Foreword / Gilles Dowek -- On a transformative journey -- Bayes theorem -- Logically speaking... -- Let's generalize! -- All hail prejudices -- The Bayesian prophets -- Solomonoff's demon -- Can you keep a secret? -- Game, set and math -- Will Darwin select Bayes? -- Exponentially counter-intuitive -- Ockham cuts to the chase -- Facts are misleading -- Quick and not too dirty -- Wish me luck -- Down memory lane -- Let's sleep on it -- The unreasonable effectiveness of abstraction -- The Bayesian brain -- It's all fictions -- Exploring the origins of beliefs -- Beyond Bayesianism.

The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge. The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician. This book also shows how Bayesianism sheds new light on nearly all areas of knowledge, from philosophy to mathematics, science and engineering, but also law, politics and everyday decision-making. Bayesian thinking is an important topic for research, which has seen dramatic progress in the recent years, and has a significant role to play in the understanding and development of AI and Machine Learning, among many other things. This book seeks to act as a tool for proselytising the benefits and limits of Bayesianism to a wider public. Features Presents the Bayesian approach as a unifying scientific method for a wide range of topics Suitable for a broad audience, including professionals, students, and academics Provides a more accessible, philosophical introduction to the subject that is offered elsewhere

Annotation. For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture. Publication coincides with the World Year of Physics: "http://www.wyp2005.nl">www.wyp2005.nl "This beautifully designed book deserves a place on the coffee table .[..] Sander Bais confides the reader in the exciting secrets of the laws of nature, and does so in a clear, surprisingly poetic language." "The Equations is a catalogue. A catalogue that belongs to an exhibition of 17 typographic works of art - which gallery will frame them and hang them on the wall? The formulas, displayed in white symbols on a bright red background, are of an untouchable beauty ." 'Untouchable icons' - NRC Handelsblad "The Equations is an absolute feast for everyone who is interested in what physicists have to say about the structure of the world and the beauty that emanates from this. It is a jewel of knowledge, written with love for the field but also with a great compassion for the reader." 'Knowledge smoothly surpasses the fear of formulas' - de Volkskrant This title can be previewed in Google Books - http://books.google.com/books?vid=ISBN9789053567449.

Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation. The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Explains the mathematical properties of universal emotional truths, describing how during a time of personal loss the author developed "emotional equations" as a mechanism for recognizing changeable and unchangeable factors in his healing.

How the tools of STS can be used to understand art and science and the practices of these knowledge-making communities. In Art, Science, and the Politics of Knowledge, Hannah Star Rogers suggests that art and science are not as different from each other as we might assume. She shows how the tools of science and technology studies (STS) can be applied to artistic practice, offering new ways of thinking about people and objects that have largely fallen outside the scope of STS research. Arguing that the categories of art and science are labels with specific powers to order social worlds—and that art and science are best understood as networks that produce knowledge—Rogers shows, through a series of cases, the similarities and overlapping practices of these knowledge communities. The cases, which range from nineteenth-century artisans to contemporary bioartists, illustrate how art can provide the basis for a new subdiscipline called art, science, and technology studies (ASTS), offering hybrid tools for investigating art–science collaborations. Rogers’s subjects include the work of father and son glassblowers, the Blaschkas, whose glass models, produced in the nineteenth century for use in biological classification, are now displayed as works of art; the physics photographs of documentary photographer Berenice Abbott; and a bioart lab that produces work functioning as both artwork and scientific output. Finally, Rogers, an STS scholar and contemporary art–science curator, draws on her own work to consider the concept of curation as a form of critical analysis.