LIVE | Lección 30: Combinatorics

30 LIVE: Combinatorics

From 7/12 to 8/8

Ma/Mi/J/V/L 5:00–6:30pm (hora del Este de EE. UU.)

inscribirse Todos los detalles del curso

El curso de LIVE tiene un total de 30 horas de formación de video en vivo (~23/hora), más 1 año de acceso a los videos pregrabados del curso del Prof. Loh.

We’ve carefully designed our courses to maximize engagement. Each of our LIVE classrooms has at least one staff member for every 7 students. The typical class size is around 20–30 students.

* The official meeting time for this course is 5:00pm in New York.

Pruebas de diagnóstico:

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Calendario

Las clases se darán en las fechas resaltadas. Haz clic en cualquier fecha para ver los temas del día.

Clave de color:

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Analiza el examen asignado como tarea

Jul 2022

Ago 2022

Comentarios

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

I have high respect for Po-Shen, and was hoping for a while to get a first-hand view of this approach to online classes. [My daughter] didn't really let me observe too much, but she did confirm that this class was better than any other online classes she's had, and better than some in-person classes too. That's very impressive. Great job, everyone involved!

Thank you very much for explaining [my son's learning situation] in detail… I asked him about this course and he expressed that he was very interested and enjoyed learning this course. The school had a test for the most recent class, so I watched the replay in the afternoon. I think he gained something from this course. Thank you teacher!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

I fall asleep to prof. loh music every night and listen to his ted talk every night

We appreciate how much [our son] is learning and growing in this class. Thank you for making the world a better place through math and kindness!

[My daughter] enjoyed really much all the sessions she attended, thank you for the great teaching and animation!

u guys are my favorite pair of teachers

Tiring casework that is simplified by combinatorics class

Thanks so much for the detailed class participation summary! It is very helpful! [My daughter] said the class is very useful and more interactive activities than other virtual class she had before!

Plan de estudios

Los 20 encuentros del curso se dividen en 16 lecciones (llamadas Día 1 hasta Día 16) y 4 horas para analizar los exámenes de tarea. Cada encuentro para analizar un examen es luego de 4 lecciones.

Día 1

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

Día 2

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

Día 3

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

Día 4

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

Día 5

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

Día 6

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

Día 7

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

Día 8

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

Día 9

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

Día 10

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

Día 11

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

Día 12

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

Día 13

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

Día 14

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

Día 15

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

Día 16

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

Co-Estrellas

JESSE BRODTMAN

Harvard Class of 2028 • National President of Math Honor Society • AIME Qualifier • Placed top 4 in national math competitions • Perfect score on APCSA

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JESSIE WANG

USAJMO Qualifier • MPFG Qualifier • Attended MATHCOUNTS State (TX) twice • Enjoys watching hockey

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Poliza De Reembolso

Las solicitudes de reembolso no se aceptarán después de la tercera sesión del estudiante de LIVE; Cantidad devuelta: 90% de reembolso en el método original de pago o 100% de reembolso en créditos para cursos.