Principal Connections

The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is devoted to the theory of connections on principal sheaves, incorporating connections on vector and associated sheaves. Topics such as the moduli sheaf of connections, classification of principal sheaves, curvature, flat connections and flat sheaves, Chern-Weil theory, are also treated. The study brings to light fundamental notions and tools of the standard differential geometry which are susceptible of the present abstraction, and whose role remains unexploited in the classical context, because of the abundance of means therein. However, most of the latter are nonsensical in ADG.

The path to becoming a leader for your students, faculty, and community begins here. The Principal: Leadership for a Global Society is the core textbook for aspiring and practicing K-12 school principals. Taking a practical and research-grounded approach, this inspiring text prepares school leaders to successfully face the challenges that they will deal with on a day-to-day basis and throughout their careers. From curriculum development to staff development to policy and discipline, it addresses the most up-to-date practices in developing leadership skills. The book provides a wide array of pedagogical features to help practicing and aspiring school principals improve programs, create a safer and more enriching environment for students and faculty; meet school, district, community, state, and national ideologies and standards; and much more. After reading The Principal, the educational leaders of tomorrow will be equipped with innovative, practical, and successful leadership concepts and ideas that will help them make a powerful impact on not just those who walk through the school doors, but the community as well.

Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections. The book requires standard undergraduate knowledge on super differential geometry and super Lie groups.

Many of today’s learning environments are dominated by technology or procedure-driven approaches that leave learners feeling alone and disconnected. The authors of Centring Human Connections in the Education of Health Professionals argue that educational processes in the health disciplines should model, integrate, and celebrate human connections because it is these connections that will foster the development of competent and caring health professionals. Centring Human Connections in the Education of Health Professionals equips educators working in clinical, classroom, and online settings with a variety of teaching strategies that facilitate essential human connections. Included is an overview of the educational theory that grounds the authors’ thinking, enabling the educators who employ the strategies included in the book to assess their fit within curriculum requirements and personal teaching philosophies and understand how and why they work.

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The 36 lectures presented at the July 1996 conference all contain new developments in their respective subjects. Beyond the traditional differential geometry subjects, several popular ones such as Einstein manifolds and symplectic geometry are well represented. Subjects include almost Grassmann structures; harmonic maps between almost para-Hermitian manifolds; coeffective cohomology of quaternionic Kahler manifolds; time-dependent mechanical systems with non-linear constraints; the equation defining isothermic surfaces in Laguere geometry; optimal control problems on matrix Lie groups; and leaves of transversely affine foliations. No index. Annotation copyrighted by Book News, Inc., Portland, OR

This hands-on school leadership guide for new and veteran principals and administrators offers practical advice for leading a school successfully. Want honest student input? Try texting. Got a group of angry parents? Arrange one-on-one meetings—you’ll avoid a mob scene and give each family the attention it deserves. Trying to make a teacher feel appreciated? Shoot a quick email after stopping by his classroom and describe something cool you saw him do. It takes ten seconds but has a big impact. These tips and hundreds more are the collective wisdom of three experienced principals who know how to connect with kids, staff, families, and stakeholders, and help students succeed.