{"product_id":"applied-nonstandard-analysis-9780486442297","title":"Applied Nonstandard Analysis","description":"Geared toward upper-level undergraduates and graduate students, this text explores the applications of nonstandard analysis without assuming any knowledge of mathematical logic. It develops the key techniques of nonstandard analysis at the outset from a single, powerful construction; then, beginning with a nonstandard construction of the real number system, it leads students through a nonstandard treatment of the basic topics of elementary real analysis, topological spaces, and Hilbert space.\u003cbr\u003eImportant topics include nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. The focus on compact operators on a Hilbert space includes the Bernstein-Robinson theorem on invariant subspaces, which was first proved with nonstandard methods. Ever mindful of the needs of readers with little background in these subjects, the text offers a straightforward treatment that provides a strong foundation for advanced studies of analysis\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAbout the Author\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eMartin Davis: Computer Science Pioneer \u003cbr\u003e\u003c\/b\u003eDover's publishing relationship with Martin Davis, now retired from NYU and living in Berkeley, goes back to 1985 when we reprinted his classic 1958 book \u003ci\u003eComputability and Unsolvability, \u003c\/i\u003e widely regarded as a classic of theoretical computer science. A graduate of New York's City College, Davis received his PhD from Princeton in the late 1940s and became one of the first computer programmers in the early 1950s, working on the ORDVAC computer at The University of Illinois. He later settled at NYU where he helped found the Computer Science Department. \u003c\/p\u003e\u003cp\u003eNot many books from the infancy of computer science are still alive after several decades, but \u003ci\u003eComputability and Unsolvability\u003c\/i\u003e is the exception. And \u003ci\u003eThe Undecidable\u003c\/i\u003e is an anthology of fundamental papers on undecidability and unsolvability by major figures in the field including Godel, Church, Turing, Kleene, and Post. \u003c\/p\u003e\u003cp\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eCritical Acclaim for \u003ci\u003eComputability and Unsolvability\u003c\/i\u003e: \u003cbr\u003eThis book gives an expository account of the theory of recursive functions and some of its applications to logic and mathematics. It is well written and can be recommended to anyone interested in this field. No specific knowledge of other parts of mathematics is presupposed. Though there are no exercises, the book is suitable for use as a textbook. -- J. C. E. Dekker, \u003ci\u003eBulletin of the American Mathematical Society\u003c\/i\u003e, 1959\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eCritical Acclaim for \u003ci\u003eThe Undecidable\u003c\/i\u003e: \u003cbr\u003eA valuable collection both for original source material as well as historical formulations of current problems. -- \u003ci\u003eThe Review of Metaphysics\u003c\/i\u003e \u003c\/p\u003e\u003cp\u003eMuch more than a mere collection of papers . . . a valuable addition to the literature. -- \u003ci\u003eMathematics of Computation\u003c\/i\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":50324829929746,"sku":"9780486442297","price":10.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_a4498fc0-51bb-4e47-8f4a-23092e645086.jpg?v=1727675568","url":"https:\/\/surprise-castle.myshopify.com\/products\/applied-nonstandard-analysis-9780486442297","provider":"Surprise Castle","version":"1.0","type":"link"}