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Algebra --- Number theory --- 511.5 --- Diophantine equations --- 511.5 Diophantine equations --- Fermat's last theorem --- Last theorem, Fermat's --- Diophantine analysis --- Fermat's theorem --- Congresses

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Curated by the Fields Institute for Research in Mathematical Sciences from their COVID-19 Math Modelling Seminars, this first in a series of volumes on the mathematics of public health allows readers to access the dominant ideas and techniques being used in this area, while indicating problems for further research. This work brings together experts in mathematical modelling from across Canada and the world, presenting the latest modelling methods as they relate to the COVID-19 pandemic. A primary aim of this book is to make the content accessible so that researchers share the core methods that may be applied elsewhere. The mathematical theories and technologies in this book can be used to support decision makers on critical issues such as projecting outbreak trajectories, evaluating public health interventions for infection prevention and control, developing optimal strategies to return to a new normal, and designing vaccine candidates and informing mass immunization program. Topical coverage includes: basic susceptible-exposed-infectious-recovered (SEIR) modelling framework modified and applied to COVID-19 disease transmission dynamics; nearcasting and forecasting for needs of critical medical resources including personal protective equipment (PPE); predicting COVID-19 mortality; evaluating effectiveness of convalescent plasma treatment and the logistic implementation challenges; estimating impact of delays in contact tracing; quantifying heterogeneity in contact mixing and its evaluation with social distancing; modelling point of care diagnostics of COVID-19; and understanding non-reporting and underestimation. Further, readers will have the opportunity to learn about current modelling methodologies and technologies for emerging infectious disease outbreaks, pandemic mitigation rapid response, and the mathematics behind them. The volume will help the general audience and experts to better understand the important role that mathematics has been playing during this on-going crisis in supporting critical decision-making by governments and public health agencies.

Numerical methods of optimisation --- Operational research. Game theory --- Mathematics --- Biomathematics. Biometry. Biostatistics --- Biology --- Hygiene. Public health. Protection --- Planning (firm) --- Computer science --- Computer. Automation --- volksgezondheid --- biomathematica --- biologie --- automatisering --- informatica --- mathematische modellen --- wiskunde

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Srinivasa Ramanujan was a mathematician brilliant beyond compare. There is extensive literature available on the work of Ramanujan, but what is more difficult to find in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by G. H. Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work is still having an impact on many different fields of mathematical research. The book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors, focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.  .

Mathematics --- Number theory --- Algebra --- Algebraic geometry --- Harmonic analysis. Fourier analysis --- Discrete mathematics --- Mathematics --- Fourieranalyse --- algebra --- discrete wiskunde --- functies (wiskunde) --- wiskunde --- wiskunde --- getallenleer --- anno 2000-2099

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This book brings together technical expertise, best practices, case studies and ground-level application of the ideas for empowering the rural population of the world to live economically prosperous, environmentally sustainable, and socially progressive lives, on par or comparable with the quality of life enjoyed by the global urban population. The idea of Smart Villages takes on greater urgency in light of the investments made in this millennium on "Smart Cities", taking advantage of the technological advances, particularly in digital connectivity. These investments have and will continue to expand the urban-rural divide, unless similar investments are made in the villages as well. The book provides a much-needed guide for a holistic development of a Smart Village, by defining the need, developing the framework, and describing the delivery, complete with successful case studies. Contributors to the book, from Canada, USA, Africa and India bring years of academic, industry and governmental experience, including organization of several Smart Village conferences. The knowledge base in the book will be of great value to anyone interested in or active in rural planning, including governmental and non-governmental organizations, industrial solution providers, public healthcare professionals, public policy professionals and students, as well as rural communities around the world. Consolidates all the aspects of creating/developing a Smart Village; Delivers an effective tool-kit for practitioners in the area of Smart Villages; Provides a policy-based framework for the development of an ideal Smart Village; Illustrates, through case studies, the fulfillment of key requirements of a Smart Village; Brings together experts from around the world to share their vision of a Smart Village; Highlights the importance of balancing development with social/gender equity and cultural traditions.

Telecommunication technology --- Mass communications --- Computer architecture. Operating systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Environmental planning --- Architecture --- Social geography --- ruimtelijke ordening --- IoT (Internet of Things) --- architectuur --- tekstverwerking --- duurzame ontwikkeling --- KI (kunstmatige intelligentie) --- communicatietechnologie