Lecture 1 Notes Introduction and Fundamentals of Computuer Science

Lecture 1 Notes Introduction and Fundamentals of Computuer Science

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Unformatted text preview: Lecture 1 Notes: Introduction 1 A dminist rivia Welcome to Great Ideas in Theoretical Computer Science. Please refer to the syllabus for course information. The only prerequisite for the class is “ mathematical maturity,” which means that you know your way around a proof. What is a proof? There’s a formal deFnition of proof where each statement must follow from previous statements according to speciFed rules. This is a deFnition we will study in this course, but it’s not the relevant deFnition for when you’re doing your homework. ¡or this class, a proof is an argument that can withstand all criticism from a highly ca f einated adversary. Please interrupt if anything is ever unclear; the simplest questions are often the best. If you are not excited and engaged then complain. 2 W hat is comput er science? Computer science is not gloriFed programming. Edsger Dijkstra, Turing Award winner and ex-tremely opinionated man, famously said that computer science has as much to do with computers as astronomy has to do with telescopes. We claim that computer science is a mathematical set of tools, or body of ideas, for understanding just about any system—brain, universe, living organism, or, yes, computer. Scott got into computer science as a kid because he wanted to understand video games. It was clear to him that if you could really understand video games then you could understand the entire universe. After all, what is the universe if not a video game with really, really realistic special e f ects? OK, but isn’t physics the accepted academic path to understanding the universe? Well, physi-cists have what you might call a top-down approach: you look for regularities and try to encapsulate them as general laws, and explain those laws as deeper laws. The Large Hadron Collider is sched-uled to start digging a little deeper in less than a year. Computer science you can think of as working in the opposite direction. (Maybe we’ll eventually meet the physicists half-way.) We start with the simplest possible systems, and sets of rules that we haven’t necessarily conFrmed by experiment, but which we just suppose are true, and then ask what sort of complex systems we can and cannot build. 3 St udent Calibrat ion Quest ions A quine is a program that prints itself out. Have you seen such a program before? Could you write one? Here’s a quine in English: Print the following twice, the second time in quotes. “ Print the following twice, the second time in quotes.” Perhaps the most exciting self-replicating programs are living organisms. DNA is slightly di f erent from a quine because there are mutations and also sex. Perhaps more later. Do you know that there are di f erent kinds of inFnities? In particular, there are more real numbers than there are integers, though there are the same number of integers as even integers. We’ll talk about this later in the course, seeing as it is one of the crowning achievements of human thought....
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