In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.

Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships.

Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust's work on and contributions to the theory of fractal interpolation, and the author uses a number of tools-including analysis, topology, algebra, and probability theory-to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content.

Geometry with Trigonometry Second Edition is a second course in plane Euclidean geometry, second in the sense that many of its basic concepts will have been dealt with at school, less precisely. It gets underway with a large section of pure geometry in Chapters 2 to 5 inclusive, in which many familiar results are efficiently proved, although the logical frame work is not traditional. In Chapter 6 there is a convenient introduction of coordinate geometry in which the only use of angles is to handle the perpendicularity or parallelism of lines. Cartesian equations and parametric equations of a line are developed and there are several applications. In Chapter 7 basic properties of circles are developed, the mid-line of an angle-support, and sensed distances. In the short Chaper 8 there is a treatment of translations, axial symmetries and more generally isometries. In Chapter 9 trigonometry is dealt with in an original way which e.g. allows concepts such as clockwise and anticlockwise to be handled in a way which is not purely visual. By the stage of Chapter 9 we have a context in which calculus can be developed. In Chapter 10 the use of complex numbers as coordinates is introduced and the great conveniences this notation allows are systematically exploited. Many and varied topics are dealt with , including sensed angles, sensed area of a triangle, angles between lines as opposed to angles between co-initial half-lines (duo-angles). In Chapter 11 various convenient methods of proving geometrical results are established, position vectors, areal coordinates, an original concept mobile coordinates. In Chapter 12 trigonometric functions in the context of calculus are treated. New to this edition: The second edition has been comprehensively revised over three years Errors have been corrected and some proofs marginally improved The substantial difference is that Chapter 11 has been significantly extended, particularly the role of mobile coordinates, and a more thorough account of the material is given

MESH ist ein mathematisches Video ber vielfl chige Netzwerke und ihre Rolle in der Geometrie, der Numerik und der Computergraphik. Der unter Anwendung der neuesten Technologie vollst ndig computergenierte Film spannt einen Bogen von der antiken griechischen Mathematik zum Gebiet der heutigen geometrischen Modellierung. MESH hat zahlreiche wissenschaftliche Preise weltweit gewonnen. Die Autoren sind Konrad Polthier, ein Professor der Mathematik, und Beau Janzen, ein professioneller Filmdirektor.

Der Film ist ein ausgezeichnetes Lehrmittel f r Kurse in Geometrie, Visualisierung, wissenschaftlichem Rechnen und geometrischer Modellierung an Universit ten, Zentren f r wissenschaftliches Rechnen, kann jedoch auch an Schulen genutzt werden.

This book presents material in two parts. Part one provides an introduction to crossed modules of groups, Lie algebras and associative algebras with fully written out proofs and is suitable for graduate students interested in homological algebra. In part two, more advanced and less standard topics such as crossed modules of Hopf algebra, Lie groups, and racks are discussed as well as recent developments and research on crossed modules.

Flatland is a fascinating nineteenth century work - an utterly unique combination of multi-plane geometry, social satire and whimsy. Although its original publication went largely unnoticed, the discoveries of later physicists brought it new recognition and respect, and its popularity since has justly never waned. It remains a charming and entertaining read, and a brilliant introduction to the concept of dimensions beyond those we can perceive. This is a reworking of the expanded 2nd edition of 1884, with particularly large, clear text, and all the original author's illustrations.

Nowadays, students are struggling to learn math and pass exams. They are overwhelmed with information from lengthy textbooks, review books, and many math websites. With limited time, students cannot benefit from all these resources. Our students need only one concise book to help them review and prepare for the Geometry Regents exam. This is the book "No more. No less. Just right." This book is structured in three parts: 1. A Geometry review that will help students remember all the key topics and build their problem solving skills through the use of examples. 2. A practice section with real Regents questions. 3. Answers and explanations. The topics for the practice questions correspond to the sections in the Geometry review. Students can easily refer back to the matching review sections, while they are doing the practice. This review book is geared towards helping students succeed with high scores on the Regents exams.

The innovative use of sliceforms to explore the properties of surfaces is produced in a systematic way, providing the tools to build surfaces from paper to explore their mathematics. The extensive commentary explains the mathematics behind particular surfaces: an exercise in practical geometry that will stimulate ideas for the student and the enthusiast, as well as having practical applications in engineering and architecture.