{"title":"Mathematics: Discrete","description":"","products":[{"product_id":"game-theory-basics","title":"Game Theory Basics","description":"\u003cspan data-mce-fragment=\"1\"\u003eGame theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.\u003c\/span\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":40354608971952,"sku":"9781108824231","price":34.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781108824231.jpg?v=1628954796"},{"product_id":"the-discrete-mathematical-charms-of-paul-erdos","title":"The Discrete Mathematical Charms of Paul Erdos","description":"Paul Erdős published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-Rényi-Sós Friendship Theorem, Erdős-Rényi random graphs, the Chvátal-Erdős theorem on Hamilton cycles, and other results of Erdős, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdős, this book offers a behind-the-scenes look at interactions with the legendary collaborator.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43240177631471,"sku":"9781108927406","price":22.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781108927406i.jpg?v=1661611813"},{"product_id":"introduction-to-random-graphs","title":"Introduction to Random Graphs","description":"From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43240186839279,"sku":"9781107118508","price":60.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781107118508i.jpg?v=1661612246"},{"product_id":"lectures-on-random-lozenge-tilings","title":"Lectures on Random Lozenge Tilings","description":"Over the past 25 years, there has been an explosion of interest in the area of random tilings. The first book devoted to the topic, this timely text describes the mathematical theory of tilings. It starts from the most basic questions (which planar domains are tileable?), before discussing advanced topics about the local structure of very large random tessellations. The author explains each feature of random tilings of large domains, discussing several different points of view and leading on to open problems in the field. The book is based on upper-division courses taught to a variety of students but it also serves as a self-contained introduction to the subject. Test your understanding with the exercises provided and discover connections to a wide variety of research areas in mathematics, theoretical physics, and computer science, such as conformal invariance, determinantal point processes, Gibbs measures, high-dimensional random sampling, symmetric functions, and variational problems.","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":43248174989551,"sku":"9781108843966","price":49.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/products\/9781108843966i.jpg?v=1661846288"},{"product_id":"the-art-of-mathematics","title":"The Art of Mathematics","description":"\u003cp\u003eCan a Christian escape from a lion? How quickly can a rumour spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime.\u003c\/p\u003e\n\u003cdiv class=\"contentHidden\"\u003e\n\u003cul class=\"academicArrowList\"\u003e\n\u003cli\u003eAimed at a broad audience ranging from professional mathematicians to interested amateur\u003c\/li\u003e\n\u003cli\u003eEntertaining mix of problems ranging from the frivolous to others that show how mathematicians discover new ideas\u003c\/li\u003e\n\u003cli\u003eInspired by two of the twentieth century's leading mathematicians, Paul Erdos and J. E. 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Tangles offer a new, structural, approach to artificial intelligence that can help us understand, classify, and predict complex phenomena.\u003cbr\u003eThis has become possible by the recent axiomatization of the mathematical theory of tangles, which has made it applicable far beyond its origin in graph theory: from clustering in data science and machine learning to predicting customer behaviour in economics; from DNA sequencing and drug development to text and image analysis. Such applications are explored here for the first time. Assuming only basic undergraduate mathematics, the theory of tangles and its potential implications are made accessible to scientists, computer scientists, and social scientists.\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eExplains how the mathematical theory of tangles offers a structural approach to AI in all the empirical sciences\u003c\/li\u003e\n\u003cli\u003eFeatures examples from a wide range of disciplines\u003c\/li\u003e\n\u003cli\u003eAssumes no mathematics beyond a first-year undergraduate course, and the basic language of sets and functions\u003c\/li\u003e\n\u003cli\u003eEnables readers to test the tangle approach to AI in their own field, using the book with the software available free from the author\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Cambridge University Press Bookshop","offers":[{"title":"Default Title","offer_id":55747064332674,"sku":"9781009473316","price":49.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0475\/2031\/7597\/files\/9781009473316i.jpg?v=1759418930"}],"url":"https:\/\/www.cambridgebookshop.co.uk\/collections\/mathematics-discrete.oembed","provider":"Cambridge University Press Bookshop","version":"1.0","type":"link"}