Clear explanations are detailed with many current examples.

    For mathematicians, physicists, engineers, and everyone else with an interest in mathematics' cutting edge, The Millennium Problems is the definitive account of a subject that will have a very long shelf life.

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    I just wish I had known all of this twelve years ago...'When you speak to the likes of Dylan Wiliam, Doug Lemov, Daisy Christodoulou, Kris Boulton and the Bjorks, you are bound to learn a thing or two. But when he started his Mr Barton Maths Podcast, Craig Barton wasn't expecting to have his whole outlook on teaching and learning turned upside down. How I Wish I'd Taught Maths is the story of an experienced and successful maths teacher's journey into the world of research, and what it looks like in the classroom.Along the way we meet practical, easy-to-implement strategies including Supercharged Worked Examples, Silent Teacher, SSDD problems, low-stakes quizzes, diagnostic questions, Purposeful Practice, self-explanations, harnessing the power of the hypercorrection effect, how to (and how not to) teach problem-solving and much more. No matter your experience, teaching style or favourite number, every maths teacher will find something to think about in this book.

    Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

    In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.

    In this Very Short Introduction, Peter M. Higgins, a renowned popular-science writer, unravels the world of numbers, demonstrating its richness and providing an overview of all the number types that feature in modern science and mathematics. Indeed, Higgins paints a crystal-clear picture of the number world, showing how the modern number system matured over many centuries, and introducing key concepts such as integers, fractions, real and imaginary numbers, and complex numbers. Higgins sheds light on such fascinating topics as the series of primes, describing how primes are now used to encrypt confidential data on the internet. He also explores the infinite nature of number collections and explains how the so-called real numbers knit together to form the continuum of the number line. Written in the fashion of Higgins' highly popular science paperbacks, Numbers accurately explains the nature of numbers and how so-called complex numbers and number systems are used in calculations that arise in real problems.

    I also hope that it will serve as a useful reference too for the many workers engaged in one type of solid state research activity or another, who may be without formal training in the subject.

    It has an algebra and trigonometry prerequisite, but calculus is preferred.

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    Contains 640 problems including solutions; additional practice problems with answers; explanations of complex variable theory; coverage of applications of complex variables in engineering, physics, and elsewhere, with accompanying sample problems and solutions.

    But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity... and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia, contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books!

    In Making Numbers Count, Chip Heath argues that it's crucial for us all to be able to interpret and communicate numbers and stats more effectively so that data comes alive. By combining years of research into making ideas stick with a deep understanding of how the brain really works, Heath has discerned six critical principles that will give anyone the tools to communicate numbers with more transparency and meaning. These ideas - including simplicity, concreteness and familiarity - reveal what's compelling about a number and show how to transform it into its most understandable form. And if we can do this when we're using numbers, Heath tells us, then the idea of data won't drive people to panic. We're not hungry for numbers - there's an unfathomable amount of information being generated each year - but we are starved for meaning. The ability to communicate and understand numbers has never mattered more.

    Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.