This collection of essays examines the key achievements and likely developments in the area of automated reasoning. In keeping with the group ethos, Automated Reasoning is interpreted liberally, spanning underpinning theory, tools for reasoning, argumentation, explanation, computational creativity, and pedagogy. Wider applications including secure and trustworthy software, and health care and emergency management. The book starts with a technically oriented history of the Edinburgh Automated Reasoning Group, written by Alan Bundy, which is followed by chapters from leading researchers associated with the group. Mathematical Reasoning: The History and Impact of the DReaM Group will attract considerable interest from researchers and practitioners of Automated Reasoning, including postgraduates. It should also be of interest to those researching the history of AI.
By presenting state-of-the-art results in logical reasoning and formal methods in the context of artificial intelligence and AI applications, this book commemorates the 60th birthday of Jörg H. Siekmann. The 30 revised reviewed papers are written by former and current students and colleagues of Jörg Siekmann; also included is an appraisal of the scientific career of Jörg Siekmann entitled "A Portrait of a Scientist: Logics, AI, and Politics." The papers are organized in four parts on logic and deduction, applications of logic, formal methods and security, and agents and planning.
This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.
This user-friendly book on group theory introduces topics in as simple a manner as possible and then gradually develops those topics into more advanced ones, eventually building up to the current state-of-the-art. By using simple examples from physics and mathematics, the advanced topics become logical extensions of ideas already introduced. In addition to being used as a textbook, this book would also be useful as a reference guide for graduates and researchers in particle, nuclear and hadron physics.
Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.
One of Slate’s 10 Best Books of the Year Anthony Gottlieb’s landmark The Dream of Reason and its sequel challenge Bertrand Russell’s classic as the definitive history of Western philosophy. Western philosophy is now two and a half millennia old, but much of it came in just two staccato bursts, each lasting only about 150 years. In his landmark survey of Western philosophy from the Greeks to the Renaissance, The Dream of Reason, Anthony Gottlieb documented the first burst, which came in the Athens of Socrates, Plato, and Aristotle. Now, in his sequel, The Dream of Enlightenment, Gottlieb expertly navigates a second great explosion of thought, taking us to northern Europe in the wake of its wars of religion and the rise of Galilean science. In a relatively short period—from the early 1640s to the eve of the French Revolution—Descartes, Hobbes, Spinoza, Locke, Leibniz, and Hume all made their mark. The Dream of Enlightenment tells their story and that of the birth of modern philosophy. As Gottlieb explains, all these men were amateurs: none had much to do with any university. They tried to fathom the implications of the new science and of religious upheaval, which led them to question traditional teachings and attitudes. What does the advance of science entail for our understanding of ourselves and for our ideas of God? How should a government deal with religious diversity—and what, actually, is government for? Such questions remain our questions, which is why Descartes, Hobbes, and the others are still pondered today. Yet it is because we still want to hear them that we can easily get these philosophers wrong. It is tempting to think they speak our language and live in our world; but to understand them properly, we must step back into their shoes. Gottlieb puts readers in the minds of these frequently misinterpreted figures, elucidating the history of their times and the development of scientific ideas while engagingly explaining their arguments and assessing their legacy in lively prose. With chapters focusing on Descartes, Hobbes, Spinoza, Locke, Pierre Bayle, Leibniz, Hume, Rousseau, and Voltaire—and many walk-on parts—The Dream of Enlightenment creates a sweeping account of what the Enlightenment amounted to, and why we are still in its debt.
