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.

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.

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.

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.

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.

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.

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.

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.

In this Very Short Introduction, Gerhard L. Weinberg provides an introduction to the origins, course, and impact of the war on those who fought and the ordinary citizens who lived through it. Starting by looking at the inter-war years and the German invasion of Poland in September 1939, he examines how the war progressed by examining a number of key events, including the war in the West in 1940, Barbarossa, the German Invasion of the Soviet Union, the expansion of Japan's war with China, developments on the home front, and the Allied victory from 1944-45.

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 lively and engaging book is the ideal introduction for anyone who has ever been puzzled by what philosophy is or what it is for. Edward Craig argues that philosophy is not an activity born from another planet; learning about it is just a matter of broadening and deepening what most of us do already. He shows that philosophy is no mere intellectual pastime.

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.

Linguistics falls in the gap between arts and science, on the edges of which the most fascinating discoveries and the most important problems are found. Rather than following the conventional organization of many contemporary introductions to the subject, the author of this stimulating guide begins his discussion with the oldest, "arts" end of the subject and moves chronologically through to the newest research - the "science" aspects.

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.

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.

Physics, the fundamental science of matter and energy, encompasses all levels of nature from the subatomic to the cosmic, and underlies much of the technology around us. Understanding the physics of our universe is an essential aspect of humanity's quest to understand our environment and our place within it. Doing physics enables us to explore the interaction between environment and human society, and can help us to work towards the future sustainability of the planet.

Exciting new developments in brain science are continuing the debates on these issues, and the field has now expanded to include biologists, neuroscientists, psychologists, and philosophers. This controversial book clarifies the potentially confusing arguments, and the major theories, while also outlining the amazing pace of discoveries in neuroscience. Covering areas such as the construction of self in the brain, mechanisms of attention, the neural correlates of consciousness, and the physiology of altered states of consciousness, Susan Blackmore highlights our latest findings.

How does the brain work? How different is a human brain from other creatures' brains? Is the human brain still evolving? In this fascinating book, Michael O'Shea provides a non-technical introduction to the main issues and findings in current brain research, and gives a sense of how neuroscience addresses questions about the relationship between the brain and the mind.

In this Very Short Introduction audiobook, Jan Zalasiewicz gives a brief introduction to the fascinating field of geology. Describing how the science developed from its early beginnings, he looks at some of the key discoveries that have transformed it before delving into its various subfields, such as sedimentology, tectonics, and stratigraphy.

The process by which nations escape poverty and achieve economic and social progress has been the subject of extensive examination for hundreds of years. The notion of development itself has evolved from an original preoccupation with incomes and economic growth to a much broader understanding of development. In this Very Short Introduction, Ian Goldin considers the contributions that education, health, gender, equity, and other dimensions of human well-being make to development.

From the contours of coastlines to the outlines of clouds, and the branching of trees, fractal shapes can be found everywhere in nature. In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a revolution in our mathematical understanding of patterns in the 20th century, and explores the wide range of applications in science, and in aspects of economics.

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.

For many, the terrorist attacks of September 2001 changed the face of the world, pushing terrorism to the top of political agendas, and leading to a series of world events, including the war in Iraq and the invasion of Afghanistan. The recent terror attacks in various European cities have shown that terrorism remains a crucial issue today. Charting a clear path through the efforts to understand and explain modern terrorism, Charles Townshend examines the historical, ideological, and local roots of terrorist violence.

This very short introduction offers listeners a superb overview of the teachings of the Buddha, as well as a succinct guide to the integration of Buddhism into daily life.