Mathematics

This book presents four lectures on Rees rings and blow-ups, Koszul modules with applications to syzygies, Grobner bases and degenerations, and applications of Adams operations. Commutative Algebra has witnessed a number of spectacular developments in recent years, including the resolution of long-standing problems; the new techniques and perspectives are leading to an extraordinary transformation in the field. The material contained in this volume, based on lectures given at a workshop held in Levico Terme, Trento, in July 2019, highlights some of these developments. The text will be a valuable asset to graduate students and researchers in commutative algebra and related fields.

An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry's rich historical past full circle into the modern era.

Without mathematics no science would survive. This especially applies to the engineering sciences which highly depend on the applications of mathematics and mathematical tools such as optimization techniques, finite element methods, differential equations, fluid dynamics, mathematical modelling, and simulation. Neither optimization in engineering, nor the performance of safety-critical system and system security; nor high assurance software architecture and design would be possible without the development of mathematical applications. De Gruyter Series on the Applications of Mathematics in Engineering and Information Sciences (AMEIS) focusses on the latest applications of engineering and information technology that are possible only with the use of mathematical methods. By identifying the gaps in knowledge of engineering applications the AMEIS series fosters the international interchange between the sciences and keeps the reader informed about the latest developments.

Chaos and complexity explained, with illuminating examples ranging from unpredictable pendulums to London's wobbly Millennium Bridge.The math we are taught in school is precise and only deals with simple situations. Reality is far more complex. Trying to understand a system with multiple interacting components-the weather, for example, or the human body, or the stock market-means dealing with two factors- chaos and complexity. If we don't understand these two essential subjects, we can't understand the real world. In Everyday Chaos, Brian Clegg explains chaos and complexity for the general reader, with an accessible, engaging text and striking full-color illustrations. By chaos, Clegg means a system where complex interactions make predicting long-term outcomes nearly impossible; complexity means complex interacting systems that have new emergent properties that make them more than the sum of their parts. Clegg illustrates these phenomena with discussions of predictable randomness, the power of probability, and the behavior of pendulums. He describes what Newton got wrong about gravity; how feedback kept steam engines from exploding; and why weather produces chaos. He considers the stock market, politics, bestseller lists, big data, and London's wobbling Millennium Bridge as examples of chaotic systems, and he explains how a better understanding of chaos helps scientists predict more accurately the risk of catastrophic Earth-asteroid collisions. We learn that our brains are complex, self-organizing systems; that the structure of snowflakes exemplifies emergence; and that life itself has been shown to be an emergent property of a complex system.

Exploiting powerful techniques from physics and mathematics, this book studies animal movement in ecology, with a focus on epidemic spread. Pulmonary syndrome is not only feared in epidemics of recent times, such as COVID-19, but is also characteristic of epidemics studied earlier such as Hantavirus. The Hantavirus is one of the book's central topics. Correlations between epidemic outbreaks and precipitation events like El Niño are analyzed and spatial reservoirs of infection in off-period of the epidemic, known as refugia, are studied. Predicted traveling waves of infection are successfully compared to field observations. Territoriality in scent-marking animals is presented, with parallels drawn with the theory of melting. The flocking and herding of birds and mammals are described in terms of collective excitations. For scientists interested in movement ecology and epidemic spread, this book provides effective solutions to long-standing problems.