This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.

"Provocative and illuminating, this book is a must read for adult educators seeking to understand and facilitate transformational learning. It showcases a stellar group of authors who not only engage each other and the reader in constructive discourse, but who also model the heart of the transformational learning process." --Sharan B. Merriam, Department of Adult Education, University of Georgia This volume continues the landmark work begun by Jack Mezirow over twenty years ago--revealing the impact of transformative learning on the theory and practice of adult education. Top scholars and practitioners review the core principles of transformation theory, analyze the process of transformative learning, describe different types of learning and learners, suggest key conditions for socially responsible learning, explore group and organizational learning, and present revelations from the latest research. They also share real-world examples drawn from their own experiences and assess the evolution of transformative learning in practice and philosophy. Learning as Transformation presents an intimate portrait of a powerful learning concept and invites educators, researchers, and scholars to consider the implications of transformative learning in their own professional work.

This book offers a concise and comprehensive exploration of the theory of transformative learning by European researchers. Exploring Mezirow’s theory of transformative learning as a ‘living theory’, the editors and contributors ask whether there a uniquely European perspective on this theory that reflects Europe’s traditions and contexts. What is the nature of that perspective, and how is it similar or different to those espoused in the USA? This book outlines how the theory of transformative learning has been developed by European researchers, and how it has built upon, critiqued, and enriched the Transformation Theory proposed by Mezirow. Consequently, this volume outlines new theoretical perspectives for the future evolution of transformative learning and explores theoretical perspectives that can be put into practice in a range of fields. This wide-ranging volume will be of interest and value to all those interested in transformative learning theory.

Expanding Transformation Theory offers a deeper understanding of the philosophy, principles and major components of Transformation Theory, which was developed by Jack Mezirow. It provides a thorough comprehension of the affinities of the theory with other emancipatory theoretical views and provides the readers with an expanded insight of the core theoretical framework that will support their research and educational practice. The book juxtaposes Mezirow’s perspective with those of ten major emancipatory educationalists – Dewey, Freire, Gould, Marsick, Socrates, Kegan, Greene, Argyris, Illeris, and Jarvis, respectively, who all share the idea of learning with the aim of changing problematic perceptions and behaviours. Such issues as convergences and divergences among the theoretical perspectives, as well as the impact of the theoretical ideas that Mezirow incorporated in his work, are addressed. The work of Mezirow is further reviewed in order to pinpoint the dimensions which appear to have been confirmed and endure over time, and, in turn, those that seem to need expansion or even revision. This book will be of great interest to researchers, academics, students, and adult educators who are interested in transformative learning theory and emancipatory education

Tonality and Transformation is a groundbreaking study in the analysis of tonal music. Focusing on the listener's experience, author Steven Rings employs transformational music theory to illuminate diverse aspects of tonal hearing - from the infusion of sounding pitches with familiar tonal qualities to sensations of directedness and attraction. In the process, Rings introduces a host of new analytical techniques for the study of the tonal repertory, demonstrating their application in vivid interpretive set pieces on music from Bach to Mahler. The analyses place the book's novel techniques in dialogue with existing tonal methodologies, such as Schenkerian theory, avoiding partisan debate in favor of a methodologically careful, pluralistic approach. Rings also engages neo-Riemannian theory-a popular branch of transformational thought focused on chromatic harmony-reanimating its basic operations with tonal dynamism and bringing them into closer rapprochement with traditional tonal concepts. Written in a direct and engaging style, with lively prose and plain-English descriptions of all technical ideas, Tonality and Transformation balances theoretical substance with accessibility: it will appeal to both specialists and non-specialists. It is a particularly attractive volume for those new to transformational theory: in addition to its original theoretical content, the book offers an excellent introduction to transformational thought, including a chapter that outlines the theory's conceptual foundations and formal apparatus, as well as a glossary of common technical terms. A contribution to our understanding of tonal phenomenology and a landmark in the analytical application of transformational techniques, Tonality and Transformation is an indispensible work of music theory.

The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.

This work is a classic reference text for metallurgists, material scientists and crystallographers. The first edition was published in 1965. The first part of that edition was revised and re-published in 1975 and again in 1981. The present two-part set represents the eagerly awaited full revision by the author of his seminal work, now published as Parts I and II. Professor Christian was one of the founding fathers of materials science and highly respected worldwide. The new edition of his book deserves a place on the bookshelf of every materials science and engineering department. Suitable thermal and mechanical treatments will produce extensive rearrangements of the atoms in metals and alloys, and corresponding marked variations in physical and chemical properties. This book describes how such changes in the atomic configuration are effected, and discusses the associated kinetic and crystallographic features. It deals with areas such as lattice geometry, point defects, dislocations, stacking faults, grain and interphase boundaries, solid solutions, diffusion, etc. The first part covers the general theory while the second part is concerned with descriptions of specific types of transformations.