Number theory
Undergraduate · Math
Syllabus focus
Theoretical / proof-based
Pricing calculator
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$1,162 · Number theory · 18 tutoring hrs
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Topics typically covered
Theoretical / proof-based
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)
Notes
Topics reflect common undergraduate number theory syllabi for mathematics majors at US universities. Some programs emphasize computational and cryptographic applications; others focus on proof-heavy classical theory.