Welcome to Compsci 120: Mathematics for Computer Science! We’re excited to have you in this paper, and cannot wait to show you some of the fundamental mathematics that underpins the field of computer science. This coursebook is possibly a bit different to ones you have seen in classes before. It has the following features:
• Each chapter opens up with a set of “motivating problems.” These are exercises and puzzles related to the theme of each chapter, chosen to illustrate how the mathematical content covered in this paper can be used to solve “real-world” tasks. After reading these problems, try pausing for a bit and solving them on your own before going on to the rest of the chapter! Doing so will help you understand the concepts in each section better than immediately reading through everything. (It will also help you appreciate the solutions to these puzzles when they show up later in the chapter!)
• We’ve placed large margins on the side of each page, for you to A mathematical poem, to start off write notes in. When you’re in class or reading the book at home, your margin notes: A dozen, a gross, and a score, plus three times the square root of four, divided by seven, plus five times eleven, is nine squared and not a bit more! use these margins to write down questions that come to mind, useful ideas from class, or as scratchwork when you’re trying to work out an exercise.
• Finally, we’ve placed even more exercises at the end of each chapter. Easier/more straightforward problems are labeled (-), while trickier ones are labeled with a (+). Try working on these problems to test your understanding! Some exercises are labeled (++); these are exceptionally hard and/or open problems in mathematics. We’re not expecting anyone to solve these problems; instead, we’re listing them so that you can see the kinds of tasks that you might study in a Ph.D programme. (If you do solve any of these, though, please let us know!) While solutions to these end-of-chapter problems are not present in this coursebook, your lecturers are happy to give you hints or walk you through the solutions to any of these problems in office hours or on Piazza (a discussion forum you can find on Canvas!)