LIVE 33: Number Theory
From 7/12 to 8/8
화ㆍ수ㆍ목ㆍ금ㆍ월 5:00pm–6:30(미국 동부 시간)
이 LIVE 강좌에는 라이브 동영상 강의 30시간과 함께(시간당 23) 이 강좌를 통해 1년간 이용할 수 있는 Loh 교수의 녹화 동영상이 포함되어 있습니다.
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.
캘린더
강조 표시된 날짜에 수업이 열립니다. 날짜를 클릭해 그날의 주제를 살펴보세요.
컬러 키:
새로운 주제 수업
숙제로 주어진 시험 토론
리뷰
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
교육과정
20개의 강좌 모임은 수업 16개(아래 1일차부터 16일차로 표시됨) 및 숙제 시험 토론 4개로 나뉩니다. 수업 4강 이후 각 시험 토론 모임이 열립니다.
1일차
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
2일차
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
3일차
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
4일차
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
5일차
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
6일차
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;
7일차
Least Common Multiple (LCM); Greatest Common Divisor (GCD); prime factorization; product of LCM and GCD; quotient of LCM and GCD; factorials
8일차
Motivation for and examples of Euclidean Algorithm for finding GCD; Fibonacci numbers; factors of 111; relatively prime numbers
9일차
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
10일차
Chinese Remainder Theorem and use with composite moduli; negative remainders; solving sets of congruences; LCM; remainders of multiples of 6 mod 5; negative remainders
11일차
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
12일차
Systems of three congruences; Euler's Totient Function; remainders modulo composite numbers; pairwise relatively prime numbers; Venn diagram; factoring; combinatorial counting
13일차
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
14일차
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
15일차
Multiplicative inverses with respect to a modulus; explanation and motivation for divisibility trick for 7; repeating cycles of remainders
16일차
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
동료 스타
ERIC ZHAN
National MATHCOUNTS competitor for Washington • 2022 USAJMO winner • Likes to swim
클릭하여 자세히 확인
LILLIAN XIA
MPFG Invite • AIME Qualifier • Enjoys playing tennis
클릭하여 자세히 확인