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Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds...
A small-town musician from North Carolina tries his luck on the biggest stage of all: New York City. And he hits the jackpot. Mere months into his NYC gambit, guitarist Jeffrey Lee Campbell is catapulted from selling candy in Broadway theaters to touring the world with rock legend Sting. Go behind the scenes with the provincial, wide-eyed rookie as he fakes his way around the globe, shoulder-to-shoulder with his longtime musical hero. Do Stand So Close is a layered, coming-of-age memoir, recounting Jeffrey Lee Campbell's glamorous (and grueling) twenty-five country, six-continent trial by fire on Sting's "Nothing Like The Sun" World Tour. Filled with humorous anecdotes and poignant revelations, Do Stand So Close follows Jeffrey's amazing odyssey--from relocating to NYC and miraculously landing the high-profile gig, to life on the road with one of the planet's biggest rock stars, to his humbling crash-and-burn after the tour. Buckle up
In Online Predators: An Internet Insurgency, Jeffrey A. Lee brings his ten plus years’ experience in the fight against online child exploitation to bear in an easy to follow guide for all with a stake in the life of a child. This book equips parents, guardians, extended family, educational professionals with practical strategies to help keep kids safe in a technology connected world. Instead of focusing on ever changing technology, Lee proposes a key fundamental change in the fight against online predation—develop an insatiable curiosity about their child’s online life, then get in the front lines and stay there.
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
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Molly's life was turned upside down by the car accident that injured her and crippled her father, but at her new middle school she teams up with a weird misfit for a science competition and makes a true blue friend.
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for furthe...
Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the fir...
In A Young Actor Prepares, Jeff Alan-Lee masterfully delivers kids' and teens' acting classes presented as plays in script form. The classes are based on actual semesters at the Young Actor's Studio in Los Angeles and provide step-by-step approaches to help children and teenagers portray complex characters and tackle emotionally challenging roles. For over thirty years, Alan-Lee has worked with thousands of young people, teaching the work presented in this book. His work has been the springboard for award-winning artists in acting, directing, playwriting, screenwriting, and music. Inspired by Stanislavski's An Actor Prepares, Alan-Lee has developed engaging and exciting ways to create great ...
The definitive classic that has helped more than 400,000 people defeat obsessive-compulsive behavior, with all-new material from the author An estimated 5 million Americans suffer from obsessive-compulsive disorder (OCD) and live diminished lives in which they are compelled to obsess about something or to repeat a similar task over and over. Traditionally, OCD has been treated with Prozac or similar drugs. The problem with medication, aside from its cost, is that 30 percent of people treated don't respond to it, and when the pills stop, the symptoms invariably return. In Brain Lock, Jeffrey M. Schwartz, M.D., presents a simple four-step method for overcoming OCD that is so effective, it's no...