h1.ps:
Ceci n'est pas un Math 155 syllabus.
If you find a mistake, omission, etc., please let me know by e-mail.
The orange balls mark our current location in the course, and the current problem set.
h0.ps:
introductory handout, showing different views of the
projective plane of order 2 (a.k.a. Fano plane)
and Petersen Graph [see also the background pattern for this page]
h1.ps:
Ceci n'est pas un Math 155 syllabus.
h2.ps:
Handout #2, containing
some basic definitions and facts about finite fields
h3.ps:
Handout #3, outlining
a proof of the simplicity of the finite groups
PSL_2(F) for |F|>4 and PSL_n(F) for n>2
(F a finite field, see Handout #2)
h4.ps:
Handout #4, using the existence and uniqueness
of the Steiner (3,4,8) system to prove that the
linear groups PSL_2(Z/7) and L_3(Z/2), both
simple (see Handout #3) and of order 168,
are isomorphic
h5.ps:
Handout #5, concerning the isomorphism between
the linear group L_4(Z/2) and the alternating
group A_8, both simple and of order 20160
h6.ps:
Handout #6, containing a sketch (to be filled-in
in class) of the existence and uniqueness of
the Moore graph of degree 7, a.k.a. the
Hoffman-Singleton graph. Can you deduce
the size of the automorphism group of this graph?
p1.ps:
First problem set, exploring the Fano plane (and generalizations)
and Petersen graph from the introductory handout.
p2.ps:
Second problem set, mostly on square designs and intersection
triangles.