{"title":"Rod Downey","description":null,"products":[{"product_id":"turing-s-legacy-book-rod-downey-9781107043480","title":"Turing's Legacy","description":"Alan Turing was an inspirational figure who is now recognised as a genius of modern mathematics. In addition to leading the Allied forces' code-breaking effort at Bletchley Park in World War I, he proposed the theoretical foundations of modern computing and anticipated developments in areas from information theory to computer chess. His ideas have been extraordinarily influential in modern mathematics and this book traces such developments by bringing together essays by leading experts in logic, artificial intelligence, computability theory and related areas. Together, they give insight into this fascinating man, the development of modern logic, and the history of ideas. The articles within cover a diverse selection of topics, such as the development of formal proof, differing views on the Church Turing thesis, the development of combinatorial group theory, and Turing's work on randomness which foresaw the ideas of algorithmic randomness that would emerge many years later.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49603697443089,"sku":"GOR007703497","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1107043484.jpg?v=1750751722"},{"product_id":"computability-and-complexity-book-rod-downey-9783031537431","title":"Computability and Complexity","description":"\u003cp\u003eThis is a book about computation, something which is ubiquitous in the modern world. More precisely, it examines computability theory and computational complexity theory. Computability theory is the part of mathematics and computer science which seeks to clarify what we mean by computation or algorithm. When is there a computational solution possible to some question? How can we show that none is possible? How computationally hard is the question we are concerned with? Arguably, this area lead to the development of digital computers. (Computational) complexity theory is an intellectual heir of computability theory. Complexity theory is concerned with understanding what resources are needed for computation, where typically we would measure the resources in terms of time and space. Can we perform some task in a feasible number of steps? Can we perform some algorithm with only a limited memory? Does randomness help? Are there standard approaches to overcoming computational difficulty?\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52618809049361,"sku":"NLS9783031537431","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53402672005393,"sku":"NIN9783031537431","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031537431.jpg?v=1770286165"},{"product_id":"aspects-of-complexity-book-rod-downey-9783110168105","title":"Aspects of Complexity","description":"The book contains 8 detailed expositions of the lectures given at the Kaikoura 2000 Workshop on Computability, Complexity, and Computational Algebra. Topics covered include basic models and questions of complexity theory, the Blum-Shub-Smale model of computation, probability theory applied to algorithmics (randomized alogrithms), parametric complexity, Kolmogorov complexity of finite strings, computational group theory, counting problems, and canonical models of ZFC providing a solution to continuum hypothesis. The text addresses students in computer science or mathematics, and professionals in these areas who seek a complete, but gentle introduction to a wide range of techniques, concepts, and research horizons in the area of computational complexity in a broad sense.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52675496083729,"sku":"NLS9783110168105","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783110168105.jpg?v=1762302038"},{"product_id":"the-moralist-book-rod-downey-9781887650403","title":"The Moralist","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52843035918609,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":52843036410129,"sku":"GOR002942856","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781887650403.jpg?v=1764775730"},{"product_id":"hierarchy-of-turing-degrees-book-rod-downey-9780691199665","title":"A Hierarchy of Turing Degrees","description":"\u003cp\u003eComputability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications in topology, group theory, and other subfields.\u003cbr\u003e\u003cbr\u003eIn \u003ci\u003eA Hierarchy of Turing Degrees\u003c\/i\u003e, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers.\u003cbr\u003e\u003cbr\u003eBlending traditional and modern research results in computability theory, \u003ci\u003eA Hierarchy of Turing Degrees \u003c\/i\u003eestablishes novel directions in the field.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":53366374138129,"sku":"NIN9780691199665","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691199665.jpg?v=1786614120"},{"product_id":"hierarchy-of-turing-degrees-book-rod-downey-9780691199658","title":"A Hierarchy of Turing Degrees","description":"\u003cp\u003eComputability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. 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