Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Exploring the full scope of differential topology, this comprehensive account of geometric techniques for studying the topology of smooth manifolds offers a wide perspective on the field. Building up from first principles, concepts of manifolds are introduced, supplemented by thorough appendices giving background on topology and homotopy theory. Deep results are then developed from these foundations through in-depth treatments of the notions of general position and transversality, proper actions of Lie groups, handles (up to the h-cobordism theorem), immersions and embeddings, concluding with the surgery procedure and cobordism theory. Fully illustrated and rigorous in its approach, little prior knowledge is assumed, and yet growing complexity is instilled throughout. This structure gives advanced students and researchers an accessible route into the wide-ranging field of differential topology.

The biennial meetings at Sao Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.

Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.

Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

In 1977 several eminent mathematicians were invited to Durham to present papers at a short conference on homological and combinatorial techniques in group theory. The lectures, published here, aimed at presenting in a unified way new developments in the area. Group theory is approached from a geometrical viewpoint and much of the material has not previously been published. The various ways in which topological ideas can be used in group theory are also brought together. The volume concludes with an extensive set of problems, ranging from explicit questions demanding detailed calculation to fundamental questions motivating research in the area. These lectures will be of interest mainly to researchers in pure mathematics but will also prove useful in connection with relevant postgraduate courses.

Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.

The Traumatic Event Crisis Intervention Plan (TECIP(c)), the flagship program of Crisis Oriented Planning and Educational Services, LLC., is a field tested school-based framework designed to meet the emotional and psychological needs of students and staff in the AFTERMATH of a traumatic event.

This book contains marketing techniques for travel professionals that will show them how to benefit from current technology using orthodox marketing methods and also online and social media. It is current and contains vital information to help travel agent propel themselves to success.

The 18th century was a wealth of knowledge, exploration and rapidly growing technology and expanding record-keeping made possible by advances in the printing press. In its determination to preserve the century of revolution, Gale initiated a revolution of its own: digitization of epic proportions to preserve these invaluable works in the largest archive of its kind. Now for the first time these high-quality digital copies of original 18th century manuscripts are available in print, making them highly accessible to libraries, undergraduate students, and independent scholars.The Age of Enlightenment profoundly enriched religious and philosophical understanding and continues to influence present-day thinking. Works collected here include masterpieces by David Hume, Immanuel Kant, and Jean-Jacques Rousseau, as well as religious sermons and moral debates on the issues of the day, such as the slave trade. The Age of Reason saw conflict between Protestantism and Catholicism transformed into one between faith and logic -- a debate that continues in the twenty-first century.++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification: ++++Huntington LibraryN046211With a half-title.London: printed for J. Robinson, 1703. 4],24p.; 4

A humorous, anecdotal story about how a small entrepreneur becomes a 'collection agent' just to collect accounts receivable. This book is divided into four sections; history, collection processes, anecdotes, and samples of forms and letters. Learn and laugh. It's Your Money Far more fun than a boring how-to book