Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 567: Elementary Number Theory

Frequency: 

Fall

Student Body: 

Math majors and graduate students in related areas

Background and Goals: 

This course is an undergraduate introduction to number theory.

Alternatives: 

N/A

Subsequent Courses: 

N/A

Course Content: 
  • Divisibility, the Euclidean algorithm and the GCD, linear Diophantine equations, prime numbers and uniqueness of factorization.
  • Congruences, Chinese remainder theorem, Fermat's "little" theorem, Wilson's theorem, Euler's theorem and totient function, the RSA cryptosystem.
  • Number-theoretic functions, multiplicative functions, Mobius inversion.
  • Primitive roots and indices.
  • Quadratic reciprocity and the Legendre symbol.
  • Perfect numbers, Mersenne primes, Fermat primes.
  • Pythagorean triples, Fermat's "last" theorem with proofs of special cases.
  • Fibonacci numbers.
  • Continued fractions.
  • Distribution of primes, discussion of prime number theorem.
  • Primality testing and factoring algorithms.
credits: 
3 (N-A)
semester: 
Fall
prereqs: 
Math 340 or con reg.

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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