The theory of natural dualities, as presented in this text, is broad enough to encompass many known dualities through a rich assortment of substantive theorems, yet concrete enough to be used to generate an array of previously undiscovered dualities. This text will serve as a user manual for algebraists, for category theorists and for those who use algebra in their work, particularly mathematicians and computer scientists interested in non-classical logics. It will also give the specialist a complete account of the foundations, leading to the research frontier of this rapidly developing field. As the first text devoted to the theory of Natural Dualities, it provides an efficient path through a large body of results, examples and applications in this subject which is otherwise available only in scattered research papers. To enable the book to be used in courses, each chapter ends with an extensive exercise set. Several fundamental unsolved problems are included.

Post traumatic stress disorder develops after exposure to one or more terrifying events that have caused, or threatened to cause the sufferer grave physical harm. This book discusses how trauma-focused cognitive therapy can be used to help children and adolescents who suffer from post traumatic stress disorder. Cognitive therapy is frequently used to treat adults who suffer from PTSD with proven results. Post Traumatic Stress Disorder provides the therapist with instructions on how CT models can be used with children and young people to combat the disorder. Based on research carried out by the authors, this book covers: assessment procedures and measures formulation and treatment planning trauma focused cognitive therapy methods common hurdles. The authors provide case studies and practical tips, as well as examples of self-report measures and handouts for young people and their parents which will help the practitioner to prepare for working with this difficult client group. Post Traumatic Stress Disorder is an accessible, practical, clinically relevant guide for professionals and trainees in child and adolescent mental health service teams who work with traumatized children and young people.

The notion of "freedom" has long been associated with a number of perceptions deemed fundamental to an understanding of Scotland and the Scots. Thus Scottish history is viewed, resistance to the Roman Empire, to the Wars of Independence against England, to the eighteenth-century Jacobite uprisings, to the birth of the Labour and Trade Union movements. Key Scottish texts have the concept of liberty at their core: the Declaration of Arbroath, Barbour's Brus, Blind Hary's Wallace, the poems of Robert Burns and Hugh MacDiarmid and the novels of Janice Galloway and Irvine Welsh. Scottish thinkers have written extensively on the philosophies of freedom, be it individual, economic, or religious. These essays examine the question of "freedom", its representations and its interpretations within the literatures of Scotland.

Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation. Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry. The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority. This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Math Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

A ground-breaking argument for better treatment of mental health from Richard Layard (author of Happiness) and David M. Clark. Britain has become a world leader in providing psychological therapies thanks to the work of Richard Layard and David Clark. But, even so, in Britain and worldwide the majority of people who need help still don't get treatment. This is both unjust and a false economy. This book argues for change. It shows that mental ill-health causes more of the suffering in our society than physical illness, poverty or unemployment. Moreover, greater spending on helping people to recover from mental health problems - and stay well - would generate massive savings to national economies, as those who suffer from depression and anxiety disorders account for nearly a half of all disability and are predominantly of working age. Modern talking therapies, such as CBT (Cognitive Behavioural Therapy), are highly effective, and if more sufferers got these treatments, lives would be turned around and the cost would be fully covered by the huge savings. Thrive explores the new effective solutions to the misery and injustice caused by mental illness. It describes how successful psychological treatments have been developed and explains what works best for whom. It also urges us to do all we can to prevent these problems in the first place, through better schools and a better society. And, most importantly, it offers real hope. 'This book is an inspiring success story and a stirring call to further action. Its message is as compelling as it is important: the social costs of mental illness are terribly high and the costs of effective treatments are surprisingly low' Daniel Kahneman 'Extremely easy and pleasurable to read. It's the most comprehensive, humane and generous study of mental illness that I've come across' Melvyn Bragg 'Remarkable . . . presents the issues in a style that easy for the professional, the general public, and policy makers to understand' Aaron T Beck 'Professors Layard and Clark (the Dream Team of British Social Science) make a compelling case for a massive injection of resources into the treatment and prevention of mental illness. This is simply the best book on public policy and mental health ever written' Martin Seligman RICHARD LAYARD is one of the world's leading labour economists, and in 2008 received the IZA International Prize for Labour Economics. A member of the House of Lords, he has done much to raise the public profile of mental health. His 2005 book Happiness has been translated into 20 languages. DAVID M. CLARK, Professor of Psychology at Oxford, is one of the world's leading experts on CBT, responsible for much progress in treatment methods. With Richard Layard, he was the main driver behind the UK's Improving Access to Psychological Therapies programme.

