Discusses, from a working mathematician's point of view, the mystery of mathematical intuition: Why are certain mathematical concepts more intuitive than others? And to what extent does the 'small scale' structure of mathematical concepts and algorithms reflect the workings of the human brain?

Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world -- and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world -- and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.

The use of computer-based image analysis systems for all kinds of images, but especially for microscope images, has become increasingly widespread in recent years, as computer power has increased and costs have dropped. Software to perform each of the various tasks described in this book exists now, and without doubt additional algorithms to accomplish these same things more efficiently, and to perform new kinds of image processing, feature discrimination and measurement, will continue to be developed. This is likely to be true particularly in the field of three-dimensional imaging, since new microscopy methods are beginning to be used which can produce such data. It is not the intent of this book to train programmers who will assemble their own computer systems and write their own programs. Most users require only the barest of knowledge about how to use the computer, but the greater their understanding of the various image analysis operations which are possible, their advantages and limitations, the greater the likelihood of success in their application. Likewise, the book assumes little in the way of a mathematical background, but the researcher with a secure knowledge of appropriate statistical tests will find it easier to put some of these methods into real use, and have confidence in the results, than one who has less background and experience. Supplementary texts and courses in statistics, microscopy, and specimen preparation are recommended as necessary.

The widespread availability of high-quality, high-frequency data has revolutionised the study of financial markets. By describing not only asset prices, but also market participants' actions and interactions, this wealth of information offers a new window into the inner workings of the financial ecosystem. In this original text, the authors discuss empirical facts of financial markets and introduce a wide range of models, from the micro-scale mechanics of individual order arrivals to the emergent, macro-scale issues of market stability. Throughout this journey, data is king. All discussions are firmly rooted in the empirical behaviour of real stocks, and all models are calibrated and evaluated using recent data from Nasdaq. By confronting theory with empirical facts, this book for practitioners, researchers and advanced students provides a fresh, new, and often surprising perspective on topics as diverse as optimal trading, price impact, the fragile nature of liquidity, and even the reasons why people trade at all.

Unbiased Stereology, Second Edition is a practical guide to making unbiased 3-D measurements via the microscope. Only those stereological techniques which have been tried and tested by real application are included. Although this technology is essentially mathematical and statistical, the authors do not immerse the reader in complex analysis, but rather provide simple heuristic explanations and references to the original proof, and illustrate the theory by analogies drawn from everyday experience. To give practical experience in application of the techniques, exercises are provided at the end of each chapter, complete with detailed worked answers.

This is a brief history of the development of microscopy, from the use of beads and water droplets in ancient Greece, through the simple magnifying glass, to the modern compound microscope. The technology and optical theory are developed in a straightforward manner, and this leads to a description and explanation of the most modern technologies in electron microscopy, and scanning electron microscopy as well as the new scanning probe microscopies. A series of very interesting applications of the various microscopic techniques are described. The most recent pioneering techniques in near field and confocal optical microscope technologies are described and evaluated for their future importance.

This book provides readers with a superior understanding of the mathematical principles behind imaging.