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 highly-motivated 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 course-consulting@poshenloh.com to discuss.


Syllabus

  • 02
    Day 1 Challenge: Modular Arithmetic
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  • 03
    Day 2 Challenge: Remainders Modulo 3 and 9
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    • 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
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    • 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
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    • 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
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    • Week 1 Challenge: Try Your New Skills
  • 07
    What's Next
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    • Week 1: Help Us Learn More About Your Learning Experience
  • 08
    Day 5 Challenge: Factors
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    • 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
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    • 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
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    • 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
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    • 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
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    • Week 2 Challenge: Try Your New Skills
  • 13
    What's Next
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    • Week 2: Help Us Learn More About Your Learning Experience
  • 14
    Day 9 Challenge: Repeating Patterns
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    • 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
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    • 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
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    • 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
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    • 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
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    • 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
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    • 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
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    • 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
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    • 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
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    • 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
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    • Week 4 Challenge: Try Your New Skills
  • 25
    What's Next
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    • 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 mini-problems 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

    Po-Shen Loh is a social entrepreneur, working across the full spectrum of mathematics and education, all around the world. He is the founder of the free personalized learning platform expii.com, an education technology social enterprise which algorithmically curates openly licensed math/science lessons and problems contributed by the world. Sales of these online courses support the development of these social initiatives.

    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 in-person events, and he has featured in or co-created 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).

    Po-Shen Loh

    Math Professor

    Po-Shen Loh