Sieve Methods, Math 595, Spring 2011




Instructor

Kevin Ford (Altgeld 304, phone 265-6255, e-mail: ford@math.uiuc.edu )
Office hours: MWF 11:00-12:00 or by appointment

Textbook

There is no official textbook, although the books Sieve methods (Halberstam and Richert, Academic Press, 1974) and Opera de Cribro (J. Friedlander, H. Iwaniec; 2010) are useful references for general sieve methods.

References

Paper on the Brun-Hooley sieve . The notation is slightly different than that presented in class.
Exposition of the Goldston-Pintz-Yildirim work , by K. Soundararajan.

Class Notes, Part 1 (Brun-Hooley sieve)

Class Notes, Part 2 (Selberg sieve)

Class Notes, Part 3 (Goldston-Pintz-Yildirim theorems)

Class Notes, Part 4 (smooth numbers and large gaps between consecutive primes)

Class Notes, Part 5 (shifted primes and the distribution of totients)

Class Notes, Part 6 (the linear sieve)

Class Notes, Part 7 (the large sieve)

Class Notes, Part 8 (Buchstab's function and irregularities in the distribution of primes)

Homework

Homework problems will be assigned periodically, with various point values.

Exams

There will be no exams

Grades

Your grade is determined entirely by the number of homework points you accumulate during the semester. Here is the breakdown:
Grade Points
A+ 100
A 60
A- 50
B+ 40
B 30
B- 20
C+ 10
C 0