Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves—and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

How a modern radio works, told through mathematics, history, and selected puzzles The modern radio is a wonder, and behind that magic is mathematics. In The Mathematical Radio, Paul Nahin explains how radios work, deploying mathematics and historical discussion, accompanied by a steady stream of intriguing puzzles for math buffs to ponder. Beginning with oscillators and circuits, then moving on to AM, FM, and single-sideband radio, Nahin focuses on the elegant mathematics underlying radio technology rather than the engineering. He explores and explains more than a century of key developments, placing them in historical and technological context. Nahin, a prolific author of books on math for the general reader, describes in fascinating detail the mathematical underpinnings of a technology we use daily. He explains and solves, for example, Maxwell’s equations for the electromagnetic field. Readers need only a familarity with advanced high school–level math to follow Nahin’s mathematical discussions. Writing with the nonengineer in mind, Nahin examines topics including impulses in time and frequency, spectrum shifting at the transmitter, the superheterodyne, the physics of single-sideband radio, and FM sidebands. Chapters end with “challenge problems” and an appendix offers solutions, partial answers, and hints. Readers will come away with a new appreciation for the beauty of even the most useful mathematics.

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 2020 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday aspects of math, and take readers behind the scenes of today’s hottest mathematical debates. Here, Steven Strogatz reveals how calculus drives advances in virology, Paul Thagard argues that the power of mathematics stems from its combination of realistic and fictional qualities, and Erica Klarreich describes how Hao Huang used the combinatorics of cube nodes to solve a longstanding problem in computer science. In other essays, John Baez tells how he discovered the irresistible attractions of algebraic geometry, Mark Colyvan compares the radically different explanatory practices of mathematics and science, and Boris Odehnal reviews some surprising properties of multidimensional geometries. And there’s much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

The Four Corners of Mathematics: A Brief History, from Pythagoras to Perelman describes the historical development of the ‘big ideas’ in mathematics in an accessible and intuitive manner. In delivering this bird's-eye view of the history of mathematics, the author uses engaging diagrams and images to communicate complex concepts while also exploring the details of the main results and methods of high-level mathematics. As such, this book involves some equations and terminology, but the only assumption on the readers’ knowledge is A-level or high school mathematics. Features Divided into four parts, covering Geometry, Algebra, Calculus and Topology Presents high-level mathematics in a visual and accessible way with numerous examples and over 250 illustrations Includes several novel and intuitive proofs of big theorems, so even the nonexpert reader can appreciate them Sketches of the lives of important contributors, with an emphasis on often overlooked female mathematicians and those who had to struggle.

Following the success of The Quantum Universe, first published in 1987, a host of exciting new discoveries have been made in the field of quantum mechanics. The New Quantum Universe provides an up-to-date and accessible introduction to the essential ideas of quantum physics, and demonstrates how it affects our everyday life. Quantum mechanics gives an understanding of not only atoms and nuclei, but also all the elements and even the stars. The book explains quantum paradoxes and the eventful life of Schroedinger's Cat, along with the Einstein–Podolsky–Rosen paradox and Bell's Inequality. It then looks ahead to the nanotechnology revolution, describing quantum cryptography, quantum computing and quantum teleportation, and ends with an account of quantum mechanics and science fiction. Using simple non-mathematical language, this book is suitable for final-year school students, science undergraduates, and anyone wishing to appreciate how physics allows the new technologies that are changing our lives.

Analog computing is one of the main pillars of Unconventional Computing. Almost forgotten for decades, we now see an ever-increasing interest in electronic analog computing because it offers a path to high-performance and highly energy-efficient computing. These characteristics are of great importance in a world where vast amounts of electric energy are consumed by today’s computer systems. Analog computing can deliver efficient solutions to many computing problems, ranging from general purpose analog computation to specialised systems like analog artificial neural networks. The book “Analog Computing” has established itself over the past decade as the standard textbook on the subject and has been substantially extended in this second edition, which includes more than 300 additional bibliographical entries, and has been expanded in many areas to include much greater detail. These enhancements will confirm this book’s status as the leading work in the field. It covers the history of analog computing from the Antikythera Mechanism to recent electronic analog computers and uses a wide variety of worked examples to provide a comprehensive introduction to programming analog computers. It also describes hybrid computers, digital differential analysers, the simulation of analog computers, stochastic computers, and provides a comprehensive treatment of classic and current analog computer applications. The last chapter looks into the promising future of analog computing.

Cryptography and Vedic Mathematics are one of the fundamental branches of Mathematics and this book aims to serve as a reference book for the researchers. It can also be read with great interest by students of engineering. The material of the book has been arranged into sections spread out over seven chapters. Each chapter begins with a brief introduction which provides motivation and a keen desire to proceed with the material of the chapter. Several examples have been given for ready reference for solving problems in Cryptography and Vedic Mathematics. Remarks and notes at places and exercises have been given at the end of each section to increase the knowledge by applying previous results. The exercises have also been graded appropriately and followed by answers. Our sincere thanks are also due to the Publishers for undertaking the publication of the manuscript and bringing it timely in the market for the use of readers

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

This is a college-level introductory textbook of algorithms and data structures with application to graphics and geometry. This textbook, released under a Creative Commons Share Alike (CC BY SA) license, is presented in its original format with the academic content unchanged. It was authored by Jurg Nievergelt (ETH Zurich) and Klaus Hinrichs (Institut fur Informatik) and provided by the University of Georgia's Global Textbook Project. Textbookequity.org/algorithms-and-data-structures/ Photo Credit: Renato Keshet (GFDL) commons.wikimedia.org Contents Part I: Programming environments for motion, graphics, and geometry Part II: Programming concepts: beyond notation Part IV: Complexity of problems and algorithms Part V: Data structures Textbook Equity Edition http: //textbookequity.org/algorithms-and-data-structures