Anatomy of integers and random permutations, Math 595, Fall 2017
Instructor
Kevin Ford (Altgeld 304, phone 2656255, email:
ford126 (at) illinois (dot) edu
Office hours: MWF 2:002:45 or by appointment
Textbook
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 BigO notation. A good refresher can be
found in Professor Hildebrand's notes:
Background: Basics of arithmetc functions
Background: BigO 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
Homework
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)
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
