Anatomy of integers and random permutations, Math 595, Fall 2017


Kevin Ford (Altgeld 304, phone 265-6255, e-mail: ford126 (at) illinois (dot) edu
Office hours: MWF 2:00-2:45 or by appointment


There is no official textbook, although the book Divisors (Hall and Tenenbaum, Cambridge Tracts in Mathematics, vol. 90, 1988) is a useful reference for much of the material on the anatomy of integers.
The course requires some prerequisite background material from number theory: basics of arithmetic functions, elementary prime number theory (Mertens' estimates, etc), partial summation, and familiarity with Big-O notation. A good refresher can be found in Professor Hildebrand's notes:
Background: Basics of arithmetc functions
Background: Big-O notation (and friends), Arithmetc functions: summation estimates
Background: Elementary theory of primes . You need to know the estimates of Chebyshev and Mertens.

Lecture Notes

Most of the material will be written up as lecture notes, which will be periodically updated : Lecture Notes, through Ch. 4. 2nd Draft.

Other useful links

Table of useful inequalities , compiled by Laszlo Kozma


Three homework assignments, spread through the semester. Each problem has a prescribed point value.
Homework set 1 . Due Friday, October 6. Solutions
Homework set 2 . Due Friday, November 17. Solutions
Homework set 3 . Due Wednesday, December 13. Solutions (with typos corrected)


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