J. J. P. Veerman
Professor of Mathematics
Affiliate Professor of Physics
Portland State University
1825 SW Broadway, Portland, OR 97201, USA
FMH, rm 464B
Newspaper (El Pais, Spain) articles August
28, 1988 and March 19, 1989.
Papers starting 1985
Papers starting 1995
Papers starting 2005
Papers starting 2015
Papers starting 2020
Research seminar series at Portland State University (2005, 2006, 2010, 2011)
Research seminar series at Rockefeller University (1996, 1997, 2008, 2009)
A language page.
Short Bio and
Description of Research
I have designed 2 new
courses which I am very
excited to teach. Please, ask me about this material.
I am writing an ambitious set of notes covering an introduction to several areas of number
theory. Here is the flyer for the full year course. It is designed to emphasize connections
with other areas of mathematics such as analysis, algebra and complex analysis, as well
as to make some classical results accessible to a wider audience of non-specialists.
In the summer of 2019, I participated in a summer school in Italy where I gave a mini-course
on the theory of directed graphs. This resulted in the design of the 1 or 2 trimester course
"Directed Networks". Here is the flyer for the course. Some of the material has been worked
into slides: see part 1, part 2, part 3, and part 4.
All this material is "work in progress"; expect errors and other shortcomings.
I appreciate if you report errors and welcome constructive criticism.
You can find my email at the top of this page.
IMPORTANT 1: All answers on home
works and exams must be justified, even if that is
not evident from
the phrasing of the question. Answers without justification will receive partial credit at best.
IMPORTANT 2: Before turning in exams or HW's, write your first plus last name in the top right corner
of each sheet you turn in (even if you staple them together)!
IMPORTANT 3: While I actively encourage collaboration among students and may assign
take home exams on which you are allowed to collaborate:
you must write your own exam yourself in your own words !!!
Copying, or even using something else as a template for your answers, is plagiarism
and will receive no credit whatsoever.
Winter 2022, MTH 610, Number Theory:
I will teach a full year
course on newly designed course in Number Theory with freely
lecture notes. Here is a flyer, the syllabus, and free lecture notes for all three terms of the course (with
the copyright statement here). Below follows an informal syllabus.
This term, we start with principles of algebraic number theory (currently Chapters 7, 8, 9) and follow
it up with the most important and iconic theorem of analytic number theory: the prime number
theorem (currently Chapters 12, 13 , and 14). Note that at the time of this writing, Chapters
8 and 9 are still very incomplete.
The material requires substantial excursions into abstract algebra and complex analysis, which
will be integral part of this class. In spring, we plan on doing a survey of probabilistic number theory,
in particular ergodic theory plus perhaps some other topics if time permits.
Roughly every two weeks we will do one chapter.
The first of those two weeks is dedicated the theory as
outlined in the main text, and the second week we dedicate to the going through all the HW problems of
that chapter. Exams will consist of turning in to be graded a small selection of HW's, probably two or three
for each chapter. In doing this course, it is important to understand that the best measure of success
in this course is not your grade, but that you have done every single problem in the assigned chapters.
As soon as we start discussing a new chapter, start working on the problems!
ASSIGNMENTS: Every second week, all HW's of the
chapter just discussed in class.
IMPORTANT: Before studying or working the problems, ALWAYS refresh your screen,
as I update the book very often.
Exams: Grades will be based on
performance in class. In the absence of evidence,
HW will be collected, or exams will be given.
Winter 2022, MTH 255, Calculus 5:Here is the syllabus for the course. Towards the end of the course and if time permits, we'll look
Exam 1, in-class: Chapter 15 (including assigned
HW), April 26 (1 hr).
Exam 2, in-class: Chapter 16 (including assigned HW), May 12 (1 hr).
Exam 3 (final): Chapter 17 (including assigned HW) but cumulative, CHANGED: May 31 (2 hrs).
In most of my classes you will be either strongly
encouraged, or even obliged
(graduate students) to turn in your HW in *.pdf format based on LATEX.
Here is a website where LATEX is explained: