This semester the seminar will be dedicated to the study of various geometries (especially projective and affine geometries), linear and near-linear spaces.
Our text will include the first four chapters of Lynn Margaret Batten's excellent textbook Combinatorics of finite geometries (Cambridge University Press 1986. QA 167.2 .B38 1986.), and the second chapter of Tim Anderson's Modern Algebra - an Introduction (Charles E. Merrill Publishing Company). It can be purchased as 640:195 text for $14 from Pequod (119 Somerset Street, New Brunswick, 732-214-8787).
We will also rely on seminar notes. Some of these are already posted at this site; further notes will be added by professors and students as we go along, so do check this site frequently. The names of the student speakers, more lecture titles, and other details will be added to the list of talks as they become known.
There are some useful notes posted by students of this seminar. As inspiring examples from the Fall '03 semester, look in particular at Aron Samkoff's Non-Euclidean Geometry and Vidya Venkateswaran's Fields and Constructible Numbers.
For bibliographical data, go to the excellent Scottish website of the University of St Andrews. You may want to start at the history page and browse, or go directly to the index of biographies.
Gino Fano (1871-1952)
September 2
(Profs):
A short history of geometry.
Reading:
A Short History of Geometry
on geometryalgorithms.com.
September 9
(Profs):
A general notion of subspaces; closure operations.
Reading:
Seminar notes on closure operations.
September 16, 23
(Amanda Yan and Anthony Barker):
Near-linear spaces: points, lines, subspaces, spanning sets,
independent sets, bases, dimension.
Reading:
Sections 1.1-1.4;
seminar notes on linear algebra.
September 30, October 7
(Kathy Cammidge and Alex Conway):
Linear spaces, numerical properties,
the de Bruijn-Erdös theorem.
Reading:
Sections 1.5-6 and 2.1-3.
October 14, 21
(Mev Fudda and Aori Nevo):
Functions, linear functions, collineations.
Reading:
Sections 1.7 and 2.6.
October 28
(Profs):
Groups, fields, finite fields.
Reading:
The second part of our text: Congruences and Abstract Number Systems.
See also our past seminar notes on basic algebraic structures,
and on groups and fields.
(For a gentle introduction to group theory visit
dogschool.)
November 4
(Amrita Aranake):
Back to bases.
Reading:
Sections 1.4 and 2.4.
Seminar notes on subspaces.
November 11
(Jessica Chen and Matt Astel):
Projective planes.
Reading:
Sections 3.1-3 and 3.7.
November 18
(Lia Hidalgo and Rob Burton):
Affine planes.
Reading:
Sections 4.1-3 and 4.6.
December 2
December 9
(Prof. Diane Maclagan):
The game of SET
and its relation to affine planes and coding theory.
Reading: