#### Combinatorics

A systematic introduction to one of the most interesting math subjects which is not taught in the standard school curriculum, but which often appears in hard problems on math contests. Covers concepts in MATHCOUNTS, AMC 8, AMC 10, AMC 12, and AIME.

Si aún no conoces nuestro método revolucionario de enseñanza, visit our home page first, para **pulverizar tus expectativas** sobre cómo son las clases de Matemáticas en línea.

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### ¿Para quién es este curso?

Are you taking any math class from 6th Grade Math through Pre-Calculus, and already know the content in our Introduction class? If so, then you are already ready to understand this course. It will efficiently teach you the challenging concepts in Combinatorics which are not taught in regular school curriculum.

Pruebas de diagnóstico:

### Estructura del curso

Este curso contiene 20 videos en vivo de LIVE de 1 hora. 16 son lecciones y 4 son análisis de examen donde se comentan los 4 exámenes de práctica de 1 hora del curso (tarea). Dos de nuestras Stars enseñan la clase conjuntamente. En total, hay más de 150 problemas.

Cada lección contiene distintos problemas diseñados para que sean desconocidos para ti, para inspirarte a imaginar tus propias soluciones. En el formato de clase de video en vivo de LIVE, tu propones ideas y pensamos juntos para inventar varias soluciones alternativas con las ideas propuestas en clase. Así participas activamente en el descubrimiento de las matemáticas.

Cada examen de práctica contiene 20 problemas. La mitad son de dificultad media y la otra mitad son más complejos.

### Comentarios

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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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

### Plan de estudios

**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

### Inscribirse

Este curso puede ser en vivo o a tu propio ritmo. Es más recomendable seguir el formato en vivo, ya que está diseñado para ser tan envolvente que los estudiantes amarán el desafío. Nunca existió nada así. Todos los horarios están en la zona horaria del Este de EE. UU. y se respetará el cambio de hora de verano de EE. UU. el domingo 6 de noviembre.

Los estudiantes que no puedan ajustarse a nuestro horario, o que ya tengan la motivación, tienen la versión a tu propio ritmo con toda la enseñanza del Prof. Loh sobre el tema. Inscríbete y elige el formato de tu preferencia: