J. J. P. VeermanProfessor of MathematicsAffiliate Professor of PhysicsPortland State University1825 SW Broadway, Portland, OR 97201, USAFMH, rm 464Bemail: veerman@pdx.edu
Website:
http://web.pdx.edu/~veerman/ |
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
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:
https://www.euro-acad.eu/news?
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Lecture Notes on
Number Theory
Teaching SPRING
2021:
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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)!
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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
relevance,
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).
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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):
Exam1: 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).
Final: May 25,
17:00. Perform all computations in Transients Prop1 and Thm3 when
c+=2/3 and c-=1/3.
General Announcements for Students:
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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:
http://www.ctan.org/tex-archive/info/Math_into_LaTeX-4/