From High School Arithmetic to Group Cohomology

course notes
Mathcamp
algebra
Group extensions and exact sequences, arrived at by taking carrying in multi-digit addition seriously.
Published

July 2, 2019

\[ 0 \longrightarrow \mathbb{Z}/10 \longrightarrow \mathbb{Z}/100 \longrightarrow \mathbb{Z}/10 \longrightarrow 0 \]

A week-long class from Mathcamp 2019 based on a fun paper by Dan Isaksen titled A cohomological viewpoint on elementary school arithmetic. It introduces group extensions and exact sequences as a way to interpret the addition of multi-digit numbers.

It is designed in an IBL format. The prerequisites are group theory.