This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

This book is essential for anyone involved or thinking about being involved in teaching and learning mathematics at school. It is packed full of practical and fun lesson ideas and activities, combining the author’s infectious enthusiasm for school mathematics with the relentless challenge of engaging students with the nature of the subject. Using humour, enthusiasm and years of teaching expertise, Jim Noble presents the features and potential of ideas and experiments he has used in his classroom. He draws on his extensive experience of using these activities to demonstrate their pros and cons, what you might expect and where they might lead. In a humorous and engaging account, alongside noting successes the author also includes the moments where things have gone slightly awry. These experiences and the context are used as a vehicle for thinking about the broader goals and issues of mathematics education and challenging some of the stereotypical misunderstandings. Each chapter draws out an important idea for teachers to think about, following a basic three-part structure: • The lesson and how it works • What happens and why it matters • How could it be different? Variations and similar tasks. Without preaching anything other than the joy of mathematics, this intelligent, humorous and practical book will act as a catalyst and inspiration for teachers looking to develop their own understanding and practice.

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.

"Magical Mathematics" reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician.

This book re-examines the dichotomy between the everyday and the disciplinary in mathematics and science education, and explores alternatives to this opposition from points of view grounded in the close examination of complex classroom events. It makes the case that students' everyday experience and knowledge in their entire manifold forms matter crucially in learning sciences and mathematics. The contributions of 13 research teams are organized around three themes: 1) the experiences of students in encounters with everyday matters of a discipline; 2) the concerns of curriculum designers, including teachers, as they design activities intended to focus on everyday matters of a discipline; and 3) the actions of teachers as they create classroom encounters with everyday matters of a discipline. As a whole the volume reflects the shift in the field of educational research in recent years away from formal, structural models of learning toward emphasizing its situated nature and the sociocultural bases of teaching and learning. At least two trends--increasing awareness that formal theories can be useful guides but are always partial and provisional in how they disclose classroom experiences, and the widespread availability of video and audio equipment that enables effortless recording of classroom interactions--have reoriented the field by allowing researchers and teachers to look at learning starting with complex classroom events rather than formal theories of learning. Such examinations are not meant to replace the work on general theoretical frameworks, but to ground them in actual complex events. This reorientation means that researchers and teachers can now encounter the complexity of learning and teaching as lived, human meaning-making experiences. Immersion in this complexity compels rethinking assumptions about the dichotomies that have traditionally organized the field's thinking about learning. Further, it has important implications for how the relationship between theory and practice in understanding teaching and learning is viewed. Everyday Matters in Science and Mathematics: Studies of Complex Classroom Events is an important resource for researchers, teacher educators, and graduate students in mathematics and science education, and a strong supplemental text for courses in these areas and also in cognition and instruction and instructional design.

Japan is a tiny country that occupies only 0.25% of the world’s total land area. However, this small country is the world’s third largest in economy: the Japanese GDP is roughly equivalent to the sum of any two major countries in Europe as of 2012. This book is a first attempt to ask leaders of top Japanese companies, such as Toyota, about their thoughts on mathematics. The topics range from mathematical problems in specific areas (e.g., exploration of natural resources, communication networks, finance) to mathematical strategy that helps a leader who has to weigh many different issues and make decisions in a timely manner, and even to mathematical literacy that ensures quality control. The reader may notice that every article reflects the authors’ way of life and thinking, which can be evident in even one sentence. This book is an enlarged English edition of the Japanese book What Mathematics Can Do for You: Essays and Tips from Japanese Industry Leaders. In this edition we have invited the contributions of three mathematicians who have been working to expand and strengthen the interaction between mathematics and industry. The role of mathematics is usually invisible when it is applied effectively and smoothly in science and technology, and mathematical strategy is often hidden when it is used properly and successfully. The business leaders in successful top Japanese companies are well aware of this invisible feature of mathematics in applications aside from the intrinsic depth of mathematics. What Mathematics Can Do for You ultimately provides the reader an opportunity to notice what is hidden but key to business strategy.

Explains the orgins of over 1500 mathematical terms used in English. This book concentrates on where those terms come from and what their literal meanings are.