Have you ever learned something that contradicted what you thought you knew? Have you ever had your teacher tell you a rule you learned before is no longer true? Have you ever felt like everything you'd ever known was a lie and math was meaningless? Okay, maybe that one is a bit extreme, but the truth is that there are many times in our mathematics careers when we are told that something we previously learned no longer holds, or worse, is a complete falsehood. Knowing this, I endeavored to create this book, a piece meant to illustrate some of the most obvious times we are led to the wrong idea about mathematical phenomena. For example, did you know that f(x)=3x+4 is not a linear function, that probability 0 does not necessarily mean impossible, or that there are different sizes of infinity? Do you think you've learned all the truths presented here, or has your math education left you with misconceptions?
This book is an interactive investigation into what mathematical lies we are told, why they are told, whether you still believe them, and what the reality actually is. At the beginning of each section, there is a warm-up activity for you to complete. Then after reading the section there is an opportunity for you to reflect on your answers in light of what you read. Chapters 1-3 are intended to be accessible to anyone proficient in high school algebra and middle school geometry and probability. The topics of chapter 4 are more advanced, but are intended to still be accessible to those who have a good understanding of calculus. The hope is that at least some of the information presented here will be new, perhaps even mind-blowing.
