Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation.

The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.

Few things are as certain as societal changes—and the pressing need for educators to prepare students with the knowledge and ways of thinking necessary for the challenges in a changing world. In the forward-thinking pages of Designs for Learning Environments of the Future, international teams of researchers present emerging developments and findings in learning sciences and technologies at the infrastructure, curricular, and classroom levels.Focusing on ideas about designing innovative environments for learning in areas such as biology, engineering, genetics, mathematics, and computer science, the book surveys a range of learning technologies being explored around the world—a spectrum as diverse as digital media, computer modeling, and 3D virtual worlds—and addresses challenges arising from their design and use. The editors’ holistic perspective frames these innovations as not only discrete technologies but as flexible learning environments that foster student engagement, participation, and collaboration. Contributors describe possibilities for teaching and learning in these and other cutting-edge areas:

Designs for Learning Environments of the Future will enhance the work of a wide range of professionals, including researchers and graduate students in the learning and cognitive sciences, and educators in the physical and social sciences.

This unique book provides the first comprehensive overview of wood based bioenergy in the northern hardwood forests of the Eastern United States. This includes a holistic look at the topic of wood based bioenergy, as well as focused analyses of key topics. This book is relevant to engineers, project developers, foresters, economists, sociologists, environmental scientists and natural resource managers. Most chapters also provide practical hands-on advice for the practitioner, and provide a valuable resource for anyone who is considering developing a woody bioenergy project.

Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation.

The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.

Few things are as certain as societal changes—and the pressing need for educators to prepare students with the knowledge and ways of thinking necessary for the challenges in a changing world. In the forward-thinking pages of Designs for Learning Environments of the Future, international teams of researchers present emerging developments and findings in learning sciences and technologies at the infrastructure, curricular, and classroom levels.Focusing on ideas about designing innovative environments for learning in areas such as biology, engineering, genetics, mathematics, and computer science, the book surveys a range of learning technologies being explored around the world—a spectrum as diverse as digital media, computer modeling, and 3D virtual worlds—and addresses challenges arising from their design and use. The editors’ holistic perspective frames these innovations as not only discrete technologies but as flexible learning environments that foster student engagement, participation, and collaboration. Contributors describe possibilities for teaching and learning in these and other cutting-edge areas:

Designs for Learning Environments of the Future will enhance the work of a wide range of professionals, including researchers and graduate students in the learning and cognitive sciences, and educators in the physical and social sciences.

This unique book provides the first comprehensive overview of wood based bioenergy in the northern hardwood forests of the Eastern United States. This includes a holistic look at the topic of wood based bioenergy, as well as focused analyses of key topics. This book is relevant to engineers, project developers, foresters, economists, sociologists, environmental scientists and natural resource managers. Most chapters also provide practical hands-on advice for the practitioner, and provide a valuable resource for anyone who is considering developing a woody bioenergy project.