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Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery. Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries. Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.","brand":"WoB","offers":[{"title":"GB \/ LIKE_NEW \/ INTERNAL","offer_id":49587445006609,"sku":"GOR013396488","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ GOOD \/ INTERNAL","offer_id":49727049236753,"sku":"GOR013772543","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50469775147281,"sku":"CIN0691115036VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51846904643857,"sku":"GOR007431470","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0691115036.jpg?v=1750816605"},{"product_id":"art-of-the-conductor-book-john-j-watkins-9780595433964","title":"The Art of the Conductor","description":"John Watkins has used his years of experience on both sides of the baton to create a charming introduction to the art of conducting. There are not many reference books that deal with the 'how to' of directing a group of musicians. This practical guide to conducting wisely stays away from musical theory and concentrates on how to communicate with musicians from base amateur to seasoned professional.This is a must for a newly aspiring conductor, and an experienced conductor could very well use this as a refresher. \u003cbr\u003e -John Tozer, music director, Scarborough, Ontario\u003cp\u003e An invaluable reference guide for musicians of all types, The Art of the Conductor contains clear and detailed descriptions of universally accepted techniques used by the world's best and most successful music conductors.\u003c\/p\u003e\u003cp\u003e Classically trained musician and conductor John J. Watkins discusses the evolution of conducting technique and how it relates to various forms of music, and he outlines the wide array of skills conductors need today. He also explains the finer points of technique and control, including beat patterns and signals, tempo changes, and using the left hand, to make the conducting experience as rewarding as possible.\u003c\/p\u003e\u003cp\u003e The Art of the Conductor will help conductors, choristers, and instrumentalists build their skills and confidence for more relaxed, enjoyable, and polished performances that audiences will love.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49621718630673,"sku":"GOR004792626","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51004647407889,"sku":"NIN9780595433964","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52138257285393,"sku":"NLS9780595433964","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0595433960.jpg?v=1751074077"},{"product_id":"across-the-board-book-john-j-watkins-9780691154985","title":"Across the Board","description":"Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens? Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery. Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.","brand":"WoB","offers":[{"title":"US \/ WELL_READ \/ SBYB","offer_id":49757977739537,"sku":"CIN0691154988A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ GOOD \/ INTERNAL","offer_id":50818197192977,"sku":"GOR011696368","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50833870717201,"sku":"GOR005822452","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51005690577169,"sku":"NIN9780691154985","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":53370709541137,"sku":"CIN0691154988G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0691154988.jpg?v=1750700235"},{"product_id":"topics-in-commutative-ring-theory-book-john-j-watkins-9780691127484","title":"Topics in Commutative Ring Theory","description":"Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":50925452656913,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50925454688529,"sku":"CIN0691127484VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ GOOD \/ INTERNAL","offer_id":51733578514705,"sku":"GOR014383570","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":52465535418641,"sku":"GOR014531600","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0691127484.jpg?v=1750816623"},{"product_id":"number-theory-book-john-j-watkins-9780691159409","title":"Number Theory","description":"Emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the subjects in mathematics. 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