# Math 401

This is a course about symmetrical group and bunch of applications in other fields of math.

Prof. Renado Fere is teaching this course.

The course is split into two parts:

1. Symmetrical group
2. Summer research project

## Symmetrical group (Spring 2025 Course)

Notes from N1-N3.

Basically are overview of some interesting topics related to symmetrical group or other related math topics.

I don't record them carefully, but I will try to update them if they are necessary for my future reference.

## Summer research project

### Schedule

Presentation starts next week

Start with examples, do exploratory work, it's just a summer.

Final work: Find certain topic you are interested in, and do a expository paper.

Find the motivation, background, definition, theorem, example, application for the theory you are interested in.

At least 3 presentations is required.

Collect the papers you interested in as you go the research, it is not linear.

Symposium on November.

Lightning talk (3 minutes) on end of July.

### Topic of interest

I am interested in the following topics:

1. Quantum error correction
2. Von Neumann algebra and other operator algebras which are related to quantum algorithms

### Notes

T1-T7 should be the notes for the spring course Math 444. Taught by Prof. Renado Fere on Spring 2025 but I don't know that and they are helpful for understanding the material for the book that might contains my subject of interest.

[The Functional Analysis of Quantum Information Theory](https://arxiv.org/abs/1410.7188)

The original lecture notes, by Prof. Renado Fere, are here, may move to other places. Last updated on 2025-06-14.

[Math 444 Spring 2025 Notes, Lecture 1](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes01.pdf)

[Math 444 Spring 2025 Notes, Lecture 2](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes02.pdf)

[Math 444 Spring 2025 Notes, Lecture 3](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes03.pdf)

[Math 444 Spring 2025 Notes, Lecture 4](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes04.pdf)

[Math 444 Spring 2025 Notes, Lecture 5](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes05.pdf)

[Math 444 Spring 2025 Notes, Lecture 6](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes06.pdf)

[Math 444 Spring 2025 Notes, Lecture 7](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes07.pdf)

[Math 444 Spring 2025 Notes, Lecture 9](https://www.math.wustl.edu/~feres/Math444Spring25/Math444Spring25Notes09.pdf)