Who Should Take This Course
This course is for you if you are looking for a fun, challenging and efficient introduction to Number Theory, a relatively obscure but surprisingly useful subject that will help you not only with solving familiar problems, but the unfamiliar as well.
To take this course, students should have a solid background in Algebra (or have completed our Module 4: Algebra Tools course). A highlymotivated student who has just completed Algebra 1 will find this course challenging, but manageable with effort. A student who is currently doing well in Geometry or Algebra II will learn a lot from this course and discover some interesting facets of math that they had never realized before. Still not sure if this is the right course? Feel free to contact us at courseconsulting@poshenloh.com to discuss.
Syllabus

02
Day 1 Challenge: Modular Arithmetic
Show Content Day 1: Something to Think About FREE PREVIEW
 Day 1: Challenge Explanation (1 of 7) FREE PREVIEW
 Day 1: Challenge Explanation (2 of 7) FREE PREVIEW
 Day 1: Challenge Explanation (3 of 7) FREE PREVIEW
 Day 1: Challenge Explanation (4 of 7) FREE PREVIEW
 Day 1: Challenge Explanation (5 of 7) FREE PREVIEW
 Day 1: Challenge Explanation (6 of 7)
 Day 1: Challenge Explanation (7 of 7)
 Day 1: Your Turn
 Day 1: Your Turn Explanation (1 of 2)
 Day 1: Your Turn Explanation (2 of 2)

03
Day 2 Challenge: Remainders Modulo 3 and 9
Show Content Day 2: Something to Think About
 Day 2: Challenge Explanation (1 of 4)
 Day 2: Challenge Explanation (2 of 4)
 Day 2: Challenge Explanation (3 of 4)
 Day 2: Challenge Explanation (4 of 4)
 Day 2: Your Turn
 Day 2: Your Turn Explanation (1 of 3)
 Day 2: Your Turn Explanation (2 of 3)
 Day 2: Your Turn Explanation (3 of 3)

04
Day 3 Challenge: Remainders Modulo 2, 4, and 8
Show Content Day 3: Something to Think About
 Day 3: Challenge Explanation (1 of 4)
 Day 3: Challenge Explanation (2 of 4)
 Day 3: Challenge Explanation (3 of 4)
 Day 3: Challenge Explanation (4 of 4)
 Day 3: Your Turn
 Day 3: Your Turn Explanation (1 of 4)
 Day 3: Your Turn Explanation (2 of 4)
 Day 3: Your Turn Explanation (3 of 4)
 Day 3: Your Turn Explanation (4 of 4)

05
Day 4 Challenge: Another Modulus
Show Content Day 4: Something to Think About
 Day 4: Challenge Explanation (1 of 5)
 Day 4: Challenge Explanation (2 of 5)
 Day 4: Challenge Explanation (3 of 5)
 Day 4: Challenge Explanation (4 of 5)
 Day 4: Challenge Explanation (5 of 5)
 Day 4: Your Turn
 Day 4: Your Turn Explanation (1 of 2)
 Day 4: Your Turn Explanation (2 of 2)

06
Week 1 Challenge
Show Content Week 1 Challenge: Try Your New Skills

07
What's Next
Show Content Week 1: Help Us Learn More About Your Learning Experience

08
Day 5 Challenge: Factors
Show Content Day 5: Something to Think About
 Day 5: Challenge Explanation (1 of 3)
 Day 5: Challenge Explanation (2 of 3)
 Day 5: Challenge Explanation (3 of 3)
 Day 5: Your Turn
 Day 5: Your Turn Explanation (1 of 4)
 Day 5: Your Turn Explanation (2 of 4)
 Day 5: Your Turn Explanation (3 of 4)
 Day 5: Your Turn Explanation (4 of 4)

09
Day 6 Challenge: Trailing Zeroes
Show Content Day 6: Something to Think About
 Day 6: Challenge Explanation (1 of 4)
 Day 6: Challenge Explanation (2 of 4)
 Day 6: Challenge Explanation (3 of 4)
 Day 6: Challenge Explanation (4 of 4)
 Day 6: Your Turn
 Day 6: Your Turn Explanation (1 of 3)
 Day 6: Your Turn Explanation (2 of 3)
 Day 6: Your Turn Explanation (3 of 3)

