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A Path to Combinatorics for Undergraduates: Counting Strategies

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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.

Author: Andreescu Titu
Publisher: BIRKHAUSER
Pages: 228
ISBN: 9780817642884
Cover: Paperback
Edition Number: 1
Release Year: 2012

Dr. Titu Andreescu is an Associate Professor at the University of Texas at Dallas in the Science and Mathematics Education department.

Kathy Cordeiro, MBA, is a leading developer of education initiatives for business and academia. She founded Eudaimonia Academy, where she coached mathematics teams and worked with highly and profoundly gifted students.

Alina Andreescu, MA, is the co-founder and Operations Director of AwesomeMath and founder of XYZ Press. She fosters an international community of staff, students, and instructors that values critical thinking, creativity, passionate problem solving, and lifetime mathematical learning.

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