Description : Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts. But its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Description : “Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You'll never forget the Pythagorean theorem again!”—Scientific American Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations. Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, explaining just how Google searches the internet, or determining how many people you should date before settling down, Strogatz shows how math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the math teacher you wish you’d had. Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.
Description : Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Description : Each year, some two million people in the United Kingdom experience visual hallucinations. Infrequent, fleeting visual hallucinations, often around sleep, are a usual feature of life. In contrast, consistent, frequent, persistent hallucinations during waking are strongly associated with clinical disorders; in particular delirium, eye disease, psychosis, and dementia. Research interest in these disorders has driven a rapid expansion in investigatory techniques, new evidence, and explanatory models. In parallel, a move to generative models of normal visual function has resolved the theoretical tension between veridical and hallucinatory perceptions. From initial fragmented areas of investigation, the field has become increasingly coherent over the last decade. Controversies and gaps remain, but for the first time the shapes of possible unifying models are becoming clear, along with the techniques for testing these. This book provides a comprehensive survey of the neuroscience of visual hallucinations and the clinical techniques for testing these. It brings together the very latest evidence from cognitive neuropsychology, neuroimaging, neuropathology, and neuropharmacology, placing this within current models of visual perception. Leading researchers from a range of clinical and basic science areas describe visual hallucinations in their historical and scientific context, combining introductory information with up-to-date discoveries. They discuss results from the main investigatory techniques applied in a range of clinical disorders. The final section outlines future research directions investigating the potential for new understandings of veridical and hallucinatory perceptions, and for treatments of problematic hallucinations. Fully comprehensive, this is an essential reference for clinicians in the fields of the psychology and psychiatry of hallucinations, as well as for researchers in departments, research institutes and libraries. It has strong foundations in neuroscience, cognitive science, optometry, psychiatry, psychology, clinical medicine, and philosophy. With its lucid explanation and many illustrations, it is a clear resource for educators and advanced undergraduate and graduate students.
Description : The articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. This second volume contains solely a ground breaking paper by Gromov, which provides a fascinating look at finitely generated groups. For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.
Description : A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries. Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetry Covers both point-group and space-group symmetries Includes tutorial solutions
Description : Symmetry and Economic Invariance (second enhanced edition) explores how the symmetry and invariance of economic models can provide insights into their properties. Although the professional economist of today is adept at many of the mathematical techniques used in static and dynamic optimization models, group theory is still not among his or her repertoire of tools. The authors aim to show that group theoretic methods form a natural extension of the techniques commonly used in economics and that they can be easily mastered. Part I provides an introduction that minimizes prerequisites including prior knowledge of group theory. Part II discusses recent developments in the field.
Description : A broad-ranging survey of our current understanding of visual languages and their theoretical foundations. Its main focus is the definition, specification, and structural analysis of visual languages by grammars, logic, and algebraic methods and the use of these techniques in visual language implementation. Researchers in formal language theory, HCI, artificial intelligence, and computational linguistics will all find this an invaluable guide to the current state of research in the field.