Misc. Notes, Slides, and Writeups
Most of my mathematical notes are handwritten and most of my talks have
been given on a whiteboard. Below is a list of exceptions.
Cryptography Slides
Here are slides from talks given to an audience of graduate students with
no prior background assumed on the topic of mathematical cryptography.
The other talks I gave were whiteboard talks.
Here is a talk I gave to an audience of graduate students who didn't have a
background in algebraic geometry, but wanted to know how analyzing systems
of polynomial equations gets translated into commutative algebra: The affine algebraic
connection
Solution Sets
At some point I had the itch to typeset solution sets to "baby" Rudin and
Atyiah-MacDonald's Introduction to Commutative Algebra.
Both sets are fairly comprehensive for the chapter range listed.
Use at your own risk, but feel free to send me comments or corrections.
Interactions with other students
The following notes came out of interactions with other graduate students.
Sometimes when I am asked a question, it bugs me until I write up the answer.
- The question of whether taking fixed points commutes with base-change
for group representations was asked at tea.
Fixed points and base change
- A friend asked for a concise refresher on measure theory.
Measure theory synopsis
- Another student said something about complex numbers raised to
rational powers as having two definitions. I wrote a note to clarify
the implications of "multi-valued" functions.
Multi-valued complex
exponents
- The question was asked about the relation between topologies of
Z_p[[x]]. The (x)-adic topology is courser tha that (p,x)-adic topology.
Topologies on Z_p[[x]]
- A a followup to a discussion with a friend who was working through
Qing Liu's book. He wanted a better grasp of flatness and the functor
of points.
Flatness and the
functor of points
- Explicit elementary demonstration of a presentation for the Quaternion group of
order 8. Typeset in my capacity as a TA for graduate algebra.
A presentation of Q8
- Classification of groups of order 12. Typeset in my capacity as the
leader of algebra qualifying exam preparation.
Groups of order
12
- Classification of groups of order 2015. Typeset in my capacity as the
leader of algebra qualifying exam preparation.
Groups of order
2015
- All normal subgroups of the permutation group of a finite set are
subgroups of the alternating group. Typeset in my capacity as the
leader of algebra qualifying exam preparation.
Normal
subgroups of finite permutation groups
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