(HEADS UP) Lecture 0 on Mar 24 will be a watch party of Lijie Chen's [virtual talk] ( https://iiis.tsinghua.edu.cn/show-10741-1.html ) on "Theoretical limitations of multi-layer Transformers". See below for details.

Compared to regular "Algorithms and data structures", there are two main adaptations:

1. This course will be presented in languages comfortable to mathematicians. In addtion, materials with richer mathematical structures are prioritized.

2. There will be a bit more computer architecture (i.e. hardware) knowledge as mathematicians have less access to it, despite its importance in dictating algorithm design and hence the mathematics of computer science.

It works the best if the audience have an idea of a regular "Algorithms and data structures" and would like to understand better as a mathematician. In a sense, the course is designed for my freshman/sophomore self, in the hope of saving the later year detours.

Plan:

1. Computer architecture and why we care (2 lectures)

2. How to store math object in computer memory: hash table, union-find, graph. We may cover the recent breakthrough result of arxiv:2501.02305 (4-8 lectures)

3. Some algorithms are "meta" algorithms that work across many different data types. We'll cover two (or more, depending on time) of them:

3.1 greedy (4-6 lectures)

3.2 Gaussian elimination (4-6 lectures)

We'll study their various incarnations including minimal spanning tree, shortest path and Kleene's algorithm.

Language: depends on audience

Lecture 0:

The talk starts 9:45. I'll review some history at 9:30. Then we all sit in the classroom and watch the virtual talk. All are welcome.

Registration: https://www.wjx.top/vm/Ohx2vsb.aspx#