{"product_id":"the-discrepancy-method-randomness-and-complexity-hardback-9780521770934","title":"The Discrepancy Method; Randomness and Complexity (Hardback) 9780521770934","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Discrepancy Method\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eRandomness and Complexity\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eExplores the link between discrepancy theory and randomized algorithms.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eBernard Chazelle (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521770934, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 July 2000\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e494 pages, 160 b\/w illus.\u003cbr\u003e22.9 x 15.2 x 3.2 cm, 0.89 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e' … the main point is that by presenting the discrepancy method in such an impressive way as this book does, the author helps us to imagine the fantastic possibilities that randomization opens up to everybody, and he shows that current research in theoretical computer science has an astonishing impact on common fundamentals of all sciences. I believe that any reader interested in principal questions will enjoy this book.' The Computer Journal\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal to students and researchers in computer science, operations research, pure and applied mathematics, and engineering.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Combinatorial discrepancy\u003cbr\u003e 2. Upper bounds in geometric discrepancy\u003cbr\u003e 3. Lower bounds in geometric discrepancy\u003cbr\u003e 4. Sampling\u003cbr\u003e 5. Geometric searching\u003cbr\u003e 6. Complexity lower bounds\u003cbr\u003e 7. Convex hulls and Voronoi diagrams\u003cbr\u003e 8. Linear programming and extensions\u003cbr\u003e 9. Pseudo-randomness\u003cbr\u003e 10. Communication complexity\u003cbr\u003e 11. Minimum spanning trees\u003cbr\u003e A. Probability theory\u003cbr\u003e B. Harmonic analysis\u003cbr\u003e C. Convex geometry.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical theory of computation [\u003ca title=\"See our other books on Mathematical theory of computation\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20theory%20of%20computation%20%5BUYA%5D%22\"\u003eUYA\u003c\/a\u003e], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46001022730520,"sku":"9780521770934","price":97.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521770934i_eadd9261-3092-431b-8fd4-7908cbf9b844.jpg?v=1691367771","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-discrepancy-method-randomness-and-complexity-hardback-9780521770934","provider":"Freshly Printed Books","version":"1.0","type":"link"}