Counting

M. Koh, Tay Eng Guan, Eng Guan Tay

World Scientific Publishing Company | 2002 | 124 páginas | RAR - PDF | 2,40 Mb

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Descrição:

This book is a useful, attractive introduction to basic counting techniques for upper secondary and junior college students, as well as teachers. Younger students and lay people who appreciate mathematics, not to mention avid puzzle solvers, will also find the book interesting. The various problems and applications here are good for building up proficiency in counting. They are also useful for honing basic skills and techniques in general problem solving. Many of the problems avoid routine and the diligent reader will often discover more than one way of solving a particular problem, which is indeed an important awareness in problem solving. The book thus helps to give students an early start to learning problem-solving heuristics and thinking skills.

Índice

Contents

Preface v

1. The Addition Principle 1

2. The Multiplication Principle 9

3. Subsets and Arrangements 17

4. Applications 25

5. The Bijection Principle 35

6. Distribution of Balls into Boxes 47

7. More Applications of (BP) 53

8. Distribution of Distinct Objects into Distinct Boxes 63

9. Other Variations of the Distribution Problem 67

10. The Binomial Expansion 73

11. Some Useful Identities 77

12. Pascal's Triangle 85

x Counting

13. Miscellaneous Problems 95

Books Recommended for Further Reading 105

Answers to Exercises 107

Index 111