A Path to Combinatorics for Undergraduates: Counting StrategiesSpringer Science & Business Media, 01.12.2013 - 228 Seiten 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. |
Inhalt
Properties of Binomial Coefficients | 43 |
Bijections | 69 |
Recursions | 91 |
Inclusion and Exclusion | 117 |
Fubinis Principle | 143 |
Generating Functions | 165 |
Review Exercises | 195 |
Glossary | 213 |
Andere Ausgaben - Alle anzeigen
A Path to Combinatorics for Undergraduates: Counting Strategies Titu Andreescu,Zuming Feng Eingeschränkte Leseprobe - 2003 |
A Path to Combinatorics for Undergraduates: Counting Strategies Titu Andreescu,Zuming Feng Keine Leseprobe verfügbar - 2003 |
Häufige Begriffe und Wortgruppen
A₁ AIME Andreescu answer ARML assume b₁ B₂ bijection binomial coefficients cards chessboard choose circle coloring schemes column combinatorics congruence relations consecutive consider containing convex polygon coordinate count the number cube denote the number denote the set Determine the number digits distinct dominoes equal equation exactly Example Figure Find the number functions Hence Inclusion-Exclusion Principle International Mathematical Olympiads k₁ knights least length Let A1 Mathematical Association Mathematical Olympiads matrix multiplication n-tuples nonnegative integers number of elements number of ordered obtain P₁ PA(x pairs partition Pascal's triangle path permutations pick players polygon polynomial positive integer possible values prime probability problem Prove real numbers recursive relations S₁ satisfying segments sequence Solution solved subsets surjective functions Theorem 3.2 tiles total number triplets trominoes unit squares USAMO Vandermonde Identity vertex vertices Σ Σ