## A Path to Combinatorics for Undergraduates: Counting StrategiesThe 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. |

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### Other editions - View all

A Path to Combinatorics for Undergraduates: Counting Strategies Titu Andreescu,Zuming Feng Limited preview - 2013 |

A Path to Combinatorics for Undergraduates: Counting Strategies Titu Andreescu,Zuming Feng No preview available - 2003 |

### Common terms and phrases

AIME answer appears arrangements assume base bijection calculate called cards choices choose circle coefficient coloring column combinations combinatorics Compute consecutive consider containing coordinate corresponds count define denote denote the number denote the set desired Determine the number digits distinct divisible dominoes elements entries equal equation exactly Example Figure five four functions given hand Hence identity least length letters Mathematical matrix moves multiplication nonnegative integers Note objects obtain pairs partition path permutations pick players points positive integer possible prime Principle probability problem Prove recursion relations respectively result satisfying seats segments sequence sides Solution solved steps subsets term Theorem tiles triangle uniquely unit squares values vertex vertices