A self-guided journey to patch up my knowledge gaps

Patching up holes in my knowledge

Published: 2025-11-07

Imposter Syndrome? Or real gap in knowledge?

For the longest time, I have been feeling my foundation in science is sloppy. This includes Mathematics, Statistics, Computer Science, and even physics. During my undergraduate and graduate studies, I was laser focus on research, which gave me an unusal breath in what I kind of know about. However, this means I did not go deep enough in many fundamental areas. Just to list a few: Linear Algebra, Probability Theory, Algorithms, Data Structures, Electromagnetism, Classical Mechanics, etc. Not like I don’t know about them, but if a random undergradute student roll up and start asking me to explain what is a measure or why certain machine learning algorithm works, I would have to look it up.

After so many years in research setting, this insecurity has been growing. I feel like I am starting to rely on just googling thing too much. By all means, knowing how to look for solutions and implement them is extremely useful, and way more relevant to research than grinding through pills of textbooks and storing knowledge in my brain that I may never use. If you survey a wide distribution of academics, they may say “oh this is normal, I only actively know my field.” While there is some truth to that, I am not quite satistified with this state. I have met many people that seems to know many things deeply all the time, and I always wonder whether I am just dumber or have I just not put enough time into reading and reflecting. And that’s why I decided to finally do something about it.

A self-guided pilgrimage

In order to maintain an optimal body condition for high jump, I have very strict sleep schedule, which includes staying off screens at least an hour before sleep, which is 2100 every night. Also, I figured 1600-2100 everyday is considered peak hour for electricity usage in my area, which makes using my computer setup super expensive. On top of these two factors, because now I do not have any academic pressure or work deadlines, I have a lot of time in the evening to read books and learn things. So I decided to dedicate my evening every day to finally going through the materials I always feel I should have spent time on.

Instead of taking online courses, I am much more comfortable with self-studying from textbooks. When I was taking courses, from time to time I would feel things are too easy and I dosed off, then I figured I have missed something I shouldn’t have. In the end, courses are often structured around a textbook anyway, so I might as well just read the textbook and tailor a study plan that I know is going to work for me.

Topics and methodology

While you have find the detail topics I am going through here, here below is a list of subjects I am going to cover:

Pure Mathematics, with a focus to develop a rigou rous understanding of linear algebra, differential equations, stochastic processes, and measure theory
Foundational Physics, including Quantum Field Theory and General Relativity
Computer Science, especially low level system design, algorithm, and theoratical computer science
Electrical Engineering. Mostly entry level signal processing and communication theory, plus practical skills.
Clean up my Japanese to prepare for JLPT, and systematically learn Italian and German.

For most of them except languages, I will be following spiral learning model: first I am going to scan through the textbook and outlining some key concepts and questions for each topics, then I will go over each chapter bit by bit but not to a point that I am stuck. Once I am done with the second pass, I will revisit the entire book and type up a set of notes and guides on the GitHub repo. The first pass is to get a bird eye view of the subject so I can better orient myself, the second pass is to rigorously go through the material, and the third pass is to consolidate my understanding to make sure I have really internalized the knowledge.

At this moment, I am still just looking through university curriculums in these topics to pick suitable textbooks. From time to time I may make videos on especially interesting topics I encounter. I am quite excited to finally learn these things properly, who said we can only learn in school?