30 LIVE: Combinatorics
Ma/Mi/J/V/L 5:00–6:30pm de 7/12 (hora del Este de EE. UU.)
El curso de LIVE tiene un total de 30 horas de formación de video en vivo (~17/hora), más 1 año de acceso a los videos pregrabados del curso del Prof. Loh.
Calendario
Las clases se darán en las fechas resaltadas. Haz clic en cualquier fecha para ver los temas del día.
Clave de color:
Lección de un tema nuevo
Analiza el examen asignado como tarea
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
Leader of state-wide math competition program • Placed top 6 in national math competitions • Perfect score on USACO bronze
Haz clic para más
JESSIE WANG
Attended MATHCOUNTS State (TX) twice • AIME qualifier since 7th grade • Enjoys singing in school choir, playing with her dog
Haz clic para más