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 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.

Pescara Lecture Notes on Directed Graphs

Part 1, part2, part 3, and part 4. See also  https://www.sci.unich.it/mmcs2019/

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Lecture Notes on Number Theory

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I was awarded the (full year) 2019/20 Fulbright-Czech
Distinguished Professorship at the Czech Technical
University in Prague.

The Fulbright Scholar Program is "a program of the United States Department of State
Bureau of Educational and Cultural Affairs."

"The Fulbright Distinguished Chair Awards comprise approximately forty distinguished lecturing,
distinguished research and distinguished lecturing/research awards ranging from three to 12 months.
Fulbright Distinguished Chair Awards are viewed as among the most prestigious appointments in the
Fulbright Scholar Program. Candidates should be eminent scholars and have a significant
publication and teaching record."

Unfortunately, administrative decisions by the dean's office of Portland State University 
made it impossible for me to accept this wonderful award. So I am in Portland during 2019/20.

Teaching WINTER 2020:
=========================================================

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 421/521, Ordinary Differential Equations

Here you can find the syllabus for this course.
All assignments, homeworks, and exams are announced in class.

ASSIGNMENTS :
         Mon, Jan 13:  ch 1: 1--3, 6--15.
         Mon, Jan 20:  ch 2: 1--5, 7, 8, 11, 13, 14.
         Mon, Jan 27:  ch 3: 1--8, 11, 12, 13, 14, 15, 16.
         Mon, Feb 03: ch 4: 1--4, 7--9.
         Mon, Feb 10: ch 5: 2, 3, 4 (first reduce to triangular), 5, 6 (5 types), 8, 9, 13.
         Mon, Feb 17: ch 6: 1--5, 7--10, 12, 13.
         Mon, Feb 24: ch 7: 1--7.
         Mon, Mar 02: extra HW: euler2.pdf;

EXAMS PLANNED (may be modified in class):

         Exam 1: Febr 07, ch 1--4.
         Exam 2: Febr 28, ch 5, 6.
         Exam 3 (final): Winter FINAL 421/521: Mon, Mar 16, 12:30-14:20.
    

=========================================================
MTH 635, Algebraic Topology

Here you can find the syllabus for this course.
All assignments, homeworks, and exams are announced in class.

ASSIGNMENTS :
         Mon, Jan 13: 2.2: 1--5.
         Mon, Jan 20: 2.2: 6--10, 12, 13a, 14.
         Mon, Jan 27: 2.2: 15, 19--24, 28--30, 32, 33, 38, 40, 43.
         Mon, Feb 03: 2B: 1, 2; 2C: 2, 4, 6.
         Mon, Feb 10: 3.1: 4, 5, 6.
         Mon, Feb 17: 3.1: 7, 8, compute cohom. of complex in Ex 3.9. 3.2: 1, 3.
                              In R^3: show that d^i for i in {0,1,2}  equals grad, curl, and div.
                                          show that d.d = 0.
                                          show that Stokes induces a homo H_* to H^*.
          Mon, Feb 24: 2.C: 3; 3.2: 4, 6, 15 (only for spaces mentioned in this problem).
                              Show that Thm 3.15 does not hold if X=Y=RP^2 and G=Z.

PUBLIC LECTURES ON THE WEB:
1)  https://www.youtube.com/watch?v=RnNLHDQAjRs  (26 mins)
2)  https://www.youtube.com/watch?v=1LwkljjLBns&t=2s (56 mins)
3)  https://www.youtube.com/watch?v=cp6eudDomRY  (62 mins)
4)  https://www.youtube.com/watch?v=r_KqR5tBekQ  (58 mins)

EXAMS PLANNED (may be modified in class):

===============================================================

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: 
http://www.ctan.org/tex-archive/info/Math_into_LaTeX-4/