# Leran Cai

I am currently a final year PhD student, fully funded by Trinity College (Internal Graduate Studentship). My interest lies in algorithms, probability theory and graph theory. Now I am working on random walks on dynamic graph models and supervised by Dr. Thomas Sauerwald.

I earned my Master's degree in Advanced Computer Science from the University of Cambridge in 2016, passing with distinction.

## Publications

**Cai, L.**, Sauerwald, T. (2017) **Randomized Load Balancing on Networks with Stochastic Inputs**. *The 44 ^{th} International Colloquium on Automata, Languages, and Programming (ICALP 2017)*. [arXiv version; Conference version]

## Ambition

I have an ambition: to write a series of notes/books about all the intuitions on the maths I have learned. These notes/books should be great materials for theoretical computer science PhD students or students who want to learn advanced mathematics in a more efficient way. Textbooks are too formal since they mostly serve as references. Lecture notes on maths from OUR MATHS DEPARTMENT or other universities like MIT/Princeton/Yale/Stanford/CMU etc. also lack intuitive explanations. When you are not a student in these universities, or do not get trained for things like IMO in your high school, you would encounter a lot of touble when self learning those materials. Sometimes one typo in these notes can waste you maybe longer than 3 hours to find out whether it is a typo or it is just simply because you are too stupid to understand it. I believe that no one is too stupid to learn maths. We just need correct materials with vivid examples or nice intuitions.

I want to have all things formal and rigorous, but with very good intuitions collected from all sources, metaphors or even jokes. I hope in the end, I could say "Maths is fun to read. I wish I could have these notes when I started my PhD". I got the idea of naming these notes from the book "All of statistics" by Wasserman. Here are some sample chapters:

## Supervisions/Problem Classes

I have supervised, the following courses:

- Advanced Algorithms (Easter 2019)
- Algorithms (Lent 2019)
- Foundations of Data Science (Michaelmas 2018)
- Discrete Maths (Michaelmas 2018)
- Algorithms (Lent 2018)
- Foundations of Data Science (Michaelmas 2017)
- Advanced Algorithms (Easter 2017)
- Algorithms (Lent 2017)

I also taught the problem classes for the following courses:

- Probability and Computation (Lent 2019)

As a product of preparing these supervisions, I have also created some notes to help students revise for their exams.

## Contact

**Address:**

Leran Cai

Office FE13

Programming, Logic, and Semantics Group

Computer Laboratory

University of Cambridge

15 JJ Thomson Avenue

Cambridge CB3 0FD

United Kingdom

**Phone:** +44 (0)1223 763722

**Email:** leran [dot] cai [at] cl [dot] cam [dot] ac [dot] uk