10
Day 7 Challenge: GCD and LCM
Show Content Day 7: Something to Think About
 Day 7: Challenge Explanation (1 of 4)
 Day 7: Challenge Explanation (2 of 4)
 Day 7: Challenge Explanation (3 of 4)
 Day 7: Challenge Explanation (4 of 4)
 Day 7: Your Turn
 Day 7: Your Turn Explanation (1 of 3)
 Day 7: Your Turn Explanation (2 of 3)
 Day 7: Your Turn Explanation (3 of 3)

11
Day 8 Challenge: Euclidean Algorithm
Show Content Day 8: Challenge
 Day 8: Challenge Explanation (1 of 5)
 Day 8: Challenge Explanation (2 of 5)
 Day 8: Challenge Explanation (3 of 5)
 Day 8: Challenge Explanation (4 of 5)
 Day 8: Challenge Explanation (5 of 5)
 Day 8: Your Turn
 Day 8: Your Turn Explanation (1 of 2)
 Day 8: Your Turn Explanation (2 of 2)

12
Week 2 Challenge
Show Content Week 2 Challenge: Try Your New Skills

13
What's Next
Show Content Week 2: Help Us Learn More About Your Learning Experience

14
Day 9 Challenge: Repeating Patterns
Show Content Day 9: Challenge
 Day 9: Challenge Explanation (1 of 5)
 Day 9: Challenge Explanation (2 of 5)
 Day 9: Challenge Explanation (3 of 5)
 Day 9: Challenge Explanation (4 of 5)
 Day 9: Your Turn
 Day 9: Your Turn Explanation (1 of 5)
 Day 9: Your Turn Explanation (2 of 5)
 Day 9: Your Turn Explanation (3 of 5)
 Day 9: Your Turn Explanation (4 of 5)
 Day 9: Your Turn Explanation (5 of 5)

15
Day 10 Challenge: Chinese Remainder Theorem
Show Content Day 10: Something to Think About
 Day 10: Challenge Explanation (1 of 7)
 Day 10: Challenge Explanation (2 of 7)
 Day 10: Challenge Explanation (3 of 7)
 Day 10: Challenge Explanation (4 of 7)
 Day 10: Challenge Explanation (5 of 7)
 Day 10: Challenge Explanation (6 of 7)
 Day 10: Challenge Explanation (7 of 7)
 Day 10: Your Turn
 Day 10: Your Turn Explanation (1 of 4)
 Day 10: Your Turn Explanation (2 of 4)
 Day 10: Your Turn Explanation (3 of 4)
 Day 10: Your Turn Explanation (4 of 4)

16
Day 11 Challenge: Not Relatively Prime
Show Content Day 11: Something to Think About
 Day 11: Challenge Explanation (1 of 5)
 Day 11: Challenge Explanation (2 of 5)
 Day 11: Challenge Explanation (3 of 5)
 Day 11: Challenge Explanation (4 of 5)
 Day 11: Challenge Explanation (5 of 5)
 Day 11: Your Turn
 Day 11: Your Turn Explanation (1 of 2)
 Day 11: Your Turn Explanation (2 of 2)

17
Day 12 Challenge: More Remainders
Show Content Day 12: Something to Think About
 Day 12: Challenge Explanation (1 of 5)
 Day 12: Challenge Explanation (2 of 5)
 Day 12: Challenge Explanation (3 of 5)
 Day 12: Challenge Explanation (4 of 5)
 Day 12: Challenge Explanation (5 of 5)
 Day 12: Your Turn
 Day 12: Your Turn Explanation (1 of 4)
 Day 12: Your Turn Explanation (2 of 4)
 Day 12: Your Turn Explanation (3 of 4)
 Day 12: Your Turn Explanation (4 of 4)
 Day 12: Your Turn Explanation (5 of 5)

18
Week 3 Challenge
Show Content Week 3 Challenge: Try Your New Skills

19
What's Next
Show Content Week 3: Help Us Learn More About Your Learning Experience

20
Day 13 Challenge: Integer Equations
Show Content Day 13: Something to Think About
 Day 13: Challenge Explanation (1 of 3)
 Day 13: Challenge Explanation (2 of 3)
 Day 13: Challenge Explanation (3 of 3)
 Day 13: Your Turn
 Day 13: Your Turn Explanation (1 of 4)
 Day 13: Your Turn Explanation (2 of 4)
 Day 13: Your Turn Explanation (3 of 4)
 Day 13: Your Turn Explanation (4 of 4)

