Alan Pollack - Böcker
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Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea-transversality-the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincare-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.
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Studies of the spread and containment of disease rely at heart on a variety of mathematical and computational techniques. This collection aims to introduce the fundamentals of epidemiology and to showcase contemporary work using discrete mathematical techniques. Introductory chapters explain the fundamental concepts of epidemiology, the basic tools provided by mathematics and computer science, and some of the outstanding open problems in the area. Contributed articles then highlight particular problems in monitoring disease outbreaks, vaccination strategies, and modelling disease survival factors, and successfully apply techniques such as formal concept analysis, support vector machines, random graph models, and systems of differential equations. Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM). Table of Contents: J. Abello, G. Cormode, D. Fradkin, D. Madigan, O. Melnik, and I. Muchnik -- Selected data mining concepts; D. Schneider -- Descriptive epidemiology: A brief introduction; W. D. Shannon -- Biostatistical challenges in molecular data analysis; L. Hirschman and L. E. Damianos -- Mining online media for global disease outbreak monitoring; D. Ozonoff, A. Pogel, and T. Hannan -- Generalized contingency tables and concept lattices; J. Abello and A. Pogel -- Graph partitions and concept lattices; K. Desai, M.-C. Boily, B. Masse, and R. M. Anderson -- Using transmission dynamics models to validate vaccine efficacy measures prior to conducting HIV vaccine efficacy trials; A. Vazquez -- Causal tree of disease transmission and the spreading of infectious diseases; S. Eubank, V. S. Anil Kumar, M. V. Marathe, A. Srinivasan, and N. Wang -- Structure of social contact networks and their impact on epidemics; J. Abello and M. Capalbo -- Random graphs (and the spread of infections in a social network); S. G. Hartke -- Attempting to narrow the integrality gap for the firefighter problem on trees; J. Li, I. Muchnik, and D. Schneider -- Influences on breast cancer survival via SVM classification in the SEER database; D. Fradkin, I. Muchnik, P. Hermans, and K. Morgan -- Validation of epidemiological models: Chicken epidemiology in the UK; Index. This is a reprint of the 2006 original. (DIMACS/70.S)