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.
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 collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
In the past decade, increasing attention has been paid to the issue of gender equity in the science, technology, engineering, and mathematics (STEM) fields. The research for this report, led by Yasmin Kafai and a team of researchers at the University of California, Los Angeles, was guided by several overarching questions: (1) What types of projects have been funded within and across the various STEM disciplines? (2) Are there areas where efforts been concentrated, and areas that have been overlooked? (3) What patterns emerge among the project types and disciplines? The findings document impressive efforts in preparing girls and women for science, technology, engineering, and mathematics studies and careers and demonstrate a rich and diverse body of gender equity intervention projects within all STEM disciplines. About two-thirds of the projects involved extracurricular informal learning activities such as museum visits and field trips. Equally important were mentoring activities in many forms, ranging from traditional one-to-one to large-scale online versions, and professional development activities, such as course taking and network building, that were successfully integrated into projects. At the same time, the findings reveal some troubling trends. Many projects focused predominantly on career advice without providing access to necessary skill and content development. A majority of projects occurred outside the school curriculum. While such extracurricular projects can be effective and valuable, the overall lack of integration into the school curriculum suggests that gender equity remains on the margins of teaching and learning in the STEM fields. Finally, an absence of data on participant demographics and a lack of project evaluation make it difficult to determine who is being served and if and how project outcomes are being measured. Perhaps most notably, the findings reveal hundreds of excellent and dynamic projects but no consolidated collective strategy to advance gender equity in STEM. The recommendations in this report reflect this problem, suggesting among others the need for more integrated efforts inside and outside of school, more interdisciplinary and cross-age connections, and consistent documentation and evaluation across disciplines and project types. Appended are: (1) Methodology; and (2) Selected Data Tables. (Contains 18 tables.).
Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th