# A Path to Combinatorics for Undergraduates

## Counting Strategies

• Titu Andreescu
• Zuming Feng
Textbook

1. Front Matter
Pages i-xix
2. Titu Andreescu, Zuming Feng
Pages 1-23
3. Titu Andreescu, Zuming Feng
Pages 25-41
4. Titu Andreescu, Zuming Feng
Pages 43-67
5. Titu Andreescu, Zuming Feng
Pages 69-90
6. Titu Andreescu, Zuming Feng
Pages 91-116
7. Titu Andreescu, Zuming Feng
Pages 117-141
8. Titu Andreescu, Zuming Feng
Pages 143-164
9. Titu Andreescu, Zuming Feng
Pages 165-193
10. Titu Andreescu, Zuming Feng
Pages 195-212
11. Back Matter
Pages 213-228

### Introduction

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.

### Keywords

Combinatorics Partition Permutation Volume combinatorical geometry geometry ksa

#### Authors and affiliations

• Titu Andreescu
• 1
• Zuming Feng
• 2
1. 1.American Mathematics CompetitionsUniversity of NebraskaLincolnUSA
2. 2.Department of MathematicsPhillips Exeter AcademyExeterUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-0-8176-8154-8
• Copyright Information Birkhäuser Boston 2004
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-0-8176-4288-4
• Online ISBN 978-0-8176-8154-8
• Buy this book on publisher's site