We’ve got a steep climb up ahead of us. What exactly are we up against? And what will we see from the summit that will be worth all the effort to get there? An algebra is any system of mathematical objects together with operations that can be used to combine them. The word linear is related to the word line: this is because a function that is linear looks like a line when it’s plotted. Suppose I make $11.75/hour at my part-time job, and I want to figure out my take-home pay for last week’s work. Obviously, my paycheck (before taxes and what-not) will be 11.75 times the number of hours I worked. The great mathematician and computational scientist Stanislaw Ulam once quipped that dividing functions into linear and nonlinear is like dividing zoology into “elephant” and “non-elephant.” In a way it’s true, because there are certainly far more functions that don’t obey the above two properties than there are those that do. By the same token, though, there are far more pay schemes we could invent than just “a regular hourly rate.” But hourly rates come up very, very often, and when they do, there’s a lot of amazingly useful things we can do with them. Join us on our hike and you’ll see. Each chapter of this book comes equipped with an appendix showing how to carry out the various linear algebra calculations in a programming language called Python. Here’s the first one! Most readers will have done at least a little bit of computer programming before making it to this book. If you haven’t, don’t worry about it. We’re not really going to be programming per se, but rather using the Python language as a glorified calculator.