Differential Geometry of Singular Spaces and Reduction of Symmetry

In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces. Part II presents an effective approach to the reduction of symmetries. Concrete applications covered in the text include reduction of symmetries of Hamiltonian systems, non-holonomically constrained systems, Dirac structures, and the commutation of quantization with reduction for a proper action of the symmetry group. With each application the author provides an introduction to the field in which relevant problems occur. This book will appeal to researchers and graduate students in mathematics and engineering. This book examines narcissistic, self-absorbed attitudes and behaviors of individuals and the effects of these attitudes and behaviors on the American school system. As the effects are widespread and detrimental, the book also discusses multiple strategies to combat narcissism in schools. Extensive reading, critical observation, and nearly 35 years of combined educational experience led to the formation and completion of this project. Research was collected from over 40 sources including books, periodicals, newspaper articles, interviews, and workshops. Specifically, the book defines narcissistic qualities, identifies long-term societal effects of narcissistic living, discusses narcissism in relation to child development, and extensively examines narcissism in the school setting (the people and practices). The book challenges teachers, counselors, and administrators to reflect on their role in educating the narcissistic population and to adopt strategies to reverse the growing trend. In turn, educators are encouraged to foster a learning experience that promotes greater responsibility, durability, and independence on the part of the learner and that emphasizes the concept of living, learning, and working for the'greater good'in our society. A Narcissistic Society -- Narcissism Defined -- Societal Implications -- Stages Of Child Development -- Narcissistic Parents In The School Setting -- Narcissistic Students In The School Setting -- Education's Role In The Growth Of Narcissism -- Strategies For Examining And Reducing Narcissism In Schools -- Understanding And Addressing The Narcissistic Point Of View -- An Examination Of Case Studies. Chad Mason And Karen Brackman. Includes Bibliographical References (p. 99-102) Originally published in 1912, this book forms the fourth in four volumes of James Joseph Sylvester's mathematical papers, covering the period from 1882 to 1897. Together these volumes provide a comprehensive resource that will be of value to anyone with an interest in Sylvester's theories and the history of mathematics. This book examines narcissistic, self-absorbed attitudes and behaviors of individuals and the effects of these attitudes and behaviors on the American school system, discussing multiple strategies to combat narcissism in schools.