A Path to Combinatorics for Undergraduates

Counting Strategies

  • Titu Andreescu
  • Zuming Feng

Table of contents

  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

About this book


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.


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