Mathematical Thinking in Computer Science

开始时间: 08/01/2020 持续时间: Unknown

所在平台: Coursera

课程类别: 计算机科学

大学或机构: CourseraNew

   

课程主页: https://www.coursera.org/learn/what-is-a-proof

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课程详情

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. Do you have technical problems? Write to us: coursera@hse.ru

计算机科学中的数学思维:数学思维在计算机科学的所有领域都至关重要:算法,生物信息学,计算机图形学,数据科学,机器学习等。在本课程中,我们将学习离散数学中最重要的工具:归纳,递归,逻辑,不变式,示例,最优性。我们将使用这些工具来回答典型的编程问题,例如:如何确定解决方案的存在?我确定我的程序可以计算出最佳答案吗?这些对象是否都满足给定的要求? 在此过程中,我们将尝试所有方法,然后再尝试:您将解决许多交互式(和移动友好)难题,这些难题经过精心设计,可让您自己发明许多重要的想法和概念。 先决条件: 1.我们仅假设基本数学(例如,我们希望您知道什么是平方或如何添加分数),常识和好奇心。 2.基本的编程知识是必要的,因为某些测验要求使用Python进行编程。 你有技术上的问题吗?写信给我们:coursera@hse.ru

课程大纲

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.

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课程简介

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.

课程标签

数学基础 离散数学 计算机科学 离散数学课程 离散数学公开课 数学 课程标签 证明 什么是证明

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