Math 531, Fall 2022
Instructor: Kevin Ford; Office: 304 Altgeld. Office hours TBA.
Some course notes
Notes on big-O, little-o and related notation
Rigorous evaluation of the sum of 1/k^2
Lecture notes on the general theory of Dirichlet series
The main prerequisites are a thorough
understanding of real and complex analysis at the undergraduate level,
and the very basics of elementary number theory
(say the first half of Math 453) covering
the fundamental theorem of arithmetic, and basics
of congruences and divisibility.
Some topics from graduate complex analysis, e.g. Hadamard's theory of entire
functions, will be needed starting about 1/3 of the way through the course.
It is highly recommended to take graduate complex analysis before or concurrently
with Math 531.
The course grade will be based on
7 Homework assignments (total weight 50%), spread out evenly over the
semester, an in-class midterm exam (20%) and a Final Exam (30%).
No official text, but the books
Multiplicative Number Theory , by Harold Davenport (2nd or 3rd edition)
and Introduction to analytic and probabilistic
number theory by G. Tenenbaum, are highly recommended, and copies are
on reserve in the library.
Homework assignments and solutions (PDF files)
- DUE 9-SEPT-2022: Homework set #1 with solutions.
- DUE 23-SEPT-2022: Homework set #2 with solutions
- DUE 7-OCTOBER-2022: Homework set #3
Friday, October 28. In class at the regular time. Covers material on the first
four homework assignments.
Final Exam: Tuesday, December 13, 1:30-4:30 PM, in the regular classroom.