Why number theory?

To learn number theory, you only need a background in arithmetic and algebra. Beyond that, you need focus and drive. Number theory is a fun but challenging subject that is accessible to most anyone — making it popular with prodigies. Are you ready to #LearnMore?

Course curriculum

    1. What is Number Theory?

    2. The History of Number Theory

    3. Prime Numbers - The Building Blocks

    4. The Fundamental Theorem of Arithmetic

    5. Introduction to Proofs

    6. Number Theory in the Real World

    1. Understanding Divisibility

    2. The Division Algorithm

    3. Prime and Composite Numbers

    4. The Sieve of Eratosthenes

    5. Prime Factorization

    6. The Fundamental Theorem of Arithmetic (Revisited)

    7. Special Types of Prime Numbers

    8. Divisibility Rules and Tricks

    1. Introduction to GCD and LCM

    2. Computing the GCD

    3. Computing the LCM

    4. Extended Euclidean Algorithm

    1. Diophantine Equations with 1 Variable

    1. Introduction to Congruences & Modular Arithmetic

    2. Congruence Relations

    3. Fermat's Little Theorem

    4. Euler's Theorem

    5. Wilson's Theorem

    6. Applications of Modular Arithmetic

    7. Linear Congruences

    8. Systems of Congruences

    1. Euler's Phi Function (Totient function)

    2. Möbius Function and Möbius Inversion Formula

    3. Sigma Function and Sum of Divisors

    4. Abundant, Deficient, and Perfect Numbers

About this course

  • Free
  • 46 lessons
  • 0.5 hours of video content

Number Theory Instructor

Michael Harrison


Michael earned his BS in Math from Caltech, and did his graduate work in Math at UC Berkeley and University of Washington, specializing in Number Theory. A self-taught programmer, Michael taught both Math and Computer Programming at the college level. He applied this knowledge as a financial analyst (quant) and as a programmer at Google.