180 LIVE: Number Theory
From 6/24 to 8/28
Ma/J 8:00–9:30pm (hora del Este de EE. UU.)
El curso de LIVE tiene un total de 30 horas de formación de video en vivo (~20/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 8:00pm in New York.
Pruebas de diagnóstico:
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
Comentarios
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
Brilliant-Wonderful, thought-out well explanations to questions I never thought could be so interesting! I've learned to love to find out more with this wonderful course.
Thank you so much for creating this course. I love it, and it's the best. If you don't believe me, here's a piece of evidence. On the final test of this course, I scored a 100%. This proves that this course is very effective and helps you with number theory! - Jocelyn!
Worth everything and learned a lot
Helps you learn number theory. He includes many nifty tricks that help you solve problems quickly and efficiently.
Great job
I absolutly loved this course
This course is incredible! It taught me many, many tricks that I never knew! Very helpful!
Absolutely worth everything!!
Excellent course
Great explanation
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
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
Día 2
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
Día 3
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
Día 4
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
Día 5
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
Día 6
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;
Día 7
Least Common Multiple (LCM); Greatest Common Divisor (GCD); prime factorization; product of LCM and GCD; quotient of LCM and GCD; factorials
Día 8
Motivation for and examples of Euclidean Algorithm for finding GCD; Fibonacci numbers; factors of 111; relatively prime numbers
Día 9
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
Día 10
Chinese Remainder Theorem and use with composite moduli; negative remainders; solving sets of congruences; LCM; remainders of multiples of 6 mod 5; negative remainders
Día 11
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
Día 12
Systems of three congruences; Euler's Totient Function; remainders modulo composite numbers; pairwise relatively prime numbers; Venn diagram; factoring; combinatorial counting
Día 13
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
Día 14
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
Día 15
Multiplicative inverses with respect to a modulus; explanation and motivation for divisibility trick for 7; repeating cycles of remainders
Día 16
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