• 帕多瓦大学

组合学:计算策略和方法

Explore the wonderful world of combinatorics with this course exploring simple and efficient ways to count.

621参加此课程

在左边是威尼斯市的地图,右边是对地图的组合解释。

组合学:计算策略和方法

621参加此课程

  • 4周

  • 6个小时per week

  • Digital certificate when eligible

  • 中间的等级

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参见组合学简单,如何避免计算原理中的错误

组合学是数学领域,主要与计数有关。组合问题在纯数学的许多领域中出现,特别是代数,概率理论,拓扑和几何形状。

On this free online combinatorics course, you’ll discover a simple and efficient method to translate a combinatorial problem into counting the elements of a reference mathematical structure.

您将学习基本的计数原则,并能够解释其滥用的最常见错误。最终,您会发现Combinatorics并不像看起来那么困难。

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您可以随时注册。但是,如果您想利用教育工作者和您的导师的反馈,则可以在接下来的时期内这样做:

6月1日至7月15日

December 1 - January 15

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跳到0分3秒Hello, my name’s Albert. Hello, I’m Carlo. We both are mathematicians of the University of Padua, which is a very closer to Venice. Actually, we are both Venetians. Here are some problems that we are going to consider in this MOOC. How many hands of five cards can be dealt with a deck of 52? And how many have exactly three red cards? like that one, for instance. Or very famous birthday problem, which is the probability that in the class of 24 students, the least two of them share the same birthday? and there’s another one. Then tourists lift their passport at the desk. Afterwards, the clerk gives them back randomly. What is the probability that nobody receives is on passport?

跳到0 minutes and 56 seconds您是否知道此值与Euler号码严格相关?真正的Carlo另一个问题是计算序列的毁灭。毁灭是一种订购序列元素的完整新方法。例如,例如,我们城市岛屿威尼斯的岛屿。我们将向您展示如何解决此类问题。实际上,它们都与组合学有关。也就是说,计算集合的元素数量。听起来很容易。但是通常,这种类型的计算发生错误。真正的阿尔贝托。 But after years of teaching this topic, we developed a full proof method. Yes. We translate the problem, say, in counting the number of elements of a precise mathematical structure.

跳到2分6秒And then it’s enough to apply a specific principle and it’s done. Simple! Let us start, follow us and learn how to count.

What topics will you cover?

  • 将计数问题转换为精确的数学模型
  • 计算序列和集合等基本组合对象
  • 计算字符的应用,序列的扰动(帽子问题)
  • 计算卡片和理解惊人的魔术
  • Basic probabilities (birthday problem)
  • 代数工具允许解决微妙的组合问题

您想何时开始?

立即开始并加入全球学习者教室。如果课程尚未开始,您将看到下面列出的未来日期。

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在本课程中学习

On every step of the course you can meet other learners, share your ideas and join in with active discussions in the comments.

What will you achieve?

在课程结束时,您将能够...

  • Apply the principles of combinatorics to solve the basic combinatorial problems
  • Model some real life counting problems into that of counting precise mathematical structures
  • 确定除组合问题以外的数学结构:序列,集合,共享,组成,分区,毁灭。
  • Identify the principle to face a combinatorial problem: bijiection, multiplication, division
  • Calculate the probability of an event when the sample space is composed by equiprobable elementary events
  • Calculate the number of possible outcomes of an aleatory experiment
  • Calculate the number of sequences of prescribed length, with or without repetitions, from a given alphabet
  • Calculate the number of sets of given cardinality
  • 计算在规定的子集数量中,给定集的分区数
  • Calculate the number of permutations of a sequence without repetitions
  • 计算给定数量的编号框中可区分/无法区分的对象的分布数(可能为空)
  • 计算给定数量的数量的非空箱中可区分/无法区分的对象的分布数

谁是课程?

This course is ideal for anyone interested in mathematical problems, with a basic background in precalculus. It would be useful for anyone wanting to study or work in mathematics, or anyone who wants to develope their critical thinking and problem-solving skills.

您会和谁一起学?

我是帕多瓦大学代数的教授,我在科学与工程学院任教。我非常喜欢数学和古典音乐。

我是帕多瓦大学数学分析教授。在我的兴趣中:魔术,探戈,摄影,创新教学,技术和电子学习。

谁开发了课程?

帕多瓦大学

帕多瓦大学是欧洲最古老,最负盛名的学习席位之一。它旨在为学生提供专业培训和扎实的文化背景。

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