“Inspiring and informative...deserves to be widely read.” —Wall Street Journal “This fun book offers a philosophical take on number systems and revels in the beauty of math.” —Science News Because we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages. Paul Lockhart presents arithmetic not as rote manipulation of numbers—a practical if mundane branch of knowledge best suited for filling out tax forms—but as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining, Arithmetic invites us to experience the beauty of mathematics through the eyes of a beguiling teacher. “A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education...Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting.” —Jonathon Keats, New Scientist “What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind’s most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story...A wonderful book.” —Keith Devlin, author of Finding Fibonacci

This book explores the rich history of community college math with a specific focus on gatekeeper math classes. Gatekeeper math classes include courses such as college algebra, introduction to statistics, and all developmental math classes. For community colleges, successful completion of these classes is imperative for student retention. This book presents a decade-by-decade analysis of the history of community college mathematics. The author employs a mix of conceptual, empirical, and quantitative research. The empirical research stems from interviews with 30 community college faculty members from seven community colleges. From the 1970s to the pandemic in the early 2020s, the book explores math curricula as well as trends, initiatives, teaching practices, and mandates that have impacted community college math. The positives and negatives of such trends, initiatives, and mandates are presented along with suggestions on how to apply such knowledge going forward. The author addresses the key questions: How can we build a future model for community college gatekeeper math classes that is both successful and sustainable? Additionally, how can we learn from the past and the present to build such a model? This book will be ideal for students in graduate programs focusing on community college leadership or developmental education leadership as well as all those hoping to improve success rates in community college mathematics programs.

Fifty years after it made the transition from mimeographed lecture notes to a published book, Armand Borel's Introduction aux groupes arithmétiques continues to be very important for the theory of arithmetic groups. In particular, Chapter III of the book remains the standard reference for fundamental results on reduction theory, which is crucial in the study of discrete subgroups of Lie groups and the corresponding homogeneous spaces. The review of the original French version in Mathematical Reviews observes that “the style is concise and the proofs (in later sections) are often demanding of the reader.” To make the translation more approachable, numerous footnotes provide helpful comments.

Self-organising networks have become the dominant innovators of complex technologies and radical innovation. The growing need for co-operation to ensure innovation success calls for a broader understanding of what makes innovation projects successful and requires new concepts. The book introduces the new concept of “innovation communities”, defining them as informal networks of like-minded individuals who act as innovation promotors or champions. These key figures come from various companies and organisations and will team up in a project-related fashion, jointly promoting a certain innovation, product or idea either on one or across different levels of an innovation system. The publication presents findings from surveys that demonstrate that networks of champions are a success factor in radical innovation. Five case studies of noteworthy innovation projects illustrate why the collaboration of champions can make innovation projects more successful. Furthermore, the book presents hands-on methods and includes best-practice cases and guidelines on how to develop innovation communities. This publication comprises empirical findings and practical experiences that are valuable for the following groups in particular: Entrepreneurs; Innovation, R&D, and network managers; Innovation and strategy consultants; Innovation and start-up intermediaries; Innovation researchers; Government officials and politicians responsible for R&D and innovation programmes and funding

Language is one of the greatest predictors of personal, social, academic, and professional success. No one is born a reader; instead, learning to read is a process that requires time, effort, and availability. The only way for reading comprehension to develop is through practice: one learns to read by reading. As such, it is integral to acknowledge the importance of knowing how to read and facilitating this skill in schools and at home. Reading is a cornerstone for learning and no child will know academic success if their reading ability is compromised. Modern Reading Practices and Collaboration Between Schools, Family, and Community is a premier reference book that consolidates knowledge on reading competence. It presents the processes inherent in the act of reading and the mechanisms underlying the teaching and learning of reading, as well as all recent research in this area. Covering topics such as communication development, learning motivation, and transliteracy, this innovative title is an excellent resource for preservice teachers, childhood educators, educators of K-12 and higher education, academic libraries, teacher training lecturers, faculty and administration of K-12 and higher education, researchers, and academicians.