This Year I Tried to Teach Myself Math

I also share the sentiment that the path of the self-guided math student is a hard one, especially when there is an end goal desired, such as learning ML. The single most important lesson here (I learned) was identifying what textbooks were ideal. In general, I would say the unusual textbook preface that omits the usual prerequisites (that most others demand of a student) are safe bets. For example, I was surprised that Complex Analysis: A First Course with Applications, 3e (Zill Shanahan) actually delivered on its promises from its preface (I didn't even have to understand real analysis!).

The quagmire of breadth vs depth is an almost impossible one when it comes to mathematics. A long time ago I came across The Princeton Companion To Mathematics and bought it first when I began teaching myself mathematics. Easily the best decision I ever made in regard to shedding light on this mystery.

I should write an article about how to select textbooks since it's nepotism all the way down. In reality, there is almost always a "sweet spot" that applies to any student irregardless of prior experience or knowledge and of the given subject (not just mathematics). For example, C Programming: A Modern Approach, 2e (King) was by and far not the obvious canonical text on C (to this fact, the author concedes it's K&R) but having read K&R I found beauty, but its genius wasn't intended entirely (if at all) as a student textbook.

The fact that the textbook industry makes it near damn impossible to simply get a decent preview or general idea of a textbook before purchase, coupled with the fact that Amazon is complicit in that they profit each time you buy a unfit textbook, is truly a tragedy. This engenders the impression to a student (of any age) a certain learned helplessness they may carry for the remainder of their life. One must be prepared to toss their coin along with their book in the trash.

This problem can be solved, but for now all I can recommend as a heuristic is just write a script to crawl for PDFs that are at least 1mb in size (which I actually may do today, ha) along for other obvious meta data such as ISBN, Title, Author, etc. But this is simply to just decide on whether to buy the actual book (if possible); not many realize this, but the art of textbook publication is a parity to film production, it's expensive, exhausting, and time consuming. I personally can't tolerate a poorly digitized textbook anyways.

In my experience, one need not wander too far away from the major publishers for undergraduate textbooks and for upper division or graduate textbooks there simply is a canonical text or none at all (worthwhile). This is because, for example, almost all students are going to have to find a youtube video to demystify the Epsilon-Delta definition of a limit. Thankfully we now live in a day an age where this process only takes about five minutes. In regard to taking online courses (Udemy, Coursera, etc), all I've learned so far is that they are as hit and miss as textbooks are, if not more so.

Love and Respect,