Combinatorics 아이콘

LIVE 50: Combinatorics

토 2:00am–3:30 from 3/11(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.

We’ve carefully designed our courses to maximize engagement. Each of our LIVE classrooms has a 1:13 staff to student ratio, with a maximum of 40 students.

* The official meeting time for this course is 9:00pm in New York.

The class time will change over the duration of this session, because your country's Daylight Savings Time adjustments differ from the target time zone of this course.

진단 시험:

이해할 수 있을까요?새로운 것을 배우게 될까요?

캘린더

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

컬러 키:

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

SrinivasArun의 프로필 사진
SRINIVAS ARUN

USA(J)MO Qualifier Since 8th Grade • 2019 National MATHCOUNTS Qualifier for Colorado • 2022 MOP (Math Olympiad Program) Qualifier • 2022 USA(J)MO Bronze Medal • 2021 ARML Perfect Score

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