Irena Swanson
Some of Irena Swanson's past teaching

Three lectures (Computation of primary
decompositions, Expanded lectures on binomial ideals,
Primary decomposition in algebraic statistics,
delivered
at the EACA's Second International School On Computer Algebra and
Applications,
June 2013, Valladolid, Spain.

Reed College,
MATH 112
Introduction to Analysis,
about 300 pages.
Still adding,
feedback appreciated.
In these notes,
I assume that the set of real numbers forms a complete ordered field.
You may instead check out almost identical notes:
Introduction to Analysis,
with construction of the number systems.

Summer Graduate Workshop at MSRI, Berkeley, 6 June17 June 2011
Coorganizing and lecturing with
Daniel Erman
from Stanford University/University of Michigan and
Amelia Taylor
from Colorado College.
The workshop will involve a combination of theory and symbolic computation in commutative algebra. The lectures are intended to introduce three active areas of research: BoijSoederberg theory, algebraic statistics, and integral closure. The lectures will be accompanied with tutorials on the computer algebra system Macaulay 2.
My first introductory lecture was on resolutions
and I got to the proof of the Hilbert's Syzygy Theorem
(at least of the graded modules).
You can get here the slide version of the resolutions talk.
My lectures two and three were on the EisenbudSturmfels paper
on binomial ideals.
You can get here my notes on binomial ideals (updated in June 2013,
in Valladolid, Spain).
I did not present lattices and characters neither in my lectures
nor in these notes;
I think the omission made the lectures more easily understable to beginners.

Reed College, Spring 2011,
MATH 411 Topics in Advanced Analysis: Functional Analysis.
Banach, Hilbert spaces;
compact, Fredholm, selfadjoint operators;
spectral theory; Lp spaces.
I am an algebraist,
but I love (teaching) analysis.
These
pdf lecture notes
are work in progress.
Many examples are worked out,
including counterexamples to the conclusions of big theorems
if various hypotheses are removed.
Feedback appreciated.

My lecture notes for the
School on Local Rings and Local Study of Algebraic Varieties,
ICTP, Trieste 31 May4 June 2010 in pdf format:
Integral closure of ideals and rings (pdf).
This school and conference was in honor of
Tito Valla,
and click here (pdf) for the song/poem in his honor that we sang
at the end of my last talk.
Here is Gemma Colome's recording of it.
To hear
what the singing could have been like,
click here(mp3).
The whistling accompaniment is by
Adam Boocher.

My lecture notes on
homological algebra (pdf),
delivered at University of Rome III in MarchMay 2010.

Reed College, Spring 2009, MATH 332 Abstract Algebra:
An elementary treatment of the algebraic structures of groups,
rings, fields, and/or algebras.
(These
pdf lecture notes
are work in progress.
Feedback appreciated.
In class I scatter some nonstandard topics only on Tuesdays,
but in the pdf notes they are all in one place.)
Created: 26 August 2011