Resources I found useful as 1st year PhD student

October 29, 2023

Below are some resources that helped me build a good foundation in probability, measure theory, and related topics in applied mathematics.

First, I revisited the basics of probability through Stanford CS109. This course is a clear and concise introduction, which helped me recall essential concepts.

To dive deeper into theory, I watched the Bright Side of Mathematics Measure Theory course. It does a great job explaining why measure theory is important, which motivated me to keep learning. I also recommend Professor Lanchier’s Advanced Probability and Claudio Landim’s Measure Theory course for a more detailed approach.

After covering the basics, I looked at applications of probability in different fields. Markov Processes by J.N. Corcoran is an easy-to-follow introduction to many core ideas in applied probability, and Corcoran’s Mathematical Statistics lays out key topics from statistics. R. Vershynin’s High Dimensional Probability is a bit more advanced but offers a introduction to key tools like concentration inequalities and highdimensional tools in probability. If you want a solid introduction to theoretical machine learning, S.B. David’s Learning Theory is excellent.

Since ideas from information theory show up in both machine learning and differential privacy, I decided to study D. MacKay’s Information Theory, pattern recognition and neural networks along with the book from the same author.

When it comes to understanding differential privacy, G. Kamath’s Differential Privacy is a clear introduction to this field. Another course that I found fascinating was J. Nelson’s Sketching Algorithms, which covers a wide range of advanced topics in probabilistic algorithms. If you need optimization methods for machine learning (which can also apply to differential privacy!), check out M. Jaggi’s Optimization for Machine Learning.

Strong writing skills are important for sharing ideas. I found The Elements of Style and How to write a great paper by S.P. Jones helpful for improving my writing style. I also enjoyed reading Oded Goldreich’s blog, such as How to write a paper and On the emotional difficulty of conducting research. These pieces made me more aware of both the technical and personal sides of research.