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Mathematics to the Rescue of Democracy: What does Voting Mean and How can it be Improved?
by Paolo SerafiniThis book explains, in a straightforward way, the foundations upon which electoral techniques are based in order to shed new light on what we actually do when we vote. The intention is to highlight the fact that no matter how an electoral system has been designed, and regardless of the intentions of those who devised the system, there will be goals that are impossible to achieve but also opportunities for improving the situation in an informed way. While detailed descriptions of electoral systems are not provided, many references are made to current or past situations, both as examples and to underline particular problems and shortcomings. In addition, a new voting method that avoids the many paradoxes of voting theory is described in detail. While some knowledge of mathematics is required in order to gain the most from the book, every effort has been made to ensure that the subject matter is easily accessible for non-mathematicians, too. In short, this is a book for anyone who wants to understand the meaning of voting.
Mathematics with Applications in Business and Social Sciences
by Hawkes LearningThis application-driven title covers content from fundamental algebra to essential statistics and calculus, teaching the mathematical concepts students need to succeed in their future careers. A primary emphasis is placed on showing students how to connect mathematics to real-world contexts.
Mathematics without Apologies
by Michael HarrisWhat do pure mathematicians do, and why do they do it? Looking beyond the conventional answers--for the sake of truth, beauty, and practical applications--this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources.Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party?Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
Mathematics without Apologies: Portrait of a Problematic Vocation
by Michael HarrisWhat do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources.Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party?Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
Mathematics, Administrative and Economic Activities in Ancient Worlds (Why the Sciences of the Ancient World Matter #5)
by Karine Chemla Cécile MichelThis book focuses on the ancient Near East, early imperial China, South-East Asia, and medieval Europe, shedding light on mathematical knowledge and practices documented by sources relating to the administrative and economic activities of officials, merchants and other actors. It compares these to mathematical texts produced in related school contexts or reflecting the pursuit of mathematics for its own sake to reveal the diversity of mathematical practices in each of these geographical areas of the ancient world. Based on case studies from various periods and political, economic and social contexts, it explores how, in each part of the world discussed, it is possible to identify and describe the different cultures of quantification and computation as well as their points of contact. The thirteen chapters draw on a wide variety of texts from ancient Near East, China, South-East Asia and medieval Europe, which are analyzed by researchers from various fields, including mathematics, history, philology, archaeology and economics. The book will appeal to historians of science, economists and institutional historians of the ancient and medieval world, and also to Assyriologists, Indologists, Sinologists and experts on medieval Europe.
Mathematics, Affect and Learning
by Peter Grootenboer Margaret MarshmanThis book examines the beliefs, attitudes, values and emotions of students in Years 5 to 8 (aged 10 to 14 years) about mathematics and mathematics education. Fundamentally, this book focuses on the development of affective views and responses towards mathematics and mathematics learning. Furthermore, it seems that students develop their more negative views of mathematics during the middle school years (Years 5 to 8), and so here we concentrate on students in this critical period. The book is based on a number of empirical studies, including an enquiry undertaken with 45 children in Years 5 and 6 in one school; a large-scale quantitative study undertaken with students from a range of schools across diverse communities in New Zealand; and two related small-scale studies with junior secondary students in Australia. This book brings substantial, empirically-based evidence to the widely held perception that many students have negative views of mathematics, and these affective responses develop during the middle years of school. The data for this book were collected with school students, and students who were actually engaged in learning mathematics in their crucial middle school years. The findings reported and discussed here are relevant for researchers and mathematics educators, policy makers and curriculum developers, and teachers and school principals engaged in the teaching of mathematics.
Mathematics, Computer Science and Logic - A Never Ending Story
by Peter PauleThis book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger's successor as director of the Research Institute for Symbolic Computation.
Mathematics, Education and History: Towards A Harmonious Partnership (ICME-13 Monographs)
by Kathleen M. Clark Tinne Hoff Kjeldsen Sebastian Schorcht Constantinos TzanakisThis book includes 18 peer-reviewed papers from nine countries, originally presented in a shorter form at TSG 25 The Role of History of Mathematics in Mathematics Education, as part of ICME-13 during. It also features an introductory chapter, by its co-editors, on the structure and main points of the book with an outline of recent developments in exploring the role of history and epistemology in mathematics education. It serves as a valuable contribution in this domain, by making reports on recent developments in this field available to the international educational community, with a special focus on relevant research results since 2000. The 18 chapters of the book are divided into five interrelated parts that underlie the central issues of research in this domain: 1. Theoretical and conceptual frameworks for integrating history and epistemology in mathematics in mathematics education; 2. Courses and didactical material: Design, implementation and evaluation; 3. Empirical investigations on implementing history and epistemology in mathematics education; 4. Original historical sources in teaching and learning of and about mathematics; 5. History and epistemology of mathematics: Interdisciplinary teaching and sociocultural aspects. This book covers all levels of education, from primary school to tertiary education, with a particular focus on teacher education. Additionally, each chapter refers to and/or is based on empirical research, in order to support, illuminate, clarify and evaluate key issues, main questions, and conjectured theses raised by the authors or in the literature on the basis of historical-epistemological or didactical-cognitive arguments.
Mathematics, Grade 5 (Texas Coach)
by Triumph LearningThis book helps you strengthen your mathematics skills. These skills are important to have for every subject you study this year, not just Mathematics. Each lesson in this book has three parts: I GETTING THE IDEA: Review some of the basic concepts and skills you've already learned. II COACHED EXAMPLE: Solve a problem. There are several questions that will help you along the way! III LESSON PRACTICE: Now you're on your own! This part contains more problems to solve. There are different types of test items in Texas Coach. For some, you will have to choose one answer from several possible choices. For others, you will grid in the numbers for your answer. Be sure to read the directions carefully so you know how to answer each item.