This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible ...
This book contains a structured collection of complete solutions of all significant axially symmetric contact problems. It provides solutions for classical profiles such as the sphere, cone or flat cylindrical punch as well as a multitude of other technically relevant shapes, e.g. the truncated cone, the worn sphere, rough profiles, hollow cylinder...
The book serves both as a reference for
various scaled models with corresponding dimensionless numbers, and as a
resource for learning the art of scaling.
A special feature of the book is the emphasis on how to create software
for scaled models, based on existing software for unscaled models.
Scaling (or non-dimensionalization) is a
mathematical...
This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth o...
Consumer networks have revolutionized the way companies understand and reach their customers, making possible intricate measurement and accurate prediction at every step of every transaction. The same revolution is underway in our infrastructure, where new generations of sensor-laden power plants, cars and medical devices will generate vast quantit...
This book shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author's fifteen years of teaching at MIT, Cambridge Unive...
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.
The book explains how conceptual hurdles in the development of numbers and number systems were overcome i...
In order to represent real life situations mathematically, we often use symbols to represent unknown quantities. We call these symbols variables. Each mathematical subject requires knowledge of manipulating expressions and equations to solve for a variable. Careers such as automobile accident investigators, quality control engineers, and insurance ...