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It is essential that the student works through the exercises in order to build a bridge between ordinary high school permutation and combination exercises and more sophisticated, intricate, and abstract concepts and problems in undergraduate combinatorics. The extensive discussions of the solutions are a key part of the learning process. The concepts are not stacked at the beginning of each section in a blue box, as in many undergraduate textbooks. Instead, the key mathematical ideas are carefully worked into organized, challenging, and instructive examples. The authors are proud of their strength, their collection of beautiful problems, which they have accumulated through years of work preparing students for the International Math­ ematics Olympiads and other competitions. A good foundation in combinatorics is provided in the first six chapters of this book. While most of the problems in the first six chapters are real counting problems, it is in chapters seven and eight where readers are introduced to essay-type proofs. This is the place to develop significant problem-solving experience, and to learn when and how to use available skills to complete the proofs.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":49669488247057,"sku":"CIN0817642889G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51008349405457,"sku":"NIN9780817642884","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52507795882257,"sku":"NLS9780817642884","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0817642889.jpg?v=1750979428"},{"product_id":"mathematical-olympiad-challenges-book-titu-andreescu-9780817645281","title":"Mathematical Olympiad Challenges","description":"Why Olympiads? 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It's all there: the period of immersion in the situation, the quiet examination of possible approaches, the pursuit of various paths to solution. There is the fruitless dead end, as well as the path that ends abruptly but offers new perspectives, leading eventually to the discoveryof a better route. Perhapsmost obviously,grapplingwith a goodproblem provides practice in dealing with the frustration of working at material that refuses to yield. If the solver is lucky, there will be the moment of insight that heralds the start of a successful solution. Like a well-crafted work of ?ction, a good Olympiad problem tells a story of mathematical creativity that captures a good part of the real experience and leaves the participant wanting still more. 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