The ubiquity of polynomials and their ability to characterize complex patterns let us better understand generalizations, theorems, and elegant paths to solutions that they provide. We strive to showcase the true beauty of polynomials through a well-thought collection of problems from mathematics competitions and intuitive lectures that follow the sub-topics. Thus, we present a view of polynomials that incorporates various techniques paired with the favorite themes that show up in math contests.

Table of Contents

1 Basic Properties of Polynomials - Part I

2 Basic Properties of Polynomials - Part II

3 Second degree polynomials

4 Third degree polynomials

5 Fourth degree polynomials

6 On roots of polynomials - elementary problems

7 Number theory and polynomials

8 Introductory problems

9 Advanced problems

10 Solutions to introductory problems

11 Solutions to advanced problems

About the Author

Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is firmly involved in mathematics contests and olympiads, having been the Director of American Mathematics.