J. J. P. Veerman

Professor of Mathematics

Affiliate Professor of Physics

Fariborz Maseeh Department of Mathematics and Statistics

Portland State University

Portland, OR 97201, USA

email:

veerman@pdx.edu

                                                                         

Newspaper (El Pais, Spain) articles August 28, 1988 and March 19, 1989.

Papers starting 1985

Papers starting 1995

Papers starting 2005

Papers starting 2015

Research seminar series at Portland State University (2005, 2006, 2010, 2011)

Research seminar series at Rockefeller University (1996, 1997, 2008, 2009)

A language page.

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Join us in Italy, Summer 2019:

1) July 3-11, Pescara, Italy: I am co-organizing the 6th Ph.D.  Summer
    School-Conference on ``Mathematical Modeling of Complex Systems".
    Please, see here for more information on the school and how to apply.
2) July 1-2
, Pescara, Italy: In collaboration with the summer school and in
    preparation for it, some colleagues from Pescara and I will give a tutorial
    on information flow in directed graphs with some applications.
    See here for information.

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Teaching Winter 2019:
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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 435/535, Topology

Here you can find the syllabus.
All assignments, home works, and exams are announced in class.

ASSIGNMENTS:     Tues, Jan 08: Kaplansky 4.1 and 4.2, unstarred exercises.
                                 Tues, Jan 15: Kapl 4.3 and 4.4, unstarred exercises.
                                 Tues, Jan 22: Kapl 5.1 unstarred.
                                 Tues, Jan 29: Kapl 5.2 unstarred.

                                                    
EXAMS:                  Midterm1:    Thurs, Feb 07. Kapl. Chapters 4 and 5.
                                Midterm2:   

                          Final:       

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MTH 622, Advanced Differential Equations

Here you can find the syllabus.
All assignments, home works, and exams are announced in class.

ASSIGNMENTS:    Tues, Jan 08: --
                                Tues, Jan 15: 1a) Show exp(tA).exp(sA)=exp((t+s)A). b) Give example to exp(A).exp(B) not equal exp(A+B).
                                2)     x' =  ax+by-x(x^2+y^2)
                                        y' = -bx+ay-y(x^2+y^2)
                                    a) Transform to polar coords,  b) Identify the bifurcation in the r coordinate, c) Determine angular velocity.
                                3) x''+bx'+cx=d cos(omega t)
                                    Give a complete analysis of this system. In particular, discuss biufurcations, if any.
                                4) Extra Credit: get the correct form of Q(k,t) on page 203-204.
                                5) Let T be the unit square with sides identified to give a torus.
                                    Let c(t) be the constant (non-zero) velocity orbit starting at O.
                                    Discuss omega(c) as function of c'(0).
                                6) Extra Credit: On the torus (see probl 5), it is possible that the omega-limit set is fractal.
                                    Look up Cherry flows.
                                 Tues, Jan 22: 1) Extra Credit: Explain how Van Der Pol modeled the heartbeat with equation (10.3).
                                 2) Explore the behavior of eqn (10.5-6) when mu crosses from negative to positive. 
                                 3) In eqn (11.2), compute "x bar" and "y bar" and determine effect of non-specific insecticide.
                                 4) Linearize eqn (11.2) at the "interior" fixed point (figure 11.4).
                                 5) In eqn (11.3) case 4, find a Lyapunov fn like V to show that the (local) attractor of case 4 attracts all initial
                                     conds in the interior of the pos. quadr.
                                 Tues, Jan 29: 1) Extra Credit: Find more general criterion on the interaction matrix st Thm 11.4.2 holds.
                                 2) Give an explicit 3-dimensional example of eqn (11.6).
                                 3) Apply Hofbauer's thm to the above eqn and find the associated replicator eqn.
                                 4) Investigate (numerically or otherwise) if your system (of probl 2) has an evolutionary stable state.

                                                        
EXAMS:                  To be discussed in class.

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General Announcement 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/


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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, Applications of Graph Theory,
or others, please talk to me.