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The world changes, and sciences change with it, but the study of mathematics steps outside this transient nature of the world, and does not demand change. I think many textbooks today are written with the idea of adapting and transforming mathematics to suit the changing world, and I think that is a mistake. Rather, let the changing world glimpse something that not only does not change, but refuses to do so, and has since the beginning.  \nThe concept of the inverse can be seen in day-to-day life. A student unlocks his car and takes off on an errand. When he arrives, he exits the car and locks it so no stranger will enter his personal space. He unlocks, and then he locks. He does, and then he undoes. If you think about it, there are several actions of doing and undoing that happen when a person drives a car.  \nMuch of mathematics, if not all of it, has this at its core, the concept of doing and undoing. For example, we are told that just three more minutes and we will have been walking for an hour. We quickly realize that we have been walking for 57 minutes. Mentally we knew that the unknown, how long we had been walking, could be uncovered by subtracting 3 from 60, the number of minutes in an hour. We knew that the “addition” of 3, which happened with the statement that“three more minutes and we have walked for an hour” needed to be undone, via subtraction, to find how long we had been walking. Subtraction is the inverse of addition. This concept, though likely not these words, has been understood by just about any person since their youth.  \n1  \nWith each example, an operation is accomplished. Later in time, we undo this operation with an inverse operation.  \nIn arithmetic, we first learn to add numbers. We then introduce the concept of subtraction or taking away numbers. This is an inverse operation of the addition operation. In fact, it is so necessary for us tobe able to subtract that we find we cannot do without it. In short, to accomplish mathematics at all, any operation that we introduce must carry with it an inverse so that we can undo that operation. Multiplication eventually demands that we be able to divide. Squaring a number demands eventually that we can take the square root of a number. Finding the tangent of an angle eventually demands that we can start with the tangent value and determine the angle.  \nIt is with this fundamental concept in mind that this book is written. With every step, every topic, I hope to always keep in the back of the mind what is happening with the particular topic, and how the inverse applies to that topic.  \nYou will soon notice that I have written this book as if I was teaching you in class, or privately tutoring you. Even if you have picked up this book and are reading it as a hobby, and not as a paying student in a formal classroom situation (and if this is true you are my favorite kind of mathematician!), I want you to approach the learning as if you were relaxed in my living room, enjoying a beer or a cup of coffee, but listening intently to what I’m telling you. When you get to something that appears difficult to you, then you should pause, and practice. That’s where the work of learning happens, in the practicing of the art. Get good at whatever you stumbled on, and then continue.  \nRecitations  \nThere are phrases and slogans within this book that are worth saying so much that they should come to mind nearly instantly when you are confronted with them. Here are a few:  \n1. “The slot is what is inside the parentheses.”  \n2. “f(x) reads‘f ofx’.  \n2  \n3. “f is telling whatever is in the slot what to do.”  \n4. “Slope is rise over run.”  \n5. “f(x) means that f is telling x what to do.”  \n6. “y is f(x), and f(x) is the height of the function.”  \n7. “The zero of a function is where it crosses the x-axis.”  \n8. “The zero of a function is where in the domain the function valu","cbCait1JmEmhXw8I","https://ap.wps.com/l/cbCait1JmEmhXw8I","pdf",56007444,335,"English","# Forward\n## Recitations\n# Dedication","[{\"question\":\"What central idea does the book use to explain mathematics?\",\"answer\":\"The book centers on the concept of doing and undoing, where each operation has an inverse that allows you to reverse it.\"},{\"question\":\"How does the book connect inverse operations to everyday life?\",\"answer\":\"It uses examples like unlocking and locking a car and describes how the actions of doing and undoing mirror mathematical inverse relationships.\"},{\"question\":\"What do the recitations in the book focus on?\",\"answer\":\"The recitations provide quick-to-remember statements about function concepts, including how to interpret f(x), slope, zeros of functions, and domain/range questions.\"}]","College Algebra - An Inverse Approach - Forward - Recitations | PDF",1792132876,844]