Computer Laboratory

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.


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


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:

I also taught the problem classes for the following courses:

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


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