Mathematics is not a spectator sport; successful students of mathematics grapple with ideas for themselves. Distilling Ideas presents a carefully designed sequence of exercises and theorem statements that challenge students to create proofs and concepts. As students meet these challenges, they discover strategies of proofs and strategies of thinking beyond mathematics. In other words, Distilling Ideas helps its users to develop the skills, attitudes, and habits of mind of a mathematician, and to enjoy the process of distilling and exploring ideas. Distilling Ideas is an ideal textbook for a first proof-based course. The text engages the range of students' preferences and aesthetics through a corresponding variety of interesting mathematical content from graphs, groups, and epsilon-delta calculus. Each topic is accessible to users without a background in abstract mathematics because the concepts arise from asking questions about everyday experience. All the common proof structures emerge as natural solutions to authentic needs. Distilling Ideas or any subset of its chapters is an ideal resource either for an organized Inquiry Based Learning course or for individual study.
Finalist for the 2021 PROSE Award for Environmental Science! An integrated approach to understanding and mitigating the problem of excess nitrogen Human activities generate large amounts of excess nitrogen, which has dramatically altered the nitrogen cycle. Reactive forms of nitrogen, especially nitrate and ammonia, are particularly detrimental. Given the magnitude of the problem, there is an urgent need for information on reactive nitrogen and its effective management. Nitrogen Overload: Environmental Degradation, Ramifications, and Economic Costs presents an integrated, multidisciplinary review of alterations to the nitrogen cycle over the past century and the wide-ranging consequences of nitrogen-based pollution, especially to aquatic ecosystems and human health. Volume highlights include: Comprehensive background information on the nitrogen cycle Detailed description of anthropogenic nitrogen sources Review of the environmental, economic, and health impacts of nitrogen pollution Recommendations and strategies for reducing humanity's nitrogen footprint Discussion of national nitrogen footprints and worldwide examples of mitigation policies The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals. Read the Editors' Vox: https://eos.org/editors-vox/exploring-the-widespread-impacts-of-ongoing-nitrogen-pollution
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