Al-Jabr: Higher Algebraic Yield

This book covers the modern sort of Olympiad Algebra problems–mostly alge-bra with combinatorial ideas. Regarding the naming of the book, we have the word Al-jabr, which is an Arabic word from which the word “Algebra” is derived. The other part, Higher Algebraic Yield, was inspired by the fact that its acronym is HAY, which is the abbreviation of the authors’ names. This book is the result of three years of participating in mathematical Olympiads. The ideas and techniques presented here come from many resources: online hand-outs, solutions from the Art of Problem Solving site, and conversations with others on discord especially within the Mathematical Olympiad Discord Server. The problems are taken from contests around the world, various handouts, or even new variations of the problems from both. As we have learned from our experience in Mathematical Olympiads, learning math is mostly by doing problems. Although we have explicitly stated many techniques before solving the problems and examples, there are still many ideas that underlies in each problem that were not covered in this book. Most of the chapters of this book contains: examples, problems, and exercises ordered roughly in increasing difficulty, ranging from sub-IMO problem 1/4 level up to IMO problem 3/6 level. The main reason that motivated us to write this book on Algebra was that it was the topic we found most challenging to master, primarily due to the lack of resources on this broad subject. As a result, we spent countless hours attempting to grasp the general problem solving strategies and underlying ideas through problem solutions, which one could tell that it is not an efficient way of learning for newcomers to these topics.