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.
-------------------------------------
                                 Armstrong:
                                 Tues, Feb 12: 1.6: 1--7, 10, 14--17, 23.
                                 Tues, Feb 19: 2.1: 2, 3, 4, 9, 11, 12; 2.2: 13, 14, 16, 17, 19; 2.3: 22--26 (you'll find nice answers on the web).
                                 Tues, Feb 26: Ch 2: 27--33. Ch 3: 1,2. Show that intersection of nested closed sets is non-empty (Kapl. pg 87).
                                                       Ch 3.3: 5--12.
                                 Tues, Mar 05: Ch 3: 20 -- 23, 25, 30 -- 34, 37 -- 44; Ch 4: 1, 2, 3, 5, 7.
                                 Tues, Mar 12: Ch 4: 13, 16, 17, 18, 19.
                                 Tues, Mar 19: Ch 4: 26--29, 30a.

                                                    
EXAMS:                  Midterm1:    Thurs, Feb 07. Kapl. Chapters 4 and 5.
                                Midterm2:    Tues, Feb 26. Turn in take-home exam: type-written proof of Euler's Thm.
                                                    (Please note: Must also include the additional proofs done in-class!)  

                          Final:        Tues, Mar 19: 17:30-19.20. All material

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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 bifurcations, 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.
                                 5) Assume all letters of the alphabet occur equally often (frequ. = 1/26). Find an instantaneous
                                     binary encoding the alphabet and show that it satisfies both Shannon theorems.
                                 6) In the case of problem 5), what are the codes that satisfy the first formula on pg 144?
                                 7) Same question as 5), but now assume that A occurs with frequ = 1/2, and all other 25 letters with
                                     frequ = 1/50.
                                 Tues, Feb 05: 1) Prove that d(x,y) on page 247 is a metric.
                                  2) Prove that sigma on page 248 is continuous.
                                  3) Show that h on page 249 is continuous.
                                  4) Let F=(01101) and show the 4-step shift (binary strings). Compute the topological entropy.
                                  5) Figure out the connection between topological entropy and the entropy in Chapter11.
-----------------------------------
                                  Hofbauer-Sigmund.
                                  Tues, Feb 12: 3.3: 1, 4; 3.4: 2, 3, 4; all of 4.3 and 4.4 and 4.5.
                                  Tues, Feb 19: Ch 5: 5.5.2--5.
                                  Tues, Feb 26: Ch 6: 6.1.1, 6.3.1, 6.4.2, 6.4.3.
                                  Tues, Mar 05: Ch 7: 7.4.1--3, 5, 6.

                                                        
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.