The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied.This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.

The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.

These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.

Academic Presenting and Presentations (APP) is a research-based training course designed to help students cultivate academic presentation skills and deal with the various presentation tasks they may be expected to fulfil as part of their university or college studies. The material is suitable for a global audience and can be used in a wide range of contexts in the field of Communcation Skills, English Language Teaching and English for Academic Purposes. The instructional and practice material included not only helps students to develop their presentation skills but also deals with broader topics of interest in a study-oriented context, such as research and plagiarism. The unique content emphasises higher level task-achievement rather than discrete language points, since experience shows that this is the area most students find especially difficult. Each unit of Academic Presenting and Presentations focuses on a different presentation genre, building the students’ awareness of how to present effectively whilst at the same time focusing attention on the specific requirements of addressing an audience in an academic environment. The accompanying videos form an integral component of this course and consist of two types of presentation: Learning Presentations, which give advice to students, and Sample Presentations, which illustrate different types of presentation. The downloadable videos are included in the online support materials.

Hillier is a friendly guide for those new to the world of further and adult education or for those... finding themselves required for the first time to work towards a formal teaching qualification.' Richard Sykes, Studies in the Education of Adults 'This is a useful book... [It] systematically covers the FENTO standards for teaching and supporting learning in further education...' Ron Kirby, Youth & Policy This second edition of the best-selling textbook Reflective Teaching in Further and Adult Education has been extensively revised and updated throughout. The book has: - An updated chapter on new government policy in lifelong learning. - Details of the changing qualifications framework, foundation degrees and e-learning - An expanded chapter on professional practice - New sections on disability awareness, working with young people, and new technologies. - Checklists, examples, scenarios and figures to aid learning - Chapter summaries to aid navigation of the text - A guide to the FENTO standards at the end of each chapter - Guides for further reading and websites - A glossary of unfamiliar terms This comprehensive, accessibly-written textbook is a practical resource which will be invaluable to teachers in further and adult education, whether in-training or in-service.

Much has been written about special education and about inclusive education, but there have been few attempts to pull these two concepts and approaches together. This book does just that: sets special education within the context of inclusive education. It posits that to include, effectively, all children with special educational needs in schools requires an integration of both concepts, approaches, and techniques. It has never been more timely to publish a book that helps professionals who work with schools, such as psychologists, special education professionals, and counselors, to identify effective practices for children with special needs and provide guidelines for implementing these in inclusive schools.

Primary text for middle school language arts methods courses. Presents balanced attention to various teaching strategies, processes, and content, demonstrating how all of these connect to improve students abilities to communicate.

"Models of Teaching is a great asset for beginning teachers as they integrate their pre-service training with the standards-based curricula in schools." —Amany Saleh, Arkansas State University "Rarely have I read a text from cover to cover...however, your text provided an abundance of effective teaching strategies in ways that better informed my own teaching...I was compelled to read through the entire test! Great job!" —Carolyn Andrews, Student at University of Nevada, Reno "This is a practical text that focuses on current practices in education and demonstrates how various models of teaching can address national standards." —Marsha Zenanko, Jacksonville State University "Models of Teaching provides excellent case studies that will enable students to ′see′ models of teaching in practice in the classroom." —Margaret M. Ferrara, University of Nevada, Reno Models of Teaching: Connecting Student Learning With Standards features classic and contemporary models of teaching appropriate to elementary and secondary settings. Authors Jeanine M. Dell′Olio and Tony Donk use detailed case studies to discuss 10 models of teaching and demonstrate how the models can incorporate state content standards and benchmarks, as well as technology standards. This book provides students with a theoretical and practical understanding of how to use models of teaching to both meet and exceed the growing expectations for research-based instructional practices and student achievement. Key Features Shows how each model looks and sounds in classrooms at all levels: Each model is illustrated with two detailed case studies (elementary and secondary) and post-lesson reflections. Offers detailed descriptions of the phases of each model: Each model is accompanied by a detailed chart and discussion of the steps of the model. Applies technology standards and performance indicators: Each chapter addresses how the particular model can be implemented to meet technology standards and performance indicators. Connects philosophies of curriculum and instruction: This book connects each model to a philosophy of curriculum and instruction that undergirds that model so teachers understand both how to teach and why. Promotes student interaction with the text: Exercises at the end of each chapter provide the opportunity for beginning teachers to work directly with core curricula from their own state, and/or local school district curricula. Each model is illustrated with two detailed case studies (elementary and secondary) and post-lesson reflections. A High Quality Ancillary Package! Instructors′ Resource CD-ROM—This helpful CD-ROM offers PowerPoint slides, an electronic test bank, Web resources, a teaching guide for the case studies, lesson plan template instructions, and much more. Qualified instructors can request a copy by contacting SAGE Customer Care at 1-800-818-SAGE (7243) from 6am–5pm, PT. Student Study Site — This study site provides practice tests, flash cards, a lesson plan template, suggested assignments, links to state content and technology standards, field experience guides, and much more. Intended Audience: This is an excellent core textbook for advanced undergraduate and graduate students studying Elementary and/or Secondary Teaching Methods in the field of Education.