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.

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.

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.

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.

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.

Economics has the capacity to offer us deep insights into some of the most formidable problems of life and offer solutions to them, too. Combining a global approach with examples from everyday life, Partha Dasgupta describes the lives of two children who live very different lives in different parts of the world: the Midwest USA and in Ethiopia. He compares the obstacles facing them and the processes that shape their lives, their families, and their futures. He shows how economics uncovers these processes, finds explanations for them, and how it forms policies and solutions.

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.

The world is never finished catching up with Vaclav Smil. In his latest and perhaps most digestible book, Invention and Innovation, the prolific author—a favorite of Bill Gates—pens an insightful and fact-filled jaunt through the history of human invention. Impatient with the hype that so often accompanies innovation, Smil offers in this book a clear-eyed corrective to the overpromises that accompany everything from new cures for diseases to AI.

The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction audiobook.

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.

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.

In this new edition, Steve Bruce discusses the continuing arguments for social egalitarianism, considering issues such as gay marriage, women in combat roles, and the 2010 Equality Act to debunk contemporary arguments against parity. As gender divisions are increasingly questioned, he looks ahead to the likely consequences of this for society.

生活や仕事上の逆境に立ったとき、自分が揺るがないように心の置き場所がつくられている。二千五百年の知恵という宝刀が手に入ることは心強い。

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.