X Marks the Spot

The Lost Inheritance of Mathematics. 2. Auflage. Sprachen: Englisch. 25,4 cm / 17,8 cm ( B/H )
EAN 9781041173496
144,50 €
inkl. MwSt.
552 Seiten
März 2027
Taylor & Francis Ltd

X Marks the Spot is written from the point of view of the users of mathematics. Since the beginning, mathematical concepts and techniques (such as arithmetic and geometry) were created as tools with a particular purpose like counting sheep and measuring land areas. Understanding those purposes leads to a greater understanding of why mathematics developed as it did. Later mathematical concepts came from a process of abstracting and generalizing earlier mathematics. This process of abstraction is very powerful, but often comes at the price of intuition and understanding. This book strives to give a guided tour of the development of various branches of mathematics (and what they're used for) that will give the reader this intuitive understanding. Features - Treats mathematical techniques as tools, and areas of mathematics as the result of abstracting and generalizing earlier mathematical tools - Written in a relaxed conversational and occasionally humorous style making it easy to follow even when discussing esoterica - Unravels how mathematicians think, demystifying math and connecting it to the ways non-mathematicians think and connecting math to people's lives Discusses how math education can be improved in order to prevent future generations from being turned off by math New to the second edition - New chapters on Information Theory and Iterative Processes - Discussion of the mathematics underlying Generative AI and its limitations, and the mathematical basis for why people may mistake its output for genuine creativity.

Richard Garfinkle, for the better part of his early life, thought he wanted to be a mathematician. He went so far as to spend four years studying math at the University of Chicago before discovering that he really wanted to be a writer. He has had several science fiction and fantasy novels published. His first Celestial Matters (Tor 1996) won the Compton Crook award for best first novel. Richard and Dr David have written Three Steps to the Universe (U. of Chicago Press, 2008) a book on black holes and dark matter. For his day job, he programs computers and has multiple software patents ranging from animation through security to data structuring and search efficiency. He recently authored the programming textbook The Muse of Coding: Computer Programming as Art. David Garfinkle was born in 1958 and wanted to be a physicist ever since his first year of high school. He got a bachelors degree from Princeton University in 1980 and a PhD from The University of Chicago in 1985 where his thesis was on the gravitational properties of cosmic strings. He was then a postdoctoral researcher in general relativity at Washington University in St. Louis, University of Florida, and University of California in Santa Barbara. In 1991 he became a physics professor at Oakland University in Michigan. He has been there ever since, except for the 2003-2004 academic year when he was in Canada as a professor at the University of Guelph and an Associate at the Perimeter Institute for Theoretical Physics in Waterloo. Dr David is the author of over 140 articles in physics journals, many of them on black holes and gravitational collapse. One of his articles ("Charged black holes in string theory" written with Gary Horowitz and Andy Strominger) has been cited over 1700 times. His research has been supported by the Research Corporation, the US National Science Foundation (NSF) and Canada's Natural Sciences and Engineering Research Council (NSERC). He has also refereed articles for numerous scientific journals and has reviewed grant proposals for NSF, NASA, Research Corporation and NSERC. David's main areas of research are black holes, spacetime singularities, and gravitational radiation. He performs computer simulations of gravitational collapse to resolve questions about black holes and singularities. Dr David was named a Fellow of the American Physical Society (APS) with the citation reading "for his numerous contributions to a wide variety of topics in relativity and semiclassical gravity." He was an ITP Scholar for 1998-2000 at the Institute for Theoretical Physics in Santa Barbara. He is a Visiting Scientist at The University of Michigan in Ann Arbor. He has been both Chair and Secretary/Treasurer of the Topical Group (now Division) in Gravitation of APS. He is Secretary/Treasurer of the International Society for General Relativity and Gravitation, and has been a judge for that society's Ehlers thesis prize for mathematical and numerical general relativity. He was selected as an APS outreach speaker for World Year of Physics (2005) to give talks to general audiences on black holes. Dr David and Richard have written Three Steps to the Universe (U. of Chicago Press, 2008) a book on black holes and dark matter.

1. Why this Book? 2. Sticks, Stones, and Strings. 3. Abstraction, Mistrust, and Laziness. 4. Algebra, Geometry, Analysis. 5. Analytic Geometry. 6. Calculus. 7. The Language of Motion. 8. Sound, Notes, and Harmonics. 9. Probability and Statistics. 10. Other Geometries. 11. Algebra and the Rise of Abstraction. 12. The Smith and the Knight. 13. Building the Theoretical Universe. 14. Computers. 15. Information Theory. The Mathematics of Surprise. 16. States, Iteration, Stochastic and Markov Processes, Chaos, and Generative AI. 17. The Theoretical Universe of Modern Physics. 18. Math Education and Math in Education.

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