Graham Hall – författare

Four-Dimensional Manifolds and Projective Structure may be considered first as an introduction to differential geometry and, in particular, to 4−dimensional manifolds, and secondly as an introduction to the study of projective structure and projective relatedness in manifolds.

The initial chapters mainly cover the elementary aspects of set theory, linear algebra, topology, Euclidean geometry, manifold theory and differential geometry, including the idea of a metric and a connection on a manifold and the concept of curvature. After this, the author dives deeper into 4-dimensional manifolds and, in particular, the positive definite case for the metric. The book also covers Lorentz signature and neutral signature in detail and introduces, and makes use of, the holonomy group of such a manifold for connections associated with metrics of each of these three possible signatures. A brief interlude on some key aspects of geometrical symmetry precedes a detailed description of projective relatedness, that is, the relationship between two symmetric connections (and between their associated metrics) which give rise to the same geodesic paths.

Features:

Four-Dimensional Manifolds and Projective Structure may be considered first as an introduction to differential geometry and, in particular, to 4−dimensional manifolds, and secondly as an introduction to the study of projective structure and projective relatedness in manifolds.

The initial chapters mainly cover the elementary aspects of set theory, linear algebra, topology, Euclidean geometry, manifold theory and differential geometry, including the idea of a metric and a connection on a manifold and the concept of curvature. After this, the author dives deeper into 4-dimensional manifolds and, in particular, the positive definite case for the metric. The book also covers Lorentz signature and neutral signature in detail and introduces, and makes use of, the holonomy group of such a manifold for connections associated with metrics of each of these three possible signatures. A brief interlude on some key aspects of geometrical symmetry precedes a detailed description of projective relatedness, that is, the relationship between two symmetric connections (and between their associated metrics) which give rise to the same geodesic paths.

Features:

Method and Postmethod in Language Teaching provides a comprehensive, accessible, and engaging guide to the much-debated notions of ‘method’, ‘methods’, and ‘postmethod’ in language teaching.

Divided into three sections − ‘Contexts’, ‘Concepts’, and ‘Debates’ – the book sets out ‘traditional’ understandings of method(s), examines alternative accounts and critiques that inform, and at times go beyond, postmethod thinking within language teaching, and finally relates these issues to key practical debates and dilemmas that teachers navigate in the classrooms.

Highlighting the importance of teachers’ understandings of their own professional contexts, the volume uses the notion of method as a ‘lens’ through which teachers and other language teaching professionals can clarify their understandings of language teaching, both in terms of pedagogic practices and classroom possibilities, and with regard to the development of this diverse field more generally.

Throughout, readers are encouraged to develop their own thinking and practice in contextually appropriate ways, supported by discussion questions and key readings that accompany each chapter, a glossary of key terms, and suggestions for additional reading.

This book is an indispensable resource for language teachers and other language teaching professionals, as well as postgraduate and upper-level undergraduate students of Applied Linguistics, Language Teacher Education, and ELT/TESOL and other language teaching programmes.

Method and Postmethod in Language Teaching provides a comprehensive, accessible, and engaging guide to the much-debated notions of ‘method’, ‘methods’, and ‘postmethod’ in language teaching.

Divided into three sections − ‘Contexts’, ‘Concepts’, and ‘Debates’ – the book sets out ‘traditional’ understandings of method(s), examines alternative accounts and critiques that inform, and at times go beyond, postmethod thinking within language teaching, and finally relates these issues to key practical debates and dilemmas that teachers navigate in the classrooms.

Highlighting the importance of teachers’ understandings of their own professional contexts, the volume uses the notion of method as a ‘lens’ through which teachers and other language teaching professionals can clarify their understandings of language teaching, both in terms of pedagogic practices and classroom possibilities, and with regard to the development of this diverse field more generally.

Throughout, readers are encouraged to develop their own thinking and practice in contextually appropriate ways, supported by discussion questions and key readings that accompany each chapter, a glossary of key terms, and suggestions for additional reading.

This book is an indispensable resource for language teachers and other language teaching professionals, as well as postgraduate and upper-level undergraduate students of Applied Linguistics, Language Teacher Education, and ELT/TESOL and other language teaching programmes.

The Internationalization of Small to Medium Enterprizes uses information from annual surveys of companies in Europe during the period spanning the formation of a single European market. It addresses issues affecting small businesses such as marketing, entrepreneurship, export strategies and the single market, on an international basis. The book also contains detailed case studies of individual countries including The Netherlands, Finland, Switzerland and the UK.

The Internationalization of Small to Medium Enterprizes uses information from annual surveys of companies in Europe during the period spanning the formation of a single European market. It addresses issues affecting small businesses such as marketing, entrepreneurship, export strategies and the single market, on an international basis. The book also contains detailed case studies of individual countries including The Netherlands, Finland, Switzerland and the UK.

The Routledge Handbook of English Language Teaching is the definitive reference volume for postgraduate and advanced undergraduate students of Applied Linguistics, ELT/TESOL, and Language Teacher Education, and for ELT professionals engaged in in-service teacher development and/or undertaking academic study.

Progressing from ‘broader’ contextual issues to a ‘narrower’ focus on classrooms and classroom discourse, the volume’s inter-related themes focus on:

The Handbook’s 39 chapters are written by leading figures in ELT from around the world. Mindful of the diverse pedagogical, institutional and social contexts for ELT, they convincingly present the key issues, areas of debate and dispute, and likely future developments in ELT from an applied linguistics perspective.

Throughout the volume, readers are encouraged to develop their own thinking and practice in contextually appropriate ways, assisted by discussion questions and suggestions for further reading that accompany every chapter.

Advisory board: Guy Cook, Diane Larsen-Freeman, Amy Tsui, and Steve Walsh

The Routledge Handbook of English Language Teaching is the definitive reference volume for postgraduate and advanced undergraduate students of Applied Linguistics, ELT/TESOL, and Language Teacher Education, and for ELT professionals engaged in in-service teacher development and/or undertaking academic study.

Progressing from ‘broader’ contextual issues to a ‘narrower’ focus on classrooms and classroom discourse, the volume’s inter-related themes focus on:

The Handbook’s 39 chapters are written by leading figures in ELT from around the world. Mindful of the diverse pedagogical, institutional and social contexts for ELT, they convincingly present the key issues, areas of debate and dispute, and likely future developments in ELT from an applied linguistics perspective.

Throughout the volume, readers are encouraged to develop their own thinking and practice in contextually appropriate ways, assisted by discussion questions and suggestions for further reading that accompany every chapter.

Advisory board: Guy Cook, Diane Larsen-Freeman, Amy Tsui, and Steve Walsh