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？visit our home page first，来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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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。