (1861–1947) was equally celebrated as a mathematician, a philosopher and a physicist. He collaborated with his former student Bertrand Russell on the first edition of Principia Mathematica (published in three volumes between 1910 and 1913), and after several years teaching and writing on physics and the philosophy of science at University

Overview

Alfred North Whitehead (1861–1947) was equally celebrated as a mathematician, a philosopher and a physicist. He collaborated with his former student Bertrand Russell on the first edition of Principia Mathematica (published in three volumes between 1910 and 1913), and after several years teaching and writing on physics and the philosophy of science at University College London and Imperial College, was invited to Harvard to teach philosophy and the theory of education. A Treatise on Universal Algebra was published in 1898, and was intended to be the first of two volumes, though the second (which was to cover quaternions, matrices and the general theory of linear algebras) was never published. This book discusses the general principles of the subject and covers the topics of the algebra of symbolic logic and of Grassmann's calculus of extension.

Product Details

ISBN-13:
9781108001687
Publisher:
Cambridge University Press
Publication date:
07/20/2009
Series:
Cambridge Library Collection - Mathematics Series
Edition description:
Reissue
Pages:
620
Product dimensions:
6.60(w) x 9.60(h) x 1.40(d)

Table of Contents

Part I. Principles of Algebraic Symbolism: 1. On the nature of a calculus; 2. Manifolds; 3. Principles of universal algebra; Part II. The Algebra of Symbolic Logic: 1. The algebra of symbolic logic; 2. The algebra of symbolic logic (continued); 3. Existential expressions; 4. Application to logic; 5. Propositional interpretation; Part III. Positional Manifolds: 1. Fundamental propositions; 2. Straight lines and planes; 3. Quadrics; 4. Intensity; Part IV. Calculus of Extension: 1. Combinatorial multiplication; 2. Regressive multiplication; 3. Supplements; 4. Descriptive geometry; 5. Descriptive geometry of conics and cubics; 6. Matrices; Part V. Extensive Manifolds of Three Dimensions: 1. Systems of forces; 2. Groups of systems of forces; 3. In variants of groups; 4. Matrices and forces; Part VI. Theory of Metrics: 1. Theory of distance; 2. Elliptic geometry; 3. Extensive manifolds and elliptic geometry; 4. Hyperbolic geometry; 5. Hyperbolic geometry (continued); 6. Kinematics in three dimensions; 7. Curves and surfaces; 8. Transition to parabolic geometry; Part VII. The Calculus of Extension to Geometry: 1. Vectors; 2. Vectors (continued); 3. Curves and surfaces; 4. Pure vector formulae.

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