UIC Number Theory MATH 514
Fall 2007



The class meets in LH 206 at 1-2pm each Monday, Wednesday, Friday.
For questions, please contact Prof. Cojocaru.





Weekly schedule of lectures

For dates, look at the academic calendar.

Week 1
A.C. Cojocaru
The sieve of Eratosthenes, inclusion-exclusion principle, Euclid's proof for infinitely many primes
Week 2
A.C. Cojocaru
Arithmetic functions (def and formulae); the order of magnitude of arithmetic functions; Chebysheff's theorem
Week 3
A.C. Cojocaru
Partial summation; Mertens' theorems; average order of arithmetic functions
Week 4
A.C. Cojocaru
The normal order method, the Turan sieve, monic irreducible polynomials of fixed degree
Week 5
A.C. Cojocaru
The quadratic symbol, the square sieve, integral points on hyperelliptic curves
Week 6
A.C. Cojocaru
The sieve of Eratosthenes
Week 7
A.C. Cojocaru
The Selberg sieve
Week 8
A.C. Cojocaru
Primes in an arithmetic progression and the Brun-Titchmarsh theorem
Week 9
A.C. Cojocaru
The large sieve I
Week 10
A.C. Cojocaru
The large sieve II
Week 11
Thanksgiving week
Week 12
A.C. Cojocaru
The lower bound sieve, twin primes
Week 13
A.C. Cojocaru
Twin primes, presentations
Week 14
A.C. Cojocaru
Presentations
Week 15
A.C. Cojocaru
FINALS






PROJECTS

The Titchmarsh divisor problem
The Riemann zeta function and Mertens' theorem
The theorem of Erdos on the normal order of nu(p-1)
The Turan sieve and the Hilbert symbol
The Barban-Davenport-Halberstam theorem