Through conventional school mathematics, students all too frequently find themselves succeeding in math classes by memorizing formulas without understanding their applications or the reasoning behind them. As a result, insight gained in this way is regrettably supported by scant or no evidence. This is why it’s so important to understand the proofs! Proofs reveal the essence of mathematics and provide us with the key to appreciating its beauty. Students frequently ask themselves, “When will I ever need this in life?” even after getting over the problem of “why should this be true?” Proofs in Competition Math seeks to address these problems at many different levels, from the basics of competition math to the Olympiad level and beyond. There will be prerequisites for each ability level, so don’t worry if you don’t know all of the arithmetic in this book. This will help you identify your existing strengths and weaknesses and create reasonable goals for yourself as a math student. So, we’ve sparked your interest, mathematicians!