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


Pescara 2019 summer school and conference on
Mathematical Modeling of Complex Systems

In the summer of 2019, I participated in a summer school and conference in
Mathematical Modeling in Pescara, Italy. I gave a mini-course on the theory
of directed graphs in the summer school:
part 1, part 2, part 3, and part 4.
I also served as guest editor of the Proceedings of the conference. A description
of the meeting and links to the papers presented can be found here:


Lecture Notes on Number Theory

Here is a flyer, the syllabus, and free lecture notes  (with the copyright statement here) for a newly
designed course in number theory. This was a sequence of two courses MTH 449/549 and MTH
410/510 (fall 2020 and winter 2021). These notes are a work in progress and may contain errors.


Teaching SPRING 2021:


Teaching  Statements

Here are links to DRC, Title IX, and Zoom-FERPA statements. These are valid for all courses.


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)!

MTH 610, Directed Networks

Here is a flyer containing references to freely available lecture notes for this newly designed course  
describing theory and applications of directed graphs (MTH 610, spring 2021). This is a very current area with
applications from data science to flocking, finance, chemical networks and others. In spite of its current
good mathematics textbooks are still rare. So we developed our own course, and are writing a textbook
based on this course.
The course will by and large follow these notes:
part 1, part 2, part 3, and part 4 (with the copyright statement here)
Then, if time permits, we will discuss some of the topics in these papers:
paper0, paper1, paper2, paper3, and paper4.

ASSIGNMENTS: Do exercises as indicated in class in digraphs I through IV.
                        Study the heat equation and the wave equation on [0,1] (space) cross \R (time).
                        Study paper0 and then paper1.

PRESENTATIONS: May 20: Ed,   May 25: Choomno,   May 27: Laura,   June 01: Michael + Tessa,    June 03: Chris.                                 

EXAMS PLANNED (may be modified in class): 
Exam1: Digraphs I: exercises on  pages 12, 17, 23, 29 (1st only), and 31.
Exam2: Digraphs 2: exercises on pages 23, 2nd on pg30, and pg38.  Digraphs 3: exercises on pg 14, 15, 21, 27, 29.
Final: May 25, 14:00. Digraphs 4: exercises on pgs 6, 8, 16, 20 (L_out only), 24 (L_out only).

MTH 623, Advanced Differential Equations

Here is a flyer  and the syllabus for my advanced course in dynamical systems MTH 621/2/3. The emphasis this year
will be on surveying the wide range of this branch of mathematics and its applications, rather than
probing deep theorems. We will use a great -- and very accessible -- text written by the eminent
mathematician S. Sternberg plus some  other resources to be determined during the course.
This is three term sequence. In Fall and Winter, we will go through the entire book by Sternberg.
Spring of 2021 will most likely be organized as a 'topics' course. This will in part depend on students'
interests. Among the possibilities are topics in Ergodic Theory, Number Theory, Quantum Mechanics,
and so forth. (This year, we dedicated the term to "flocking".)

ASSIGNMENTS: Study the heat equations and the wave equation on [0,1] (space) cross \R (time).       

                        Study "Flocks and Formations".
                        Explore Def 2.2 with an explicit example (such as Q on page 7).
                        Prove first statement in Thm 3.6 (this includes: prove Gersgorin).
                        Study spectrum and eigenvectors of an example of a hierarchical flock (section 7).
                        Simulate an oriented flock numerically (section 8).
                        Complete proof of stability of a ``rotating" flock.
Prove stability if ONLY the leader changes direction (not every individual as in thm 5.2).
                        Simulate these cases.

                        Study "Signal Velocity in Oscillator Arrays".                  

                        Study "Transients in the Synchronization of Asymmetrically Coupled Oscillator Arrays".

                        Study "Dynamics of Locally Coupled Agents with Next Nearest Neighbor Interaction".              

PRESENTATIONS: May 25: Logan,    May 27: Ed,    June 01: Robert B,    June 03: Choomno.                                

EXAMS PLANNED (may be modified in class): 
Fully analyze the example given in section 6, using all the principal results in the paper.
            Ample hints are given in the text.
Exam2: Perform the analysis of "Signal Velocity" until (not including) Lemma 4 for the system in
            eqn (2) with gx=gv=-1 and rho_{x,-1}=rho_{x,1}=-1/2 and rho_{v,-1}=-2/3 and
            rho_{v,1}=-1/3. (The central rho's are equal to 1).

May 25, 17:00. Perform all computations in Transients Prop1 and Thm3 when c+=2/3 and c-=1/3.


General Announcements for Students:

In most of my classes you will be either strongly encouraged,
or even obliged 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.