Synopsis
This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
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A Path to Combinatorics for Undergraduates: Counting Strategies
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Birkhäuser, 2003
ISBN 10 : 0817642889
ISBN 13 : 9780817642884
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A Path to Combinatorics for Undergraduates Counting Strategies
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Springer/Sci-Tech/Trade, 2003
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ISBN 13 : 9780817642884
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Path to Combinatorics for Undergraduates : Counting Strategies
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A Path to Combinatorics for Undergraduates (Paperback)
Edité par
Birkhauser Boston, Berlin, 2003
ISBN 10 : 0817642889
ISBN 13 : 9780817642884
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Paperback
Vendeur : Grand Eagle Retail, Bensenville, IL, Etats-Unis
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Paperback. Etat : new. Paperback. This unique approach to combinatorics is centered around challenging examples, fully-worked solutions, and hundreds of problems---many from Olympiads and other competitions, and many original to the authors. Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions, illustrations, and exercises that are designed to encourage creativity, improve problem-solving techniques, and widen the reader's mathematical horizons.Topics encompass permutations and combinations, binomial coefficients and their applications, recursion, bijections, inclusions and exclusions, and generating functions. The work is replete with a broad range of useful methods and results, such as Sperner's Theorem, Catalan paths, integer partitions and Young's diagrams, and Lucas' and Kummer's Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.The authors' previous text, 102 Combinatorial Problems, makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors.The book's unusual problems and examples will stimulate seasoned mathematicians as well. A Path to Combinatorics for Undergraduates is a lively introduction not only to combinatorics, but also to mathematical ingenuity, rigor, and the joy of solving puzzles. The main goal of the two authors is to help undergraduate students understand the concepts and ideas of combinatorics, an important realm of mathematics, and to enable them to ultimately achieve excellence in this field. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9780817642884
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Path to Combinatorics for Undergraduates : Counting Strategies
Edité par
Birkhäuser, 2003
ISBN 10 : 0817642889
ISBN 13 : 9780817642884
Ancien ou d'occasion
Couverture souple
Vendeur : GreatBookPrices, Columbia, MD, Etats-Unis
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A Path to Combinatorics for Undergraduates: Counting Strategies
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A Path to Combinatorics for Undergraduates: Counting Strategies
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Paperback. Etat : New. N° de réf. du vendeur 6666-IUK-9780817642884
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Path to Combinatorics for Undergraduates : Counting Strategies
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Path to Combinatorics for Undergraduates : Counting Strategies
Edité par
Birkhäuser, 2003
ISBN 10 : 0817642889
ISBN 13 : 9780817642884
Ancien ou d'occasion
Couverture souple
Vendeur : GreatBookPricesUK, Woodford Green, Royaume-Uni
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Etat : As New. Unread book in perfect condition. N° de réf. du vendeur 1783941
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A Path to Combinatorics for Undergraduates
Edité par
Birkhäuser, Birkhäuser Nov 2003, 2003
ISBN 10 : 0817642889
ISBN 13 : 9780817642884
Neuf
Taschenbuch
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The main goal of the two authors is to help undergraduate students understand the concepts and ideas of combinatorics, an important realm of mathematics, and to enable them to ultimately achieve excellence in this field. This goal is accomplished by familiariz ing students with typical examples illustrating central mathematical facts, and by challenging students with a number of carefully selected problems. 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. 252 pp. Englisch. N° de réf. du vendeur 9780817642884
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