The work of the Norwegian mathematician Sophus Lie extends ideas of symmetry and leads to many applications in mathematics and physics. Ordinarily, the study of the "objects" in Lie's theory (Lie groups and Lie algebras) requires extensive mathematical prerequisites beyond the reach of the typical undergraduate. By restricting to the special case of matrix Lie groups and relying on ideas from multivariable calculus and linear algebra, this lovely and important material becomes accessible even to college sophomores. Working with Lie's ideas fosters an appreciation of the unity of mathematics and the sometimes surprising ways in which mathematics provides a language to describe and understand the physical world.Lie Groups is an active learning text that can be used by students with a range of backgrounds and interests. The material is developed through 200 carefully chosen problems. This is the only book in the undergraduate curriculum to bring this material to students so early in their mathematical careers.
Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions. One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami. Differential Equations on Fractals explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered. This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course.
This book employs Lacanian psychoanalysis to develop new ways of understanding educational domains. It analyses events, practices and policies that occur in school classrooms, teacher education and higher-degree studies including educational research. It provides an accessible introduction, description and analysis of those aspects of Lacan's work concerned with language, identity and subjectivity directly relevant to the field of education. Regulative discourses and practices in education are a central concern and the authors demonstrate how Lacanian theory empowers our understanding of how such discourses are instrumental in forming teacher and researcher identities. The book also shows how regulatory practices and discourses are relevant to research methodologies that arise in the field of action research in education.
The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Information for our distributors: Distributed within the Americas by the American Mathematical Society. All commerical channel discounts apply.
Written by 40 of the most notable Jungian psychoanalysts — spanning 11 countries, and boasting decades of study and expertise — Jungian Psychoanalysis represents the pinnacle of Jungian thought. This handbook brings up to date the perspectives in the field of clinically applied analytical psychology, centering on five areas of interest: the fundamental goals of Jungian psychoanalysis, the methods of treatment used in pursuit of these goals, reflections on the analytic process, the training of future analysts, and special issues, such as working with trauma victims, handicapped patients, or children and adolescents, and emergent religious and spiritual issues. Discussing not only the history of Jungian analysis but its present and future applications, this book marks a major contribution to the worldwide study of psychoanalysis.
In this innovative book, Nathalie Sinclair makes a compelling case for the inclusion of the aesthetic in the teaching and learning of mathematics. Using a provocative set of philosophical, psychological, mathematical, technological, and educational insights, she illuminates how the materials and approaches we use in the mathematics classroom can be enriched for the benefit of all learners. While ranging in scope from the young learner to the professioanl mathematician, there is a particular focus on middle school, where negative feeling toward mathematics frequently begin. This book offers specific recommendations to help teachers evoke and nurture their students' aesthetic abilities.