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AuthorAndreescu, Titu. author
TitleA Path to Combinatorics for Undergraduates [electronic resource] : Counting Strategies / by Titu Andreescu, Zuming Feng
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004
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Descript XIX, 228 p. 39 illus. online resource


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 familiarizยญ 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 Mathยญ 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


Preface -- Introduction -- Acknowledgments -- Abbreviations and Notations -- Addition on Multiplication?- Combinations -- Properties of Binomial Coefficients -- Bijections -- Inclusions and Exclusions -- Recursions -- Calculating in Two Ways โ{128}{147} Fubini's Principle -- Generating Functions -- Review Exercises -- Glossary -- Further Reading

Mathematics Geometry Convex geometry Discrete geometry Probabilities Combinatorics Mathematics Combinatorics Geometry Convex and Discrete Geometry Probability Theory and Stochastic Processes


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