Beyond this course

Outside reading

There are modern-day applications of the theory of groups. Here are some sources that talk about these applications, all of which are based on the theory of groups.

• Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival Links to an external site.. (The basis of "Mapper" is to create certain groups out of the shape of data, and to see at what scale these groups change.)
• From 5 to 13: Redefining the Positions in Basketball Links to an external site.Topology-based data analysis identifies 13 basketball positions. Here are the accompanying slides. Links to an external site.
• The NSA Back Door to NIST Links to an external site.. A short article about the algebra behind some common cryptography standards.

Here is also some reading that puts the history of group theory in context:

• On the work of John Thompson. A speech by Brauer explaining why Thompson was awarded the Fields Medal in 1970.
• The Wikipedia page on Galois. Links to an external site.
• The Wikipedia page on Emmy Noether, Links to an external site. who was easily one of the most influential mathematicians since 1800. Her influence is especially felt in algebra---for example, she was one of the first proponents of universal properties as a means to understand an object.