Mathematical truths are often so compelling that some mathematicians, scientists, and philosophers posit a purely nonmaterial realm of eternal truths accessible to the mind alone. Mathematical physicist Simon Altmann carefully criticizes this revival of dualistic philosophy la Plato in this highly stimulating book. Has mathematics and physics discovered a new supernatural world, or is this mental cosmos simply an outgrowth of natural evolutionary processes? This is the crucial philosophical issue that Altmann elucidates.
Altmann provides a thorough philosophical basis to understand the meaning of natural law, the scientific method, and causality in science. He reviews the classical approach to time, space, and the laws of mechanics, and discusses the implications of relativity theory. Key modern concepts, like randomness, probability, and time's arrow are explained, and the nature of mathematics and Gdel's theorems is discussed in depth. A mystery-free treatment of quantum mechanics, Schrdinger's cat, and the famous Bell inequalities follows. He also assesses the reactions of various philosophical schools to these developments - idealism, physicalism, cultural relativism and social constructivism. The book concludes with a fascinating dialogue on science and belief.
Educated lay readers will welcome Altmann's engaging and lucid exposition.

This text presents a consistent description of the geometric and quaternionic treatment of rotation operators. Covers the fundamentals of symmetries, matrices, and groups and presents a primer on rotations and rotation matrices. Also explores rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, more. Includes problems with solutions.

The structure of much of solid-state theory comes directly from group theory, but until now there has been no elementary introduction to the band theory of solids which adopts this approach. This book provides such an introduction, employing only the simplest and most basic of group theoretical ideas, and emphasizing the significance of symmetry in determining many of the essential concepts used in the subject. Given the extensive training of chemists in applying group theory, there is no quicker entry into the subject than by means of the approach used in this book. Many topics were chosen with the needs of chemists in mind, and many of the examples have a chemical flavour. Numerous problems are included which enable the reader to apply the major ideas and to complete some parts of the treatment. Chemists will find this a valuable introduction to band theory, and the book will also appeal to all physical scientists who would like to go a little beyond the elementary treatments so far available.