组合工具图标

LIVE 50: 组合工具

3月11日起,每周六上午2:00–3:30 (您所在地当地时间)

报名课程 $519课程详细介绍

该模块直播课总计30小时,课时费约为(~$17/小时)。报名直播课将同时享受该模块对应录播课程(Pre-Recorded Course)一年有效,无限次回看。

经过罗教授和课程团队反复调整,我们选择以不低于1:13的师生比进行授课。老师们将用各种方式鼓励孩子们发言、提问和思考,最大限度地提高孩子们的课堂参与度和积极性。每个班次不超过40名学生。

* 该班次直播课上课标准时间为下午9:00,纽约时间。

由于您所在国家的夏令时调整与本课程大部分学生所在地的时区不同,因此您的上课时间将在本课程期间发生变化,请注意调整您的课程安排。

选择课程前,来挑战一下能力水平测试吧!

这门课会太简单吗?(基础能力测试)这门课会难度太大吗?(分级测试)

课程日历

上课日由彩色图例标识。点击任意上课日了解当天课程内容

图例

16节日挑战课程,每节课通过不同的数学问题学习新的知识内容

4节周挑战复习课程,集中解决周挑战测试中遇到的问题,学生需要在复习课程前进入Pre-Recorded课程完成周挑战测验

2023年3月
1
2
3
4
5
6
7
8
9
10
12
13
14
15
16
17
19
20
21
22
23
24
26
27
28
29
30
31
2023年4月
2
3
4
5
6
7
9
10
11
12
13
14
16
17
18
19
20
21
23
24
25
26
27
28
2023年5月
1
2
3
4
5
7
8
9
10
11
12
14
15
16
17
18
19
21
22
23
24
25
26
28
29
30
31
2023年6月
1
2
3
4
5
6
7
8
9
11
12
13
14
15
16
18
19
20
21
22
23
25
26
27
28
29
30
2023年7月
2
3
4
5
6
7
9
10
11
12
13
14
16
17
18
19
20
21
23
24
25
26
27
28
30
31

课程大纲

LIVE在线直播课程每个模块包含16次日挑战Session(第1课到第16课)+ 4次周挑战复习课(Weekly Challenge 1到4)共20节课程。每四节日挑战Session结束后将有一次周挑战复习课,学生需要在复习课前进入Pre-Recorded课程完成周挑战测验。

第1课

Permutations; counting with restrictions; counting with symmetry; tree diagram for representing outcomes; casework; counting pairs of objects; correction for overcounting

第2课

Venn diagram; combinations; number of subsets; patterns in counting; sum of consecutive powers of 2; multiplication principle; complementary counting; counting lists of numbers with restrictions; overlapping groups

第3课

Variation on Venn diagram; union and intersection of sets; set notation; inclusion-exclusion principle; prime factors; application of counting techniques to Number Theory; divisibility

第4课

Counting on a grid; casework; patterns in counting; rotation and reflection; rotational symmetry and reflective symmetry; factorials; permutations and combinations; correcting for overcounting

第5课

Permutations with repeated elements; multiplication principle; factorials; correction for overcounting; casework; binomial coefficients; "choose" notation; rotational and reflective symmetry

第6课

Binomial coefficients; Pascal's triangle; symmetry of binomial coefficients; patterns in Pascal's triangle; Pascal's identity; comparing binomial coefficients; hockey stick identity; combinations; casework

第7课

Binomial thm; Pascal's triangle, row sum of and relation to powers of 2; symmetry of binomial coefficients; number of subsets; powers of 11; applications of Binomial thm

第8课

Casework; allocation-of-resource problems and arrangements; complementary counting; permutations with repeated elements; application of binomial coefficients

第9课

Paths on a grid; using diagrams; permutations with repeated elements; factorials; binomial coefficients; complementary counting; reduction of a problem into subproblems; symmetry; difference of squares

第10课

Tiling problems; recursive sequences; permutations with repeated elements; aₙ notation for elements of a sequence; binomial coefficients and choose notation; case analysis; Fibonacci sequences

第11课

Correction for overcounting; patterns in counting; case analysis; counting with restrictions; multiple recursions; applications to recursion and tiling problems; general form of a recursive formula

第12课

Graph theory basics; coloring problems; node, vertex, and graph; case analysis; symmetry; pigeonhole principle; four-color theorem; complementary counting; permutations; tree diagrams

第13课

Counting ordered lists; case analysis; triangular numbers and their relationship to binomial coefficients; hockey stick identity; Pascal's triangle; ways to partition N objects (stars and bars); number of subsets

第14课

Committee-type problems and ways to form pairs; correction for overcounting; permutations; factorials; multiplication principle; double factorial notation; applications of tiling techniques to word problems

第15课

Application of counting techniques to word problems; shortest path problems; representing states using diagrams; breadth-first search technique

第16课

Polyhedra vertices, edges and faces; Euler's polyhedral formula and motivation for; correction for overcounting; Platonic solids; stellated dodecahedron

启明星助教老师

Karthik Vedula 的头像
KARTHIK VEDULA

入选MATHCOUNTS全国赛Countdown Round • 2022年入选MOP(美国数学奥林匹克夏令营) • 2022年USAMO(美国数学奥林匹克)银牌获得者 • HMMT Invitational Competition数学邀请赛前十名

点击查看更多

Srinivas Arun 的头像
SRINIVAS ARUN

八年级即入选USAJMO(美国青年数学奥林匹克)资格赛 • 2019年代表科罗拉多州参加MATHCOUNTS全国赛 • 2021年ARML数学竞赛满分获得者 • 2022年入选MOP(美国数学奥林匹克夏令营) • 2022年USAMO(美国数学奥林匹克)铜牌获得者

点击查看更多