21
Day 14 Challenge: Powers
Show Content Day 14: Something to Think About
 Day 14: Challenge Explanation (1 of 5)
 Day 14: Challenge Explanation (2 of 5)
 Day 14: Challenge Explanation (3 of 5)
 Day 14: Challenge Explanation (4 of 5)
 Day 14: Challenge Explanation (5 of 5)
 Day 14: Your Turn
 Day 14: Your Turn Explanation (1 of 3)
 Day 14: Your Turn Explanation (2 of 3)
 Day 14: Your Turn Explanation (3 of 3)

22
Day 15 Challenge: Divisibility by Seven
Show Content Day 15: Something to Think About
 Day 15: Challenge Explanation (1 of 5)
 Day 15: Challenge Explanation (2 of 5)
 Day 15: Challenge Explanation (3 of 5)
 Day 15: Challenge Explanation (4 of 5)
 Day 15: Challenge Explanation (5 of 5)
 Day 15: Your Turn
 Day 15: Your Turn Explanation (1 of 3)
 Day 15: Your Turn Explanation (2 of 3)
 Day 15: Your Turn Explanation (3 of 3)

23
Day 16 Challenge: More Remainders
Show Content Day 16: Something to Think About
 Day 16: Challenge Explanation (1 of 3)
 Day 16: Challenge Explanation (2 of 3)
 Day 16: Challenge Explanation (3 of 3)
 Day 16: Your Turn
 Day 16: Your Turn Explanation (1 of 4)
 Day 16: Your Turn Explanation (2 of 4)
 Day 16: Your Turn Explanation (3 of 4)
 Day 16: Your Turn Explanation (4 of 4)

24
Week 4 Challenge
Show Content Week 4 Challenge: Try Your New Skills

25
What's Next
Show Content Congratulations on Completing This Course!
 Week 4: Help Us Learn More About Your Learning Experience
How To Use This Course
The best way to build creative thinking skills is to play with challenging new problems every day, especially those for which you don’t know how to start. This course consists of 16 Daily Challenges and 4 Weekly Challenges. Each Daily Challenge has two main math problems and their explanations, with additional miniproblems interspersed throughout the explanations to help reinforce your learning. Don’t worry if they look unfamiliar, just use the whole time given during the problem videos (and hints) to think. You’ll even get to invent your own strategies, which is the fun part!
Even if you figure out how to do the main problem yourself, watching its explanation video is still very beneficial. It will show multiple interesting ways to do the problem and introduce deeper ideas in math using everyday language.
The way to learn how to solve the widest variety of problems is to learn how to invent your own solution methods! So, we encourage you to solve new problems all on your own instead of working on repetitive exercises. You’ll spend the same time on fewer problems, every one of which needs fresh creativity.
The Discussion function is enabled for all Explanation modules; feel free to use it to dive deeper with other learners!
After every four Daily Challenges, we revisit the topics (with some twists), through a Weekly Challenge problem set that lets you focus uninterrupted for 40 minutes, on a variety of specially designed questions. After doing the problems, please read the explanations, even for the problems you solved. There are a lot of fun math coincidences and insights hidden in the problems.
We recommend pacing the course so that you can play with this way of mathematical thinking for some time every day.
The standard pace is to choose four days each week to work on the Daily Challenges, plus one hour on the weekend for the Weekly Challenge.

Instructor
Loh draws from his experience as a mathematics professor at Carnegie Mellon University, and also as the national coach of the USA International Mathematical Olympiad team. His research and educational outreach takes him to cities across the world, reaching over 10,000 people annually through public lectures and inperson events, and he has featured in or cocreated videos totaling over 5 million YouTube views.
He has been continually involved in math competitions since he was a contestant in the late 1990's: when he ranked 3rd at the National MATHCOUNTS competition, and won a silver medal for the United States of America as a contestant at the International Mathematical Olympiad. He can be followed on Instagram (@poshenloh), Twitter (@poshenloh), WeChat (罗博深数学), and Weibo (poshenloh / 罗博深).PoShen Loh
Math Professor