Number theory
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Number Theory — scope drawn from open number theory texts (e.g. Stein / Burton-style OER) and typical US elementary number theory syllabi.
Divisibility and congruences
- Divisibility and GCD — Divisibility and GCD
- The Euclidean algorithm — The Euclidean algorithm
- Bézout's identity — Bézout's identity
- Linear Diophantine equations — Linear Diophantine equations
- Prime numbers — Prime numbers; fundamental theorem of arithmetic
- Congruences and modular arithmetic — Congruences and modular arithmetic
- Fermat's little theorem — Fermat's little theorem
- Euler's theorem — Euler's theorem
Classical theorems and functions
- Wilson's theorem — Wilson's theorem
- Order of elements modulo n — Order of elements modulo n
- Chinese remainder theorem — Chinese remainder theorem
- Applications — Applications
- Euler's totient function — Euler's totient function
- Multiplicative functions — Multiplicative functions
- Quadratic residues and Legendre symbol — Quadratic residues and Legendre symbol
- Law of quadratic reciprocity (introduction or proof sketch) — Law of quadratic reciprocity (introduction or proof sketch)
Diophantine equations and cryptography
- Pythagorean triples — Pythagorean triples
- Primitive solutions — Primitive solutions
- Sums of two squares (introduction) — Sums of two squares (introduction)
- Continued fractions (optional topic) — Continued fractions (optional topic)
- RSA and public-key cryptography from number-theoretic primitives — RSA and public-key cryptography from number-theoretic primitives
- Introduction to algebraic number theory: Gaussian integers (optional) — Introduction to algebraic number theory: Gaussian integers (optional)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Divisibility and congruences
Divisibility and GCD
Coming soon - Classical theorems and functions
Wilson's theorem
Coming soon - Diophantine equations and cryptography
Pythagorean triples
Coming soon
Notes
Undergraduate Number Theory — scope drawn from open number theory texts (e.g. Stein / Burton-style OER) and typical US elementary number theory syllabi. Topic outline: `content/topics/undergraduate/number_theory.json`.