Combinatorics and Probability

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/combinatorics

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Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following. If we need to count something, can we do anything better than just counting all objects one by one? Do we need to create a list of all phone numbers to ensure that there are enough phone numbers for everyone? Is there a way to tell that our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics. In this course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations. One of the main `consumers’ of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop. In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students. Do you have technical problems? Write to us: coursera@hse.ru

组合和概率:计数是我们日常遇到的与数学相关的基本任务之一。这里的主要问题如下。如果我们需要数一数,我们能做些比仅一一计数所有对象更好的事情吗?我们是否需要创建所有电话号码的列表,以确保每个人都有足够的电话号码?有没有办法告诉我们算法在实现和实际运行之前的合理时间内运行?所有这些问题都通过一个称为组合数学的数学领域来解决。 在本课程中,我们讨论可以帮助回答此类问题的大多数标准组合设置。我们将特别专注于开发在现实生活和算法问题中区分这些设置的能力。这将帮助学习者实际实施新知识。除此之外,我们将讨论对算法实现很重要的递归计数技术。 组合学的主要“消费者”之一是概率论。这个领域与生活的各个方面联系在一起,一方面是日常生活中的重要概念,另一方面又是诸如统计学和机器学习之类的现代重要领域中必不可少的工具。在本课程中,我们将专注于提供有关该领域概率基础和良好直觉的工作知识。实践表明,这种直觉并不容易发展。 在本课程的最后,我们将创建一个程序,该程序可以成功玩一个棘手且非常违反直觉的骰子游戏。 作为前提条件,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),Python中的基本编程(函数,循环,递归),常识和好奇心。我们的目标受众是所有有志或计划在IT领域工作的人,从积极进取的高中生开始。 你有技术上的问题吗?写信给我们:coursera@hse.ru

课程大纲

Suppose we need to count certain objects. Can we do anything better than just list all the objects? Do we need to create a list all phone numbers to check whether there are enough phone numbers for everyone? Is there a way to tell whether our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics. In this module we will give an introduction to this field that will help us to answer basic versions of the above questions.

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课程简介

Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The ma

课程标签

离散数学 离散数学公开课 离散数学课程 数学 数学基础 计算机科学 组合 概率 组合和概率

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