CF relevance: Math skills are a philosophy prerequisite.
Do you want unbounded criticism? (A criticism is a reason that an idea decisively fails at a goal. Criticism can be about anything relevant to goal success, including methods, meta, context or tangents. If you think a line of discussion isn’t worth focusing attention on, that is a disagreement with the person who posted it, which can be discussed.) Yes.
I am seeking recommendations for mathematics learning materials that you’d consider high or above average quality. Beginner to intermediate skill level. Preferably with exercises, but not essential.
What math do you already know, and what math do you want to learn? “Beginner to intermediate skill level” means nothing to me; I would need more context.
I know arithmetic, some basic algebra, and some basic geometry; enough for use in my day to day life. I want to revisit these subjects to sure up my conceptual foundations so I can build on them.
Solving systems of linear equations falls under a subject called linear algebra, which is typically taught to 1st or 2nd year university students.
By contrast, prime factorizations and fractions are typically taught to elementary schoolers (according to chatGPT; it sounds right though).
Unfortunately, I can’t give you recommendations for how to learn fractions or prime factorization, because I learned about those things before I learned math from books, and I have no experience teaching them.
I could give you a recommendation for linear algebra learning material if you want, but it would probably be better to focus on things like fractions & primes first if you don’t think that you have mastered those.
I would appreciate the recommendation still. I will take your advice on where to focus first, but it would be good to know where I can find the linear algebra material when I do need it. It would also be helpful to be able to look through it and see what I do and don’t understand.
On Khan Academy’s algebra 1 course, it looks like they only learn how to solve systems of 2 equations in 2 unknowns. That is not the most general linear equation. Maybe it’s what LMD was thinking of, though.
I recall that at one point when I was in middle school, my teacher tried to teach us how to solve 3 or 4 equations in 3 or 4 unknowns as well, but it just amounted to teaching us a rote algorithm. The real explanation of why it works and what’s going on requires the concepts of linear algebra. That being said, linear algebra could probably be taught to students much earlier than it is. However, it still definitely requires fractions and primes.
Okay. I guess that the textbook I would recommend for learning linear algebra properly is Linear Algebra by Friedberg, Insel, and Spence. It meets your criterion of being better than average, and having exercises. The prerequisites are technically just high school math, but it’s more difficult than most math books with similar prerequisites, because it’s proof-based rather than computation-based. (A math course or textbook being proof-based is a good thing; it means that it is focused on explanations rather than memorizing algorithms by rote.)
I am quite unfamiliar with systems of linear equations, so didn’t have any such details in mind. I was advised that an understanding of systems of linear equations (among other algebra concepts that I considered myself more knowledgeable of) will be valuable as a prerequisite for philosophy and programming. However, I haven’t looked into the concept myself yet. That a higher skill concept like systems of linear equations is at the top of the list in my post is accidental. [edited: see original quoted in my subsequent post]
Thanks for the recommendation. Proof-based sounds like the kind of understanding I would prefer.