This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined.

"Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.

Addresses motivational immediacy from a learner-oriented perspective Provides a comprehensive conceptualization of learning engagement and learning resistance Focused specifically on workplace training contexts

Addresses motivational immediacy from a learner-oriented perspective Provides a comprehensive conceptualization of learning engagement and learning resistance Focused specifically on workplace training contexts

This book provides a fresh look at the question of learner motivation and engagement, beginning with an investigation of potential motivations not to learn, the better to help instructors find more successful ways to engage learners in any given situation. After examining various kinds of resistance to learning, the book goes on to describe effective ways of overcoming resistance and engaging learners. Grounded in the literature of many fields, such as Adult Education, Psychology, Sociology, Cultural Anthropology, and Communication (as well as the author's own decades of experience), the book connects the concepts surrounding learning resistance directly to engagement and human motivation, drawing these ideas together to make the case for practicing motivational immediacy in all learning spaces. The second section of the book focuses on the various tools effective teachers might use to mitigate learner resistance and foster authentic and lasting engagement. The author devotes a chapter to using curriculum and Instructional Systems Design (ISD) processes to effectively foster engaged learning in different learning spaces and contexts. Two chapters are devoted to applying the theory and methods to specific domains: online learning environments, and face-to-face classrooms with both undergraduate and graduate students. The last section includes a chapter that provides a potential method to measure effectual learning in the classroom, and one that addresses the ethical issues sometimes said to exist in efforts to mitigate learner resistance and foster engagement in its place. The final chapter draws the book to a close by presenting a fluid whole that will greatly improve understanding of the ideas as well as the methods best used to reduce learning resistance, increase learner engagement, and facilitate motivational immediacy and effectual learning.

This book provides a fresh look at the question of learner motivation and engagement, beginning with an investigation of potential motivations not to learn, the better to help instructors find more successful ways to engage learners in any given situation. After examining various kinds of resistance to learning, the book goes on to describe effective ways of overcoming resistance and engaging learners. Grounded in the literature of many fields, such as Adult Education, Psychology, Sociology, Cultural Anthropology, and Communication (as well as the author's own decades of experience), the book connects the concepts surrounding learning resistance directly to engagement and human motivation, drawing these ideas together to make the case for practicing motivational immediacy in all learning spaces. The second section of the book focuses on the various tools effective teachers might use to mitigate learner resistance and foster authentic and lasting engagement. The author devotes a chapter to using curriculum and Instructional Systems Design (ISD) processes to effectively foster engaged learning in different learning spaces and contexts. Two chapters are devoted to applying the theory and methods to specific domains: online learning environments, and face-to-face classrooms with both undergraduate and graduate students. The last section includes a chapter that provides a potential method to measure effectual learning in the classroom, and one that addresses the ethical issues sometimes said to exist in efforts to mitigate learner resistance and foster engagement in its place. The final chapter draws the book to a close by presenting a fluid whole that will greatly improve understanding of the ideas as well as the methods best used to reduce learning resistance, increase learner engagement, and facilitate motivational immediacy and effectual learning.

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined.

"Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors' 2007 Springer monograph "Random Fields and Geometry." While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.