A Treatise on Universal Algebra
With Applications

An introduction to universal algebra by the celebrated mathematician, physicist and philosopher.

Alfred North Whitehead (Author)

9781108001687, Cambridge University Press

Paperback / softback, published 20 July 2009

620 pages
24.4 x 17 x 3.2 cm, 0.97 kg

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.

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.

Subject Areas: Mathematics [PB]