35 LIVE: Number Theory
Ma/V/Mi/S 11:00pm–12:30am from 9/13 (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.
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 7:00pm 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.
Pruebas de diagnóstico:
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.
Remainder mod 10; definition of modular congruency; notation of a modulo b; remainders of n²; modular addition, subtraction and multiplication; remainders modulo 11; negative remainders
Explanation and motivation for divisibility rules for 3 and 9 and shortcuts for their use; sum and average of an arithmetic progression; triangular numbers; modular multiplication
Explanation and motivation for divisibility rules for 2, 4, and 8 and shortcuts for their use; permutations; divisibility by 12; sum and average of arithmetic progression; negative remainders
Remainders after dividing by 99; factors; patterns in multiples of 9 mod 1; palindromic numbers; factors of 1001 and 1111; negative remainders; remainders mod 11; arithmetic progression
Prime factorization; number of factors; sum of factors; average of factors; sum of reciprocals of factors; product of factors; factors of 111; expanding factors; sum of consecutive powers of 2; geometric series
Number of zeroes at the end of combinatorial expressions such as factorial; modular multiplication; floor function; ways to choose n objects; sum of consecutive powers of 2;
Least Common Multiple (LCM); Greatest Common Divisor (GCD); prime factorization; product of LCM and GCD; quotient of LCM and GCD; factorials
Motivation for and examples of Euclidean Algorithm for finding GCD; Fibonacci numbers; factors of 111; relatively prime numbers
Relatively prime numbers; pattern of cycling remainders; remainders of multiples of 2, 3, 4, 5, 6, 7, 8 and 9; Venn diagram; Inclusion / exclusion; Euler's Totient Function
Chinese Remainder Theorem and use with composite moduli; negative remainders; solving sets of congruences; LCM; remainders of multiples of 6 mod 5; negative remainders
Chinese Remainder Theorem with non-relatively-prime moduli; remainders of multiples of 9 mod 12; cycles of remainders of multiples of 9; LCM; reduction of systems of congruences; unsolvable congruences
Systems of three congruences; Euler's Totient Function; remainders modulo composite numbers; pairwise relatively prime numbers; Venn diagram; factoring; combinatorial counting
Factoring tricks for solving algebraic equations; area and perimeter of rectangles; number of ways to factor; equations in 1/x; impossibility of division by 0; number of integers solutions to an equation
Remainders of powers; cycles of remainders of powers; pattern of last two digits of powers of 7; remainders of powers of 7 mod 4; power towers
Multiplicative inverses with respect to a modulus; explanation and motivation for divisibility trick for 7; repeating cycles of remainders
Terminating decimals and their fraction representations; repeating periods of repeating decimals; proof of why square root of 2 is irrational; prime factorization; proof techiques and directions of logic; proof by contradiction