My Math Self-Study Journey

I have always been interested in math since secondary school.  In college, I studied electrical engineering but thought about switching to computer science because that would allow me to double major in math.  I eventually abandoned that idea and completed my engineering degree.  However, I always regret about my decision since I ended up working as a software engineer anyway.

I retired 5 years ago and the thought of self studying math came to my mind.  Based on my own understanding, the bar of getting a math degree in an American college is actually not that high, compared to, say, my homeland Hong Kong.  First of all, math majors in Hong Kong would have completed the equivalent of Calculus II in the US when they graduated from secondary school.  Therefore, first year math majors in Hong Kong would start with real analysis right away.  Contrast with the US, a majority of math majors here would spend the first 3-4 semesters studying calculus and linear algebra, and only began real analysis when they're junior, 2 years later than math majors in Hong Kong.  To obtain a math degree at my college, University of Wisconsin-Madison, only 2 upper level math courses, Advanced Calculus I (real analysis) and Advanced Algebra I (abstract algebra), were hard requirements and the rest fell into the electives category.  So, a math graduate in US may know nothing about complex analysis or topology, which would never happen in Hong Kong, at least not in my time.

But I digress.

Given my age and my lonnnnnnnnnnnnng hiatus from math, I wanted to set a relatively small achievable goal for myself.  Therefore, I used the two hard requirements for math majors at my alma mater as a reference, and set out to self study real analysis as well as abstract algebra.  Three years ago, I went through the abstract algebra YouTube series by Michael Penn.  To be honest, I already forgot most of it.  But it doesn't matter.  It's for my own interest.  I'm perfectly satisfied with the fact that I once studied it and understood it (isn't this true for most of what we studied in school anyway?).  I also enjoyed the experience, and even the frequent struggles, when going through the materials because I find them beautiful.

Recently, inspired by Field Medalists Wang Hong and Deng Yu, I picked up where I left off 2 years ago, and began self studying real analysis.  The difference this time is that AI has become much more powerful and I want to use it as a studying aid.  In other words, AI would be my math TA (teaching assistant).  I'll be reporting my progress, albeit somewhat irregularly.  In particular, I would be sharing my experience with using AI as a tool for self studying college level math.

Stay tuned.

August 2026    

P.S. I'm not trying to bash or look down on US math education.  In my opinion, its math research is world class.  I'm just trying to point out the difference between US and Hong Kong regarding math at the undergrad level.  I genuinely believe that the hurdle is higher in Hong Kong than US in terms of graduate requirements for math majors.  I'm not comparing the quality of the people or the universities.