The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and listeners of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought.

Numbers are integral to our everyday lives and factor into almost everything we do. In this Very Short Introduction audiobook, 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.

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the "building blocks" of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no one has ever been able to resolve them. But number theory has also recently become of great practical importance.

The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof first arose. To this day geometry remains a very active area of research in mathematics. This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Throughout, Maciej Dunajski outlines the role geometry plays in the broader context of science and art.

Quantum theory is the most revolutionary discovery in physics since Newton. This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed.

How much faith should we place in what scientists tell us? Is it possible for scientific knowledge to be fully "objective"? What, really, can be defined as science? In the second edition of this very short introduction, Samir Okasha explores the main themes and theories of contemporary philosophy of science and investigates fascinating, challenging questions such as these.

In this Very Short Introduction, Simon Horobin investigates how we have arrived at the English we know today and celebrates the way new speakers and new uses mean that it continues to adapt. Engaging with contemporary concerns about correctness, Horobin considers whether such changes are improvements or evidence of slipping standards.

If you move at high speed, time slows down, space squashes up, and you get heavier. Travel fast enough and you could weigh as much as a jumbo jet, be flattened thinner than a CD without feeling a thing - and live forever! As for the angles of a triangle, they do not always have to add up to 180 degrees. And then, of course, there are black holes. These are but a few of the extraordinary consequences of Einstein's theory of relativity.

Bertrand Russell wrote that mathematics can exalt "as surely as poetry". This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections.

The laws of thermodynamics drive everything that happens in the universe. From the sudden expansion of a cloud of gas to the cooling of hot metal - everything is moved or restrained by four simple laws. This powerful and compact introduction explains what these four laws are and how they work, using accessible language and virtually no mathematics.

TOEIC満点を超えて、ネイティブも驚く語彙マスターになる!■アルクの人気単語学習書「究極の英単語Vol.4」の音声版!/書籍『究極の英単語SVL Vol.4超上級の3000語』は、アルクが編集した「標準語彙水準12000」(Standard Vocabulary List、SVL 12000)の超上級レベルにあたる3000語を完全収録。Vol. 1~3とこの3000語を合わせれば、TOEICテストや英検に出題される語彙をカバーし、英文雑誌が余裕で読みこなせるレベルの語彙を習得できます。■本商品は、書籍に掲載されているSVLの単語を複数含んだ覚えやすい638の例文Power Sentencesと、単語リストWord Listの音声(ともに英語のみ)を収録したものです。全3000語の単語の発音が確認できます。テキスト情報は含まれておりません。本コンテンツの利用に際しては、書籍「究極の英単語SVL Vol.4超上級の3000語」(アルク発行)が必要です。予めご注意ください。※「標準語彙水準12000」:アルクが長年蓄積してきた膨大な英文データから「日本人英語学習者にとっての有用性」「ネイティブスピーカーの使用頻度」を基準に選び出した、12000語の重要英単語リスト。◇対象レベル◇英語上級

Brett L. Walker tackles key themes regarding Japan's relationships with its minorities, state and economic development, and the uses of science and medicine. The book begins by tracing the country's early history through archaeological remains, before proceeding to explore life in the imperial court, the rise of the samurai, civil conflict, encounters with Europe, and the advent of modernity and empire. Walker's vibrant and accessible new narrative then follows Japan's ascension from the ashes of World War II into the thriving nation of today.

The Last Leaf is a short story by O. Henry published in his 1907 collection The Trimmed Lamp and Other Stories. The story first appeared on October 15, 1905, in the New York World. The scene of the story of The Last Leaf is the Greenwich artist colony in New York City. Over the past century, it has developed from a poor literati settlement to a world-famous art center and tourist attraction.

Games are everywhere: Drivers maneuvering in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. The supermarket's price for corn flakes is decided by playing an economic game. This Very Short Introduction offers a succinct tour of the fascinating world of game theory, a groundbreaking field that analyzes how to play games in a rational way.

This book is a clear and informative introduction to cryptography and data protection - subjects of considerable social and political importance. It explains what algorithms do, how they are used, the risks associated with using them, and why governments should be concerned. Important areas are highlighted, such as Stream Ciphers, block ciphers, public key algorithms, digital signatures, and applications such as e-commerce.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves. Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes "backwards" sometimes; how to turn the tide in the fight against AIDS.

David Hume, philosopher, historian, economist, librarian, and essayist, was one of the great figures of the European Enlightenment. Unlike some of his famous contemporaries, however, he was not dogmatically committed to idealized conceptions of reason, liberty, and progress.

This Very Short Introduction presents the field of fluid mechanics by focusing on the underlying physical ideas and using everyday phenomena to demonstrate them, from dripping taps to swimming ducks. Eric Lauga shows how this set of fundamental physical concepts can be applied to a wide range of flow behaviors and highlights the role of fluid motion in both the natural and industrial worlds. This book also considers future applications of fluid mechanics in science.

Here is the extraordinary story of the unfolding of life on Earth, told by Michael J. Benton, a world-renowned authority on biodiversity. Ranging over four billion years, Benton weaves together the latest findings on fossils, earth history, evolutionary biology, and many other fields to highlight the great leaps that enabled life to evolve from microbe to human - big breakthroughs that made whole new ways of life possible - including cell division and multicellularity, hard skeletons, the move to land, the origin of forests, the move to the air.

This second edition of the Very Short Introduction on ethics has revised and updated aspects of the original to reflect changing times and mores. It highlights the importance of an understanding of approaches to ethics and its foundations, confronted as we are with a fluid and uncertain world of eroding trust, swirling conspiracy theories, and a dismaying loss of respect in public discourse.

Taking a thematic rather than strictly chronological approach, W. F. Bynum, explores the key turning points in the history of Western medicine - such as the first surgical procedures, the advent of hospitals, the introduction of anesthesia, X-Rays, vaccinations, and many other innovations, as well as the rise of experimental medicine. The book also explores Western medicine's encounters with Chinese and Indian medicine, as well as nontraditional treatments such as homeopathy, chiropractic, and other alternative medicines.

Following the discovery of the Higgs boson, Frank Close has produced this major revision to his classic and compelling introduction to the fundamental particles that make up the universe. Frank Close takes us on a journey into the atom to examine known particles such as quarks, electrons, and the ghostly neutrino, and explains the key role and significance of the Higgs boson. Along the way he provides fascinating insights into how discoveries in particle physics have actually been made, and discusses how our picture of the world has been radically revised in the light of these developments.

This Very Short Introduction discusses the key concepts of biochemistry, as well as the historical figures in the field and the molecules they studied, before considering the current science and innovations in the field, and the interaction between biochemistry, biotechnology, and synthetic biology.

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, and insight.

The tradition of ancient philosophy is a long, rich, and varied one, in which a constant note is that of discussion and argument. This book introduces listeners to some ancient debates to engage with the ancient developments of some themes. Getting away from the presentation of ancient philosophy as a succession of Great Thinkers, the book gives listeners a sense of the freshness and liveliness of ancient philosophy and of its wide variety of themes and styles.