Math 4161 Course Outline

Week 1: Induction, binomial theorem, divisibility
Week 2: More on divisibility, Euclid’s lemma, prime nunbers, linear Diophantine equations
Week 3: Fundamental theorem of arithmetic, distribution of primes
Week 4: More on distribution of primes, congruence, divisibility tests
Week 5: Chinese remainder theorem, intro. to analytic number theory ( p 1 diverges–sum
taken over the prime numbers)
Week 6: Fermat’s little theorem, First test
Week 7: Wilson’s theorem, representation of integers as sums of squares
Week 8: Number-theoretic functions (τ (n) = |{d | d|n}| and σ(n) = d|n d)
Week 9: Perfect numbers, Mersenne primes, Euler’s φ-function
Week 10: Euler’s generalization of Fermat’s theorem, order of an integer module n
Week 11: Primitive roots
Week 12: Primitive roots, Second test
Week 13: Quadratic reciprocity
Week 14: Quadratic recoprocity
Week 15: Catch up, review