Theoretical / proof-based
Number theory · Undergraduate · Math
Topics
Divisibility and congruences
- Divisibility, GCD, and the Euclidean algorithm
- Bézout's identity and linear Diophantine equations
- Prime numbers; fundamental theorem of arithmetic
- Congruences and modular arithmetic
- Fermat's little theorem and Euler's theorem
Classical theorems and functions
- Wilson's theorem and order of elements modulo n
- Chinese remainder theorem and applications
- Euler's totient function and multiplicative functions
- Quadratic residues and Legendre symbol
- Law of quadratic reciprocity (introduction or proof sketch)
Diophantine equations and cryptography
- Pythagorean triples and primitive solutions
- Sums of two squares (introduction)
- Continued fractions (optional topic)
- RSA and public-key cryptography from number-theoretic primitives
- Introduction to algebraic number theory: Gaussian integers (optional)
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$1,162 · Number theory · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.