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Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply ``There is no royal road to mathematics.'' Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when...
This fascinating book looks at the work of Flemish painter Jan van Eyck (c. 1395-1441) under a magnifying glass. Famed for his focused observation of nature, Van Eyck studied fauna and flora in their natural environment and under carefully chosen light conditions, and then achieved a breathtaking and convincing realism in his paintings. Each panel is a collection of minuscule details rendered with superb clarity from foreground to background, or at least that is the impression at first glance. As this book reveals, that is precisely where Van Eyck's exceptional talent lies: he understood that the human brain is able to supplement visual perception where necessary. Here, details from Van Eyck's paintings are organized by such themes as nature, architecture, daily life, fabrics, glass, jewelry and mirrors, and portraits. Opening with a biographical note and an introduction on the technique of oil painting on panel, the authors explain the significance of the individual details and how Van Eyck achieved his innovative artistic results. This is an unprecedented look at the work of a popular master.
Researchers agree that schools construct a particular image of science, in which some characteristics are featured while others end up in oblivion. The result is that although most children are likely to be familiar with images of heroic scientists such as Einstein and Darwin, they rarely learn about the messy, day-to-day practice of science in which scientists are ordinary humans. Surprisingly, the process by which this imagination of science in education occurs has rarely been theorized. This is all the more remarkable since great thinkers tend to agree that the formation of images — imagination — is at the root of how human beings modify their material world. Hence this process in sch...
This book collects the refereed proceedings of the 7th Indian Conference on Logic and Its Applications, ICLA 2017, held in Mumbai, India, in January 2017. The volume contains 13 full revised papers along with 4 invited talks presented at the conference. The aim of this conference series is to bring together researchers from a wide variety of fields in which formal logic plays a significant role. Areas of interest include mathematical and philosophical logic, computer science logic, foundations and philosophy of mathematics and the sciences, use of formal logic in areas of theoretical computer science and artificial intelligence, logic and linguistics, and the relationship between logic and other branches of knowledge. Of special interest are studies in systems of logic in the Indian tradition, and historical research on logic.
Since its appearance in 1995, Authentic School Science has been a resource for many teachers and schools to rethink and change what they are doing in and with their science classrooms. As others were trying to implement the kinds of learning environments that we had described, our own thinking and teaching praxis changed in part because of our dissatisfaction with our own understanding. Over the years, we have piloted ever-new ways of organizing science lessons to figure out what works and how both successful and not-so-successful ways of doing science education should be theorized. In this period, we developed a commitment to cultural-historical activity theory, which does not dichotomize i...
The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. - Completely revised and updated - includes over 25% new material - Discusses the interface between logic and language - Many of the authors are creators or active developers of the theories