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This book on symmetric geometric patterns of Islamic art has educational, aesthetic, cultural and practical purposes. Its central purpose is to bring to the attention of the world in general, and the people of Islamic culture in particular, the potential of the art for providing a unified experience of science and art in the context of mathematical education. Unlike other books on Islamic patterns, this book emphasizes the educational potential in the context of modern physics, chemistry, crystallography and computer graphics. The symmetric structure of about 250 Islamic patterns is presented. Simple, but detailed original, unpublished algorithms suitable for modern computer graphics are given for the construction of two-dimensional periodic patterns. Endorsed by prominent experts from the fields of Physics to Systems and Cybernetics, this book promises to be a must-read, not only for specialised mathematicians, but also for students, graphic artists, illustrators, computer hobbyists, as well as the lay reader keen to explore Islamic art.

This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics and engineering. It treats the dynamics of ray optics, resonant oscillators and the elastic spherical pendulum from a unified geometric viewpoint, by formulating their solutions using reduction by Lie-group symmetries. The only prerequisites are linear algebra, calculus and some familiarity with the Euler Lagrange variational principles and canonical Poisson brackets in classical mechanics at the beginning undergraduate level. The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie Poisson Hamiltonian formulations and momentum maps in physical applications. The many Exercises and Worked Answers aid the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly. The book's many worked exercises make it ideal for both classroom use and self-study. In particular, a substantial appendix containing both introductory examples and enhanced coursework problems with worked answers is included to help the student develop proficiency in using the powerful methods of geometric mechanics. Contents: Fermat s Ray Optics; Newton Lagrange, Hamilton; Differential Forms; Resonances and S1 Reduction; Elastic Spherical Pendulum; Maxwell Bloch Equations.

Discusses the efforts to develop a unified theory of physics, looks at the roles symmetry and beauty have played in scientific research, and considers superstrings and the flow of time

This book on symmetric geometric patterns of Islamic art has educational, aesthetic, cultural and practical purposes. Its central purpose is to bring to the attention of the world in general, and the people of Islamic culture in particular, the potential of the art for providing a unified experience of science and art in the context of mathematical education. Unlike other books on Islamic patterns, this book emphasizes the educational potential in the context of modern physics, chemistry, crystallography and computer graphics. The symmetric structure of about 250 Islamic patterns is presented. Simple, but detailed original, unpublished algorithms suitable for modern computer graphics are given for the construction of two-dimensional periodic patterns. Endorsed by prominent experts from the fields of Physics to Systems and Cybernetics, this book promises to be a must-read, not only for specialised mathematicians, but also for students, graphic artists, illustrators, computer hobbyists, as well as the lay reader keen to explore Islamic art.

Treats a broad segment of the macroscopic physics of dielectrics by a first principles, unified, deductive method. Beginning from a discrete particle point of view, the author constructs a continuum Lagrangian of a dialectric crystal of arbitrary symmetry, structural complexity, and nonlinearity in interaction with the elctromagnetic field. All long wavelength modes of motion of the crystal, both optic and acoustic modes, are accounted for. Once the Lagrangian has been constructed, the remainder of the book is deductively obtained from it.

This monograph presents a coherent and elementary introduction to Gauge theories of the fundamental interactions and their applications to high-energy physics. It deals with the logic and structure of local Gauge symmetries and Gauge theories, from quantum electrodynamics through unified theories of the interactions among leptons and quarks. Many explicit calculations provide the reader with practice in computing the consequences of these theories and offer a perspective on key experimental investigations. First published in 1983, this text is ideal for a one-semester course on Gauge theories and particle physics. Specialists in particle physics and others who wish to understand the basic ideas of Gauge theories will find it useful as a reference and for self-study.

This monograph presents a coherent and elementary introduction to Gauge theories of the fundamental interactions and their applications to high-energy physics. It deals with the logic and structure of local Gauge symmetries and Gauge theories, from quantum electrodynamics through unified theories of the interactions among leptons and quarks. Many explicit calculations provide the reader with practice in computing the consequences of these theories and offer a perspective on key experimental investigations. First published in 1983, this text is ideal for a one-semester course on Gauge theories and particle physics. Specialists in particle physics and others who wish to understand the basic ideas of Gauge theories will find it useful as a reference and for self-study.

This text gives a basic introduction, and a unified approach, to algebra and geometry. Alan Beardon covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups, and various aspects of geometry including groups of isometries, rotations, and spherical geometry. The emphasis is on the interaction among these topics. The text is divided into short sections, with exercises at the end of each section.

This text gives a basic introduction, and a unified approach, to algebra and geometry. Alan Beardon covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups, and various aspects of geometry including groups of isometries, rotations, and spherical geometry. The emphasis is on the interaction among these topics. The text is divided into short sections, with exercises at the end of each section.

This text gives a basic introduction, and a unified approach, to algebra and geometry. Alan Beardon covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups, and various aspects of geometry including groups of isometries, rotations, and spherical geometry. The emphasis is on the interaction among these topics. The text is divided into short sections, with exercises at the end of each section.