It's a common issues with self-learners, mathematics or not: there is no perfect course out there, and switching from courses to courses can be wasteful.
In my experience, focusing on a single, good-enough course (when in doubt, go for a famous/respected author/field contributor) and looking for other sources once in a while, has been the best approach.
Applies the same to job search too. Find one that is good enough and then work from there for future prospects. Often, the definition of “good” changes over time as priorities in life change.
We do this with all demanding endeavours. Circling around the tactical perimeter is easier than knuckling down and getting it done. But it's close enough that we can fool ourselves into thinking we are being productive.
Many examples:
- It's easier to research the "best textbook for me" than it is to study and do problems.
- It's easier to read about the optimal periodization cycle while sitting on the couch than it is to go sweat in gym.
- It's easier to read about dieting (it must be the best diet for meee!) than it is to just stop ordering pizza.
- It's easier to order business cards and redesign your logo than it is to find customers.
- It's easier to fiddle with your vim config than it is sit down and write code.
Unless you are already in top 10%, focusing on optimality is a distraction.
And if you pick up the wrong one, you might just end up dropping the whole ordeal. It's not so black and white, it makes sense to spend a bit of time and figuring out a good resource. At the least you'll get a sense of the domain's main trunk of knowledge, get into the jargon, etc.
Yeah, this is it. A year ago if I tried to find the perfect textbook to learn Linear Algebra, I would still be looking.
There are certainly good and bad textbooks, and a book good for many people might be unsuitable for your style, your goals, and your background. But there are plenty of good enough textbooks, trudging through any of them will yield far more benefits than getting that ideal book.
I like that he leaves determinants to a later chapter and doesn't _start_ with them, I never understood why they were useful or made sense. His view, represented on the cover, is great for learning
They're fine where they are useful, I guess, but my undergrad put way too much emphasis on them when they're not intuitive, don't help (me) much with comprehension, and aren't useful in that many cases compared to the other techniques.
Surely the optimal solution would be to spend a few hours / days in the first week picking the textbook, then 51 weeks studying it, as opposed to literally picking the first one you see and studying it for 52 weeks.
Not equally, better. It's intended as a book for learning the concepts of Linear Algebra intuitively and with some introductory rigor, before doing it "right" in a professional way.
The optimal solution is to find a good enough textbook and start as soon as possible to learn and tonstop procrastinating.