Strange Curves Counting Rabbits Other Mathematical Explorations

How does mathematics enable us to send pictures from space back to Earth? Where does the bell-shaped curve come from? Why do you need only 23 people in a room for a 50/50 chance of two of them sharing the same birthday? In Strange Curves, Counting Rabbits, and Other Mathematical Explorations, Keith Ball highlights how ideas, mostly from pure math, can answer these questions and many more. Drawing on areas of mathematics from probability theory, number theory, and geometry, he explores a wide range of concepts, some more light-hearted, others central to the development of the field and used daily by mathematicians, physicists, and engineers. Each of the book's ten chapters begins by outlining key concepts and goes on to discuss, with the minimum of technical detail, the principles that underlie them. Each includes puzzles and problems of varying difficulty. While the chapters are self-contained, they also reveal the links between seemingly unrelated topics. For example, the problem of how to design codes for satellite communication gives rise to the same idea of uncertainty as the problem of screening blood samples for disease. Accessible to anyone familiar with basic calculus, this book is a treasure trove of ideas that will entertain, amuse, and bemuse students, teachers, and math lovers of all ages.

Teaching Mathematics Using Interactive Mapping offers novel ways to learn basic math topics such as simple relational measures or measuring hierarchies through customized interactive mapping activities. These activities focus on interactive web-based Geographic Information System (GIS) and are relevant to today’s problems and challenges. Written in a guided, hands-on, understandable manner, all activities are designed to build practical and problem-solving skills that rest on mathematical principles and move students from thinking about maps as references that focus solely on "where is" something, to analytical tools, focusing primarily on the "whys of where." Success with this transition through interaction permits most readers to master mathematical concepts and GIS tools. FEATURES Offers custom-designed geographical activities to fit with specific mathematical topics Helps students become comfortable using mathematics in a variety of professions Provides an innovative, engaging, and practical set of activities to ease readers through typically difficult, often elementary, mathematical topics: fractions, the distributive law, and much more Uses web-based GIS maps, apps, and other tools and data that can be accessed on any device, anywhere, at any time, requiring no prior GIS background Written by experienced teachers and researchers with lifelong experience in teaching mathematics, geography, and spatial analysis Features an accompanying Solution Guide, available on the book's product page, that is beneficial for instructors, students, and other readers as an aid to gauging progress. This textbook applies to undergraduate and graduate students in universities and community colleges including those in basic mathematics courses, as well as upper-level undergraduate and graduate students taking courses in geographic information systems, remote sensing, photogrammetry, geography, geodesy, information science, engineering, and geology. Professionals interested in learning techniques and technologies for collecting, analyzing, managing, processing, and visualizing geospatial datasets will also benefit from this book as they refresh their knowledge in mathematics.

This book explores the many disciplinary and theoretical links between language, linguistics, and mathematics. It examines trends in linguistics, such as structuralism, conceptual metaphor theory, and other relevant theories,to show that language and mathematics have a similar structure, but differential functions, even though one without the other would not exist.

Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations; Euler’s formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions. New to the Fourth Edition Two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications New material on inequalities, counting methods, the inclusion-exclusion principle, and Euler’s phi function Numerous new exercises, with solutions to the odd-numbered ones Through careful explanations and examples, this popular textbook illustrates the power and beauty of basic mathematical concepts in number theory, discrete mathematics, analysis, and abstract algebra. Written in a rigorous yet accessible style, it continues to provide a robust bridge between high school and higher-level mathematics, enabling students to study more advanced courses in abstract algebra and analysis.

An “accessible and engaging” tool for understanding the branch of mathematics that is so crucial to modern computer science, using real-life problems (Mathematical Reviews). What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery? Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael’s gem of a book brings this vital but tough-to-teach subject to life using examples from the real world and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery. This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.

The Mathematics of Games: An Introduction to Probability takes an inquiry-based approach to teaching the standard material for an introductory probability course. It also discusses different games and ideas that relate to the law of large numbers, as well as some more mathematical topics not typically found in similar books. Written in an accessibl