Mathematics Rebooted ─ A Fresh Approach to Understanding

Would you like to understand more mathematics? Many people would. Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book is for you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth, using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments. If you would like to be better informed about the intrinsic elegance of mathematics, this engaging guide is the place to start.

Lara Alcock, Reader in Mathematics Education, Loughborough University

Lara Alcock is a Reader in Mathematics Education. She earned a BSc and MSc in Mathematics and a PhD in Mathematics Education at the University of Warwick, then spent four years at Rutgers University and two at Essex before taking up her present post in the Mathematics Education Centre at Loughborough, where she is now Head of Department. She conducts research in mathematical thinking and learning, with a focus on the transition from school to undergraduate mathematics. She won the 2012 Mathematical Association of America Selden Prize for research in undergraduate mathematics education, and she has written two books for undergraduates, How to Study for a Mathematics Degree (OUP, 2012) and How to Think about Analysis (OUP, 2014). She has won numerous Loughborough School of Science teaching awards, and in 2015 was awarded a National Teaching Fellowship by the Higher Education Academy.