开始时间: 06/01/2019 持续时间: Unknown
Mathematical thinking is crucial in all areas of computer science: algorithms, bioinformatics, computer graphics, data science, machine learning, etc. In this course, we will learn the most important tools used in discrete mathematics: induction, recursion, logic, invariants, examples, optimality. We will use these tools to answer typical programming questions like: How can we be certain a solution exists? Am I sure my program computes the optimal answer? Do each of these objects meet the given requirements? In the course, we use a try-this-before-we-explain-everything approach: you will be solving many interactive (and mobile friendly) puzzles that were carefully designed to allow you to invent many of the important ideas and concepts yourself. Prerequisites: 1. We assume only basic math (e.g., we expect you to know what is a square or how to add fractions), common sense and curiosity. 2. Basic programming knowledge is necessary as some quizzes require programming in Python.
What is a proof? Why do we care about proofs? Are the boring long tedious arguments usually known as `mathematical proofs' really needed outside the tiny circle of useless theoreticians that pray something called `mathematical rigor'? In this course we will try to show that proofs can be simple, elegant, convincing, useful and (don't laugh) exciting. Later we will try to show different proof techniques and tools, but first of all we should break the barrier and see that yes, one can understand a proof and one can enjoy the proof. We start with simple puzzles where one small remark can disclose "what really happens there" and then the proof becomes almost obvious.
There is a perceived barrier to mathematics: proofs. In this course we will try to convince you that this barrier is more frightening than prohibitive: most proofs are easy to understand if explained correctly, and often they are even fun.