组合工具
系统介绍数学中最有趣的数学科目之一——组合学。虽然组合学在中学标准课程中不进行教授，但却经常出现在数学竞赛的难题中。该课程难度范围覆盖MATHCOUNTS、AMC 8 和 AMC 10、AMC 12、AIME。
想了解我们独具一格的教学方法？欢迎您访问我们的主页，看看我们是如何打破线上数学课的固定框架的吧！
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这门课适合我吗？
你是否正在上从6年级数学到微积分学前课的数学课程，并且已经了解综合入门课程中的内容？如果是的话，你已经具备了足够的能力来加入这门课。这门课将带你高效学习如何理解学校课本里并不教授，但却极具挑战性的组合学概念。
不知道课程是否合适？来挑战一下能力水平测试吧！
课程结构
每个模块的课程均包含20节LIVE课程，分为16节【日挑战】课程和4节【单元考核测验】复习课程（学生需要在复习课前进入配套的Pre-Recorded课程完成测验）。每节课程都将由2位 Stars 共同授课。在该模块的学习中，我们将讨论超过150个数学问题。
【日挑战课程】每节课中，学生都会学习解决全新的数学问题，老师们将通过启发式的教学引导和鼓励学生开创自己的解题方法。我们的LIVE课堂赞赏学生们提出自己的想法，鼓励每个学生和全班同学一起集思广益，构建各种不同的解题方法，更积极地参与数学发现。
【单元考核测验】包含20道数学问题，其中10题在正常难度范围内，而另外10题则非常具有挑战性。
学生评价
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
This is definitely one of the best math courses available. Prof. Loh explains the topics in a detailed way, and makes it fun.
This is an awesome course.
The video explanations are crystal clear and the challenges are fun. 5/5 would do again.
I think that this course was an excellent tool to “skim the surface” in the world of Combinatorics!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
such big brain
The best course you can get in the world great explnation questions and tests and I can repeat again it‘s wonderful
This is sooooo much easier to understand than some of the other classes, plus, its explanations are VERY detailed
AMAZING!
It tells every way to solve a problem and for problems, you get a turn to solve and get hints!
课程大纲
第1课
排列、求限制条件下的事件总数、对称计数、树状图表示结果、分类讨论、数物体的对数、重复计数修正
第2课
维恩图、组合、子集数、计数规律、2的连续次幂之和、乘法原理、排除法计数、求有限制条件下的事件总数、重复计数更正
第3课
维恩图的变化、并集和交集、集合符号、容斥原理、质因数、计数方法在数论中的应用、整除规则
第4课
网格计数、分类讨论、计数规律、旋转和翻转、轴对称和中心对称、阶乘、排列与组合、重复计数修正
第5课
含有重复元素的排列、乘法原理、阶乘、重复计数修正、分类讨论、二项式系数、“选择”符号、轴对称和中心对称
第6课
二项式系数、帕斯卡三⻆形、二项式系数的对称性、帕斯卡三⻆形规律、帕斯卡恒等式、二项式系数的比较、“球棒”定理、组合、分类讨论
第7课
二项式定理、帕斯卡三⻆,帕斯卡三⻆形的总行数,与2的幂的联系、二项式系数的对称性、子集数、11的幂、二项式定理的应用
第8课
分类讨论、资源分配问题和安排、排除法计数、含有重复元素的排列、二项式系数的应用
第9课
网格路径、图形使用、含有重复元素的排列、阶乘、二项式系数、排除法计数、问题的简化、对称、平方差
第10课
铺瓷砖问题、递归数列、含有重复元素的排列、数列中an 的符号、二项式系数和符号的选择、分类讨论、斐波那契数列
第11课
重复计数的修正、计数规律、案例分析、特殊条件下的事件总和、多次递归、递归和“铺瓷砖”问题的应用、递归公式的一般形式
第12课
图论基础、着色问题、节点,顶点和图的定义、分类讨论、对称、抽屉原理、四色定理、排除法计数、排列、树形图
第13课
序列的计数、分类讨论、三⻆数及其与二项式系数的关系、“球棒”定理、帕斯卡三⻆、划分n个物体(星形和条形)的方法应用、子集数
第14课
会议问题和结对方式、重复计数的修正、排列、阶乘、乘法原理、双阶乘符号、“铺瓷砖问题”在应用题中的应用
第15课
计数技巧在生活问题中的应用、最短路径问题、图示分析不同情况、广度优先搜索技巧
第16课
多面体的顶点、边、和面、多面体欧拉公式和起源、重复计数更正、柏拉图立体（正多面体）、星状十二面体
报名课程
每位报名LIVE在线直播课的学生都将同时享有对应的Pre-Recorded自学录播课程一年使用权，无需额外购买。LIVE直播课经过罗教授和教学团队精心设计的，通过前所未有的引人入胜的教学方式、极为丰富的课堂交互体验，让学生在趣味学习中爱上挑战和思考。 以下所有直播课显示时间均为您的当地时间（美国将于2023年3月12日星期日进入夏令时，请其他国家和地区的学生注意课程时间调整）。
如果你有强大的自驱力可以进行自主学习，或者想比LIVE课程安排更快地完成一个模块的学习，也欢迎你选择我们的自学录播课程。录播课包含了所有罗教授关于该模块的教学视频（没有直播课堂），在过去3年中也有数千名来自世界各地的同学参与学习。