A Treatise on Universal Algebra With Applications [Paperback]

An introduction to universal algebra by the celebrated mathematician, physicist and philosopher.Alfred North Whitehead (18611947) was equally celebrated as a mathematician, a philosopher and a physicist. This volume, published in 1898, deals with the general principles of universal algebra and covers the topics of the algebra of symbolic logic and of Grassmanns calculus of extension.Alfred North Whitehead (18611947) was equally celebrated as a mathematician, a philosopher and a physicist. This volume, published in 1898, deals with the general principles of universal algebra and covers the topics of the algebra of symbolic logic and of Grassmanns calculus of extension.Alfred North Whitehead (18611947) 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. CalcululS+