 #### LIVE 22: Combinatorics

화ㆍ목ㆍ일20:00–21:30시작7월5일(미국 동부 시간)

등록 519달러전체 강좌 정보

이 LIVE 강좌에는 라이브 동영상 강의 30시간과 함께(시간당 17) 이 강좌를 통해 1년간 이용할 수 있는 Loh 교수의 녹화 동영상이 포함되어 있습니다.

### 캘린더

강조 표시된 날짜에 수업이 열립니다. 날짜를 클릭해 그날의 주제를 살펴보세요.

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새로운 주제 수업

숙제로 주어진 시험 토론

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### 교육과정

20개의 강좌 모임은 수업 16개(아래 1일차부터 16일차로 표시됨) 및 숙제 시험 토론 4개로 나뉩니다. 수업 4강 이후 각 시험 토론 모임이 열립니다.

1일차

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

2일차

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

3일차

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

4일차

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

5일차

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

6일차

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

7일차

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

8일차

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

9일차

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

10일차

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

11일차

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

12일차

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

13일차

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

14일차

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

15일차

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

16일차

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

### 동료 스타 ###### ALON RAGOLER

National MATHCOUNTS competitor for Washington • Perfect score on AMC 8 • Enjoys web development, playing instruments (piano + snare drum)

클릭하여 자세히 확인 ###### ANGELA GUO

Placed 2nd in Illinois State MATHCOUNTS Countdown Round • MPFG invitee • USESO camper, enjoys kayaking, playing viola, making videos

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