So you are a computer science (CS) major and you are sitting down to see what this book is about. It has been assigned, the course is required, you have no choice. Still you chose your institution, your major. Maybe your instructor made a good choice. Let's hope so.

Okay, you are not a computer science major, perhaps not even a student, but you have picked up this book. Maybe the title intrigued you. Will you be able to read it, to learn from it? We think so. We will try to interest you too. Or you are teaching a course that might use this book, maybe in discrete math, maybe including logics or formal language or both. If you want your CS students to see the applicability of mathematical reasoning to their own field or your math students to see the usefulness of their field outside itself, it is your students whom we have in mind.

If you are a CS major, you have already noticed that this course is different from the others you have taken so far. It is not an introduction to computing, programming, problem solving, or data structures. No, this book is about something called models-models of language and knowledge. It is also about formal methods.

You know something about models if you have built or seen a model airplane. In Kitty Hawk, North Carolina, you can see the wind tunnel that the Wright brothers built to test the lift capabilities of various wing shapes. A model can help us simplify and think more clearly about a complex problem (powered flight) by selecting a part (the wing) and focusing on some aspect of it (its aerodynamics). The other, temporarily ignored parts and aspects must ultimately be addressed, of course, if the original problem is to be solved.

The models in this book are simplifications too, but not of material objects like airplanes. For computer scientists, the objects of study lie mainly in the world of symbols. In this book, it is computer software, and especially the programming languages in which that software is written, from which we draw our models and to which we apply them.