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Would you like to understand more about mathematics? Perhaps at school you liked it for a while but were put off because you missed a key idea and kept getting stuck. Whatever the case, this book is for you.
The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today’s hottest mathematical debates. James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world—with glimpses at science, philosophy, music, art, and even crocheting. And there’s much, much more. In addition to presenting the year’s most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.
This book helps you understand what ′mastery′ is and how to effectively integrate it into classroom teaching. It explores how ′mastery′ is viewed and supported in other countries and encourages a critical examination of this topical theme. The book includes practical advice and examples of learning activities for primary teaching. It also outlines how to support children who might be weaker in their mathematical abilities and still ensure that all children master mathematics. The text also supports those who are developing whole school mastery approaches and looks at how we can assess ′mastery′ as well as how we can be confident that it is supporting good progress.
How to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory. Abstract Algebra is central in most undergraduate mathematics degrees, and it captures regularities that appear across diverse mathematical structures - many people find it beautiful for this reason. But its abstraction can make its central ideas hard to grasp, and even the best students might find that they can follow some of the reasoning without really understanding what it is all about. This book aims to solve that problem. It is not like other Abstract Algebra texts and is not a textbook containing standard content. Rather, it is designed to be read before starting an Abstract Algebra course, or as a companion text once a course has begun. It builds up key information on five topics: binary operations, groups, quotient groups, isomorphisms and homomorphisms, and rings. It provides numerous examples, tables and diagrams, and its explanations are informed by research in mathematics education. The book also provides study advice focused on the skills that students need in order to learn successfully in their own Abstract Algebra courses. It explains how to interact productively with axioms, definitions, theorems and proofs, and how research in psychology should inform our beliefs about effective learning.
NAUTILUS BOOK AWARD GOLD MEDALIST — BODY, MIND, SPIRIT PRACTICES “Combining an extraordinary range of scholarship with an accessible and entertaining writing style, The Infinite Staircase . . . provides a coherent and unified platform for a full human life.” —Midwest Book Review In this bold new book, high-tech’s best-known strategist makes a seminal contribution to the search for meaning in a secular era. Two questions fundamental to human existence have always been the metaphysical “where do I fit in the grand scheme of things?” and the ethical “how should I behave?” Religion is no longer a source of answers for many people, and nothing has replaced it. Moore uses his signature framework-based approach to answer these questions, taking us on an intellectual roller coaster ride through physics, chemistry, biology, the social sciences and the humanities. Along the way, he builds a metaphorical ladder that leads from the big bang to the need for ethical action in our daily lives. Combining an extraordinary range of scholarship with an accessible and entertaining writing style, The Infinite Staircase: What the Universe Tells Us About Life, Ethics, and Mortality provides a coherent and unified platform for a full human life.
Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a course is begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formal versions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to think productively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students who are new to advanced abstract mathematics.
Patterns in Mathematics Classroom Interaction describes, exemplifies and considers the implications of patterns and structures of mathematics classroom interaction.
Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods. The procedures used throughout make many of the calculations simpler and the concepts clearer for undergraduate students, heightening success and easing a significant burden of entry into STEM disciplines. This text features a student-friendly exposition with ample marginal notes, examples, illustrations, and more. The exercises include a wide range of difficulty levels, stretching from very simple rapid response questions to the occasional exercise meant to test knowledge. While some exercises require the use of technology to work through, none are dependent on any specific software. The answers to odd-numbered exercises in the back of the book include both simplified and non-simplified answers, hints, or alternative answers. Throughout the text, notes in the margins include comments meant to supplement understanding, sometimes including line-by-line commentary for worked examples. Without sacrificing academic rigor, Calculus Set Free offers an engaging style that helps students to solidify their understanding on difficult theoretical calculus.
Helps to ease the transition between school/college and university mathematics by (re)introducing readers to a range of topics that they will meet in the first year of a degree course in the mathematical sciences, refreshing their knowledge of basic techniques and focussing on areas that are often perceived as the most challenging. Each chapter starts with a "Test Yourself" section so that readers can monitor their progress and readily identify areas where their understanding is incomplete. A range of exercises, complete with full solutions, makes the book ideal for self-study.
A celebrated mathematician traces the history of math through the lives and work of twenty-five pioneering mathematicians In Significant Figures, acclaimed mathematician Ian Stewart explores the work of 25 of history's most important mathematicians, showing how they developed on each other's work and built the mathematics we use today. Through these short biographies, we get acquainted with the history of mathematics from Archimedes to William Thurston, and learn about those too often left out of the cannon, such as Muhammad ibn Musa al-Khwarizmi, the creator of algebra; Ada Lovelace, the world's first computer programmer; and Emmy Noether, whose research on symmetry paved the way for modern physics. Tracing the evolution of mathematics over the course of two millennia, Significant Figures will educate and delight aspiring mathematicians and experts alike.