J. J. P. Veerman

Professor of Mathematics

Affiliate Professor of Physics

Portland State University 

1825 SW Broadway, Portland, OR 97201, USA

FMH, rm 464B

email:  veerman@pdx.edu

                                                                   Website: http://web.pdx.edu/~veerman/

                                                                        Telephone: 503-725-8187


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

This can be found here and here.

I am always looking for students, and in particular PhD students, interested and willing to
participate in research projects in (or related to) the areas described here. Interested students
should consult the links given in this website to my papers, lecture notes, and course


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.




Portland State covid policy:

Valid for all classes. Please, see here.


Teaching  Statements for all classes:

Here are links to DRC, Title IX, and Zoom-FERPA statements and a statement about
classroom requirements due to covid-19. All these statements are valid for all courses/classes.

Homework and Exam Statements:

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.


TEACHING 2021-2022:


Winter 2022, MTH 610, Number Theory:

I will teach a full year course on newly designed course in Number Theory with freely available
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
into some physics applications of calculus guided by these notes
There is an abstract mathematical language that has been developed to understand and formulate
the important theorems of  Calculus 5 and more, and that is called "differential forms". That language
simplifies the formulation of all these results enormously. I will use that language, but we will not deal
with the proofs. Here are some notes
(with the copyright statement here) that describe the  main ideas.
We will go through these in class.

Homeworks and exams will be announced in class. Even if you cannot attend class, it is your responsibility
to find out from your colleagues what was discussed in class, and whether any assignments were changed.
In most cases, announcements about HW and exams will be reflected on this page.

Homework: Tue, Apr 05: 15.1: 1,2,8,15--17,19--26, 38--42; 15.2: 4--6,8,9,33--36,45--48.
                     Tue, Apr 12: 15.3: 3,4,11,12,31,32,39,40;  15.4: 4,5,9,10,29,30,35,36,45--48.
                     Tue, Apr 19: 15.5: 3--8, 19--22; 15.6: 1,2,5--12,29--32.
                     Tue, Apr 26: 16.1: 13--20,23--26,39--42, 48,49; 16.2: 9--12,19--22,27--31.
                     Tue, May 03: 16.3: 7--14,26--31; 16.4: 1--4,7--10,13--18.
                     Tue, May 10: 16.5: 5--10, 25--30. 17.1: 3--6,16,17,19,20,28,29.38--41.
                     Tue, May 17: 17.2: 1--16.
                     Tue, May 24: 17.3: 1--20.

: We plan on collecting odd-numbered HW for completion counting for 25% of your final grade and
three in-class exams that each count for 25%.

Dates and details will be announced in class and and on this website.

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).


Other General Announcements for Students:


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: 


Student Research Projects:

I have many research projects, Most are intended for 501 theses or PhD level projects.
If you are interested in doing a research project in:
Dynamical Systems, Social and Economic Networks, Coherent Motion of Flocks, Topology/Geometry,
Fractal Geometry, Discrete Mathematics, Mathematical Physics, Networks and Graph Theory,
or others, please talk to me.