J. J. P. VeermanProfessor of Mathematics

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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Teaching Fall 2017:
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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 662,
Algebraic Graph Theory II
Here is the syllabus.
All assignments, home works, and exams are discussed in
class.
BLS, Chapter 1: HW1: Tues, Jan 23: Prove formula's 1.7 and
1.8 in BLS, use the original reference stadler1996.
Give an explicit example of a Landscape and find its amplitude
spectrum.
BLS, Ch 2: HW2: Tues,
Jan 30: Prove Thms 2.12, 2.13, and 2.14. Use merris1995.
BLS, Ch 3: HW3:
Tues, Feb 06: Consider the evecs of the Laplacians in Figures 3.1,
3.2, 3.3, and 3.4.
Analyze the nodal domains using the Nodal Domain Theorem. Also
analyze these
using Theorem 2.18 in the book.
HW4: Tues, Feb 13: Prove Thms 3.11 and 3.13. Check Thm 3.12 for
the Laplacian of path graph
(hint: it is crucial to realize that the standard Lapl gives rise
to what in PDE corresponds to
``free boundary conditions").
HW5: Tues, Feb 20: Explain why does Thm 4.5 (ii) improve on the
Nodal Domain Theorem?
Describe the algorithm at the end of the proof of Thm 4.5, and
explain why it is O(n^2).
Show that every graph satisfying Prop 4.10 has the property that
a) every nontrivial connected induced subgraph has disconnected
complement,
b) cannot contain induced paths of length 4.
HW6: Tues, Feb 27: Prove Cor 4.14.
Prove that the hypercube defined in ln 1 of Section 4.3.1 has the
following properties:
a) equals K_2^n, b) is bipartite,
c) has n.2^(n1) edges.
Prove the properties of teh Walsh "functions" listed on page 60:
a) they form an orthogonal basis of R^{2^n}, b) they are
e.vecs of the Laplacian,
c) they be be recursively defined.
HW7: Write a full proof of Thm 4.18. This includes a proof
of NDT (section 3.2). Avoid
copying that proof.
HW8: 1) Continue writing a GREAT proof for HW7.
2) (Optional) Investigate FaberKrahn where volume is #vertices.
Start eg with
subgraphs of the regular lattice.
FINAL 662: Tues, Mar 20, 17:3019:20.
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MTH 470/570, Complex Variables and Boundary Value Problems
Here is the syllabus.
All assignments, home works, and exams are discussed in class.
Homework
due: Tue, Jan 16: 1.1: 2, 4, 6, 8, 10, 18;
1.2: 2, 4, 8, 13.
Tue, Jan 23: 1.3: 2, 4, 6, 8, 11;
1.4: 4, 14, examples 1.4.25 and
1.4.28.
Tue, Jan 30: 1.4: 16, 20, 21; 1.5: 2,
4, 6, 10, 18a+b+c.
Tue, Feb 06: 1.5:
24; 1.6: 2, 4, 6;
Review: 2, 4, 6, 8, 10, 12,
16, 26, 33, 34.
Tue,
Feb 13: 2.1: 2, 4, 6, 8; 2.2: 1,
2, 3, 4.
Tue, Feb 20: 2.1: 8, 10,
14; 2.2: 510.
Tue, Feb 27: 2.4: 1, 2, 5,
10, 13, 15, 16, 19.
Tue, Mar
06: 2.5: 1, 2, 7,
examples 14 and
15;
Review: 1, 2, 3, 4, 5,
7, 11, 13abc, 19, 20
, 21.
Tue,
Mar 13: 3.1: 1,
2, 3, 5, 6, 8, 11.
Mon,
Mar 19:
3.2: 1, 2, 3,
4, 5, 6, 7, 8,
9, 12, 13.
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/texarchive/info/Math_into_LaTeX4/