 Hello, and thank you for joining me in the world of mathematics. I am Abraham Smith, assistant professor in mathematics, statistics and computer science at UW-Stout. In this course we will step into the field called scientific computing. Scientific computing is a fascinating and powerful field placed at the intersection of all the mathematical sciences. Sometimes it is tempting to mentally separate everything we know into three distinct worlds. The first is the world of pure mathematics, where we build abstract structures and improve pristine theorems with crystal uncertainty. The second is the world of computers, where we debug algorithms, make simulations and animations, and throw around decimal approximations. And the third is the world of empirical science, where we collect noisy data about the physical universe and try to predict something, anything, by comparing it to simple statistical models. Scientific computing is where these worlds come crashing together. What good is an abstract theory if you can't use it to predict complicated phenomena? What good is computer approximation if you can't guarantee that the numerical answer is close to the desired exact result? And what good is collecting tons of data if you can't analyze it to find patterns? Together we're going to explore scientific computing from the perspective of both linear and non-linear problems. Through linear problems, we'll get a handle on why some mathematical operations you might think are very easy, like say, row reducing a matrix to solve a system of linear equations, are actually very subtle and very tricky to do accurately on a computer. But this study of inaccuracy will give us a deeper view into the theory of both computer arithmetic and matrix algebra. Once we have good ways to approximate linear problems, we can use those techniques iteratively to solve much more complicated, non-linear problems, like those that come from physics and biology and economics. Finally, we'll see that the techniques for solving linear and non-linear problems can be turned inside out, giving us very good ways to visualize and interpret actual real-world data. Our main textbook is Numerical Linear Algebra by Traffiton and Baal, published by Siam Society for Industrial and Applied Mathematics. This book is fantastic and universally admired. You should definitely get a copy and read it with pleasure. This excellent book will give us about 75% of the way through the course, but our perspective on scientific computing will be cutting edge and no book can cover it all by the time the ink has dried. Some of the results we will be discussing, like compressed sensing, led to major prizes in widespread celebrating in the past several years, and major research is still ongoing in these fields. Even better, we live in a time where the open-source culture is ubiquitous in mathematics and computer science, so where we want to move beyond the textbook, we'll be using the best resource of all, the actual code of major open-source scientific libraries. You don't have to be an expert programmer at the start, because as we look through the working code others have written, you'll be able to deconstruct and rebuild your own version piece by piece until everything is clear. So that's where we're headed, and that's what we're going to do. I guess it's time to get started.