Details
Proofs in Competition Math: Volume 1

All too often, math is presented formulaically and independently of exposition, with little to no contextualization or applicable real-world connection. Through common school mathematics, students often memorize and regurgitate formulas that seem meaningless in that they lack the necessary accompanying context to fully understand them beyond the surface level. Students may find themselves excelling in school math classes by memorizing formulas, but not their applications or the motivation behind them. As a consequence, understanding derived in this manner is tragically based on little or no proof.This is why studying proofs is paramount! Proofs help us understand the nature of mathematics and show us the key to appreciating its elegance. Though the formulas themselves are indeed versatile in modern day mathematics, without the rigor or motivation driving them, they lose all purpose. Simply memorizing a formula is like memorizing the spelling of a word but failing to assimilate its definition.But even getting past the concern of "why should this be true?" students often face the equally-pressing question of "when will I ever need this in life?" Proofs in Competition Math aims to remedy both of these issues at a wide range of levels, from the fundamentals of competition math all the way to the Olympiad level and beyond. The book is constructed in hopes that the reader will gain something from not only a laundry list of formulas, but their real-world applications as well, along with their proofs and several accompanying exercises involving interdisciplinary, higher-order thought.Don't worry if you don't know all of the mathematics in this book; there will be prerequisites for each skill level, giving you a better idea of your current position, your strengths and weaknesses, and, hopefully, allowing you to set realistic goals as a math student. So, mathematical minds, we set you off!