This course will cover selected topics in applied mathematics, from a pure mathematical perspective. In other words, it will focus on material with important real-world applications (ranging from signal processing to statistics to numerical analysis to cryptography), but it will emphasize connections with pure mathematics and how natural and beautiful the results are. Most of the topics will have a computational angle to them, but we'll cover many diverse areas. No special background will be required beyond a general familiarity with basic analysis, algebra, and geometry.