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所在平台: Udemy |
课程主页: https://www.udemy.com/course/permutations-and-combinations-class-11-mathematics/
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本课程“理解置换与组合以用于人工智能”由拥有三十年教学经验的数学教师 Suman Mathews 讲授。课程旨在帮助学习者掌握置换与组合的基础知识及其在高等数学（如概率论、二项式定理、离散数学）以及 SAT 和 GRE 数学考试中的应用。 课程通过引人入胜的烘焙店的例子，生动地解释了组合的概念，特别是当选择的数量和重复出现的可能都被考虑在内时。 课程内容循序渐进，从置换的基础知识开始，涵盖所有对象都不同或不全不同的情况，并介绍基本的置换公式。之后，将学习涉及字母和数字的置换问题，以及圆周置换的计算方法，并强调了在圆周置换中邻居问题的两种不同情况。 紧接着，课程将深入讲解组合的概念，包括如何计算组合以及基本组合属性的应用。学习者将接触到需要同时运用置换和组合的混合问题，并认识到它们之间的联系。 此外，课程还包含一个关于多项选择题的环节，以检验学习者对概念的理解程度，并提供相关的公式总结。最后，课程将引导学习者掌握置换与组合的高阶解题技巧。 每道置换与组合题都是独特的，没有统一的解法，因此本课程鼓励学习者积极利用提供的例题和资源进行练习，以达到融会贯通。
Once upon a time, in a quiet town there was a bakery owned by a kind hearted baker, named Mr. White. He had three types of delicious pastries, chocolate, strawberry and vanilla. As part of his sales, he had a special box of pastries where a customer could choose how many pastries to include and which pastries.There were a few conditions:1. The customer could choose two to four pastries.2. He could select any combination of flavors including duplicates.3. The order of the pastries did not matter.How many different combinations could the customer choose? Suppose the customer chooses two pastries. Since there were three types and repetition was allowed, the customer had three choices for the first and three choices for the second.Hence, the customer had 9 possibilities. Likewise, if the customer chose three pastries, then there were twenty seven possibilities. For a box of four pastries, a customer would have 81 possibilities.So the customer had 9+27+81=117 possibilities since he could choose two or three or four pastries. Note that when it is "OR' we add. This is how, Permutations and Combinations can make a seemingly complex mathematical concept come to life.Welcome to this course on Permutations and Combinations. I am Suman Mathews, qualified and experienced teacher teaching mathematics for three decades to high school and college students. Permutations and Combinations forms an integral part of higher Mathematics. It is used extensively in Probability, Binomial Theorem and Discrete Math. Also used in SAT and GRE Quant examinations. The tricky part here is that each problem is unique.There is no one solution to all problems on Permutations and Combinations. This course will introduce you to the basics and gradually lead you forward. Make use of the solved examples and resources here.The course unfolds with a basic knowledge of Permutations. You will learn cases when the objects are all different or not all different. Learn basic formulas in Permutations here.Number of problems involving letters and digits are discussed here. Moving on, you'll learn about circular permutations and how to calculate them. You'll realise how the values change in a circular permutation where no two people have the same neighbours or different neighbours. Again, practice the problems illustrated here to gain mastery of the topic. Next, you'll learn about Combinations and how to evaluate them. Realise that while a permutation is basically an arrangement, a combination is a selection.Learn basic properties of Combinations and how to use these in problem solving. You'll come across problems which use both Permutations and Combinations and work on mixed problems. You'll realise how these are interconnected.You have a session on Multiple choice questions where you realise that each problem requires a fair level of understanding. There are also formulas at the end for you.Learn higher order problem solving techniques in Permutations.
