Additive Number Theory, Math 595, Fall 2013
Course description sheet
Instructor Kevin Ford
Office hours: MWF 10:00-10:50 or by appointment
There is no official textbook for the course. The following books
contain much of the material that will be referenced.
- Sequences , 2nd ed., by H. Halberstam and K. F. Roth,
Springer-Verlag, New York-Berlin, 1983.
- The Hardy-Littlewood method , 2nd ed., by R. C. Vaughan,
Cambridge Tracts in Mathematics, vol. 125, 1997.
- Additive Number Theory: Inverse problems and the geometry of
sumsets , by M. Nathanson, Springer GTM 165 , 1996.
- Additive combinatorics , by T. Tao and V. Vu, 2006.
Here are notes on basics of
sieve methods needed for Schnirelmann's theorem (week 1)
and Romanoff's theorem (week 3).
See page 15 for the theorem on the number of solutions of p+q=2N.
Here are some
notes on standard order of magnitude notation (big O, etc)
used in the course.
will be assigned periodically, with various point values.
There will be no exams.
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