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Graphs, Surfaces and Homology
viii homology groups. A weaker result, sufficient nevertheless for our purposes, is proved in Chapter 5, where the reader will also find some discussion of the need for a more powerful in variance theorem and a summary of the proof of such a theorem. Secondly the emphasis in this book is on low-dimensional examples the graphs and surfaces of the title since it is there that geometrical intuition has its roots. The goal of the book is the investigation in Chapter 9 of the properties of graphs in surfaces; some of the problems studied there are mentioned briefly in the Introduction, which contains an in formal survey of the material of the book. Many of the results of Chapter 9 do indeed gener...
Graphs, Surfaces and Homology
Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.
Local Features in Natural Images via Singularity Theory
This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer’s eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the “apparent contours”. We do so by a mathematical analysis using a repertoire of methods in singularity theory. This is applied for generic light directions of both the “stable configurations” for these interactions, whose features remain unchanged under small viewer movement, and the generic changes which occur under changes of view directions. These may then be used to differentiate between objects and determine their shapes and positions.
Primes and Programming
In this introductory book Dr Giblin describes methods that have been developed for testing the primality of numbers, provides Pascal programs for their implementation, and gives applications to coding.
Visual Motion of Curves and Surfaces
Computer vision aims to detect and reconstruct features of surfaces from the images produced by cameras, in some way mimicking the way in which humans reconstruct features of the world around them by using their eyes. In this book the authors describe research in computer vision aimed at recovering the 3D shape of surfaces from image sequences of their 'outlines'. They provide all the necessary background in differential geometry (assuming knowledge of elementary algebra and calculus) and in the analysis of visual motion, emphasising intuitive visual understanding of the geometric techniques with computer-generated illustrations. They also give a thorough introduction to the mathematical techniques and the details of the implementations and apply the methods to data from real images using the most current techniques.
Stitches in Time
This book deals with the history of surgery in Papua New Guinea from the early 1800s until the beginning of the 21st Century. It spans the period from the first European contact to the emergence of highly educated sub-specialist national surgeons. It tells the story from the first impressions of ships surgeons to the introduction and development of surgery. Between 1870 and 1950 the country and the lives of its peoples changed greatly as a result of exploration, evangelisation, colonisation and war. The history traces the surgical challenges encountered as well as the colourful characters who provided the health services run by missions, companies, governments and armies. After World War II PNG progressed politically from an Australian Administered Territory to become an Independent Nation. Within a generation it had trained its own doctors and surgeons. The history is set within the context of tropical pathologies, introduced diseases, surgical progress and the lives of the medics who have contributed to the Stori bilong kamapim long dokta bilong katim man (The history of surgery).
Mathematical Explorations with MATLAB
This book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package Matlab. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with Matlab, no starting knowledge of the package being assumed.
Scale Space and PDE Methods in Computer Vision
Welcome to the proceedings of the 5th International Conference on Scale-Space and PDE Methods in Computer Vision. The scale-space concept was introduced by Iijima more than 40 years ago and became popular later on through the works of Witkin and Koenderink. It is at the junction of three major schools of thought in image processing and computer vision: the design of ?lters, axiomatic approaches based on partial di?erential equations (PDEs), and variational methods for image regularization. Scale-space ideas belong to the mathematically best-understood approaches in image analysis. They have entered numerous successful applications in medical imaging and a number of other ?elds where they oft...
Global Differential Geometry
Alfred Gray's work covered a great part of differential geometry. In September 2000, a remarkable International Congress on Differential Geometry was held in his memory in Bilbao, Spain. Mathematicians from all over the world, representing 24 countries, attended the event. This volume includes major contributions by well known mathematicians (T. Banchoff, S. Donaldson, H. Ferguson, M. Gromov, N. Hitchin, A. Huckleberry, O. Kowalski, V. Miquel, E. Musso, A. Ros, S. Salamon, L. Vanhecke, P. Wellin and J.A. Wolf), the interesting discussion from the round table moderated by J.-P. Bourguignon, and a carefully selected and refereed selection of the Short Communications presented at the Congress.This book represents the state of the art in modern differential geometry, with some general expositions of some of the more active areas: special Riemannian manifolds, Lie groups and homogeneous spaces, complex structures, symplectic manifolds, geometry of geodesic spheres and tubes and related problems, geometry of surfaces, and computer graphics in differential geometry.
50 Visions of Mathematics
"To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain"--Provided by publisher.
