Math 531, Fall 2022



Instructor: Kevin Ford; Office: 304 Altgeld. Office hours TBA. email: ford126(at)illinois(dot)edu


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



Prerequisites

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.

Grades

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%).

Textbook

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)

  1. DUE 9-SEPT-2022: Homework set #1 with solutions.
  2. DUE 23-SEPT-2022: Homework set #2 with solutions
  3. DUE 7-OCTOBER-2022: Homework set #3 with solutions
  4. DUE 21-OCTOBER-2022: Homework set #4 with solutions
  5. DUE 4-NOVEMBER-2022: Homework set #5 with solutions
  6. DUE 2-DECEMBER-2022: Homework set #6 with solutions

Midterm Exam: 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 329 Davenport Hall.