Mental illness is a leading cause of suffering in the modern world. In sheer numbers, it afflicts at least 20 percent of people in developed countries. It reduces life expectancy as much as smoking does, accounts for nearly half of all disability claims, is behind half of all worker sick days, and affects educational achievement and income. There are effective tools for alleviating mental illness, but most sufferers remain untreated or undertreated. What should be done to change this? In Thrive, Richard Layard and David Clark argue for fresh policy approaches to how we think about and deal with mental illness, and they explore effective solutions to its miseries and injustices. Layard and Clark show that modern psychological therapies are highly effective and could potentially turn around the lives of millions of people at little or no cost. This is because treating psychological problems generates huge savings on physical health care, as well as massive economic savings through more people working. So psychological therapies would effectively pay for themselves, generating potential savings for nations the world over. Layard and Clark describe how various successful psychological treatments have been developed and explain what works best for whom. They also discuss how mental illness can be prevented through better schools and a better society, and the urgency of doing so. Illustrating why we cannot afford to ignore the issue of mental illness, Thrive opens the door to new options and possibilities for one of the most serious problems facing us today.

This textbook provides a full and complete axiomatic development of exactly that part of plane Euclidean geometry that forms the standard content of high school geometry. It begins with a set of points, a measure of distance between pairs of points and ten simple axioms. From there the notions of length, area and angle measure, along with congruence and similarity, are carefully defined and their properties proven as theorems. It concludes with a proof of the consistency of the axioms used and a full description of their models. It is provided in guided inquiry (inquiry-based) format with the intention that students will be active learners, proving the theorems and presenting their proofs to their class with the instructor as a mentor and a guide. The book is written for graduate and advanced undergraduate students interested in teaching secondary school mathematics, for pure math majors interested in learning about the foundations of geometry, for faculty preparing future secondary school teachers and as a reference for any professional mathematician. It is written with the hope of anchoring K-12 geometry in solid modern mathematics, thereby fortifying the teaching of secondary and tertiary geometry with a deep understanding of the subject.

The Number Line through Guided Inquiry is designed to give future secondary teachers a deep understanding of the real numbers and functions on the reals. By presenting just that part of the subject that underlies the high school curriculum, this book offers an alternative to a standard real analysis sequence for advanced undergraduate or beginning graduate students. It will give any student a much deeper understanding of the mathematics that they were taught in high school. Written in a guided-inquiry format, this book consists of a carefully scaffolded sequence of definitions, problems, and theorems that guides students through each topic. Readers solve the problems and prove the theorems on their own and present their results to their peers with the instructor as a mentor and a guide. Students will learn not only the mathematics, but also how to help others learn mathematics. They will learn to think creatively and to make compelling arguments to justify their conclusions. They will learn to listen critically to others and give constructive feedback. Ultimately, they will learn to work as a team to answer the bigger questions and build a common understanding of the broader subject.

In a relatively short period of time, cognitive behaviour therapy has become the leading psychotherapy in most Western countries. Much of the appeal and success of cognitive behaviour therapy is due to the close links between science and practice which characterise the cognitive behaviour therapy movement and to the demonstrated effectiveness of the treatment approach. This book, which is divided into two parts, illustrates the links between science and practice in modern Cognitive Behaviour Therapy. Part One covers general issues and includes chapters on: The Evolution of Cognitive Behaviour Therapy (Stanley Rachman); The Foundations of Cognitive Behaviour Therapy (Michael Gelder); Information Processing Biases in Emotional Disorders (Andrew Mathews); The Relationship Between Cognition and Emotion (John D Teasdale); Efficacy and Dissemination of Psychological Treatment (David H. Barlow and Stefan G Hofmann). Part Two focuses on specific disorders and includes chapters on: Panic Disorder and Social Phobia (David M Clark); Generalized Anxiety Disorder (Adrian Wells and Gillian Butler); Obsessive-Compulsive Disorder (Paul M Salkovskis and Joan Kirk); Eating Disorders (Christopher G Fairburn); Sexual Problems (John Bancroft); Depression (J Mark G Williams); Attempted Suicide (Keith Hawton) Hypochondriasis (Paul M Salkovskis and Christopher Bass); Cardiovascular Disease (Derek W Johnston) Atypical Chest Pain (Richard Mayou); Chronic Fatigue (Michael Sharpe); Problem-Solving Treatment in Primary Care (Denis Gath and Laurence Mynors-Wallis). Each of the chapters in Part Two outlines the current cognitive behavioural conceptualization of the disorder, reviews relevant research and describes current cognitive behavioural treatment procedures. The book will be of interest to clinicians and researchers from a wide range of backgrounds, as well as students and trainees in clinical psychology, psychiatry and psychotherapy.