Connected Mathematics

We present here the English version of the Romanian first edition (V. Berinde: Ex­ plorare, investigare si descoperire in matematica, Editura Efemeride, Baia Mare, 2001). There are no major changes. Only a few printing errors were corrected. When transcribing Romanian names or denominations we did not use the diacrit­ ical marks. Our purpose is to provide an introduction to creative problem solving tech­ niques with particular emphasis on how to develop inventive skills in students. We present an array of 24 carefully selected themes that range over all the main chapters in elementary mathematics: arithmetic, algebra, geometry, analysis as well as applied mathematics. Main goal is to offer a systematic illustration of how to organize the natural transition from problem solving activity toward exploring, investigating and discovering new facts and results. The book is addressed mainly to students, young mathematicians, and teach­ ers, involved or/and actively working in mathematics competitions and training gifted people. It collects many valuable techniques for solving various classes of difficult problems and, simultaneously, offers a comprehensive introduction to cre­ ating new problems. The book should also be of interest to anybody who is in any way connected to mathematics or interested in the creative process and in mathematics as an art.

In 2003 we published a collection of articles Connected at Infinity. The editors' aims, and their travails, were explained in the two paragraphs that we reproduce from the Preface to that volume: The Editors invited a few persons to write an article that should explain to the nonspecialist an important piece of work done by an Indian mathematician in the mid-twentieth century. The contributions of these mathematicians have been major landmarks in the subject and have inspired and influenced a lot of later work.

In an increasingly globally-connected world, the ability to predict, monitor, and contain pandemics is essential to ensure the health and well-being of all. This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19. Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general. Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the societal level, the level of individuals, and the level of virus particles and the immune system. Chapters in this volume explore the latest research related to these items to demonstrate the utility of a variety of mathematical methods. Perspectives for the future are also offered.

In an increasingly globally-connected world, the ability to predict, monitor, and contain pandemics is essential to ensure the health and well-being of all. This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19. Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general. Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the societal level, the level of individuals, and the level of virus particles and the immune system. Chapters in this volume explore the latest research related to these items to demonstrate the utility of a variety of mathematical methods. Perspectives for the future are also offered.