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Although we learn the fundamentals of counting and measuring in our early years, these concepts form the foundation of complex processes, from mountain climbing and skydiving to video game design. This title examines the seemingly simple ideas of number and quantity and shows how they are used in real life.
Modeling offers us a way to explain past natural and cultural phenomena, and perhaps more importantly, it gives us mathematical forecasts for the future. This title explores familiar models such as linear regression and computer modeling to show how some aspects of everyday life, such as weather, can be shaped and predicted by mathematics.
Stopping a plague (even zombies), tomorrow’s likelihood of rain, and buying a lottery ticket are united by chance. Wildlife conservation, a baseball box score, and governmental spending are united by the need to record numbers. Statistics and probability measure the current state of something and the relative likelihood of potential future states. This book will explore how common experiences are counted, evaluated, and used to make intelligent decisions for the future based on uncertain outcomes.
The fundamental shapes of geometry can be built into the grand sweeps of the Sydney Opera House or something as small as a snowflake. This title takes geometric concepts like polygons, platonic solids, and angles and demonstrates their myriad appearances in the world around us. From the Great Pyramid of Giza to sinking a bank shot in pool, geometry abounds.
This book describes the interaction of living matter with photons, neutrons, charged particles, electrons and ions. The authors are specialists in the field of radiation protection. The book synthesizes many years of experiments with external radiation exposure in the fields of dosimetry and radiation shielding in medical, industrial and research fields. It presents the basic physical concepts including dosimetry and offers a number of tools to be used by students, engineers and technicians to assess the radiological risk and the means to avoid them by calculating the appropriate shields. The theory of radiation interaction in matter is presented together with empirical formulas and abacus. Numerous numerical applications are treated to illustrate the different topics. The state of the art in radiation protection and dosimetry is presented in detail, especially in the field of simulation codes for external exposure to radiation, medical projects and advanced research. Moreover, important data spread in different up to date references are presented in this book. The book deals also with accelerators, X-rays facilities, sealed sources, dosimetry, Monte Carlo simulation and radiation regulation. Each chapter is split in two parts depending on the level of details the readers want to focus on. The first part, accessible to a large public, provides a lot of simple examples to help understanding the physics concepts under radiation external exposure. The second part, called “Additional Information” is not mandatory; it aims on explaining topics more deeply, often using mathematical formulations. The book treats fundamental radiometric and dosimetric quantities to describe the interaction in materials under the aspects of absorbed dose processes in tissues. Definitions and applications on limited and operational radiation protection quantities are given. An important aspect are practical engineering tools in industrial, medical and research domains. Source characterization and shielding design are addressed. Also more ”exotic” topics, such as ultra intense laser and new generation accelerators, are treated. The state of the art is presented to help the reader to work with the book in a self-consistent way. The basic knowledge necessary to apply Monte Carlo methods in the field of radiation protection and dosimetry for external radiation exposure is provided. Coverage of topics such as variance reduction, pseudo-random number generation and statistic estimators make the book useful even to experienced Monte Carlo practitioners. Solved problems help the reader to understand the Monte Carlo process. The book is meant to be used by researchers, engineers and medical physicist. It is also valuable to technicians and students.
Although current views of cognitive development owe a great deal to Jean Piaget, this field has undergone profound change in the years since Piaget's death. This can be witnessed both in the influence connectionist and dynamical system models have exerted on theories of cognition and language, and in how basic work in cognitive development has begun to influence those who work in applied (e.g., educational) settings. This volume brings together an eclectic group of distinguished experts who collectively represent the full spectrum of basic to applied aspects of cognitive development. This book begins with chapters on cognition and language that represent the current Zeitgeist in cognitive science approaches to cognitive development broadly defined. Following a brief commentary on this work, the next section turns to more applied issues. Although the focus here is on arithmetic learning, the research programs described have profound implications for virtually all aspects of education and learning. The last chapter views cognitive development from the perspective of ethology and evolutionary biology, and in so doing provides a theoretical perspective that is novel and in some ways, prescient: specifically, how can our views of cognition incorporate recent work in biology?
This easy-to-read summary is an excellent tool for introducing others to the messages contained in Principles and Standards.
Transforming the standards into learning outcomes just got a lot easier In this resource, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, allowing you to see and understand which page number to turn to for standards-based teaching ideas. It’s all here, page by page: The mathematical progression of each conceptual category, starting with modeling as a unifying theme and moving through number and quantity, algebra, functions, geometry, and statistics and probability, building from eighth-grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains and to previous grade standards, so teachers can better appreciate how they relate How content standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful high school mathematics curriculum in any state or district.