Math platform for finding gaps in knowledge

Question

I'm currently pursuing a specialization in Data Science, and in need of brushing up on some of my Algebra I and II before I take on some heftier topics in Linear Algebra and Calculus.

It's proving difficult however, to properly identify where the gaps in my knowledge are, even by taking practice tests and seeing where I've gone wrong.

Does there exist a platform where there is a central test, or a test per topic, whereby through machine learning, is able to tell me the areas in my math knowledge which are in need of improvement?

Thanks!

Answer 1

I don't know how much machine learning it uses, but “a platform where there is […] a test per topic” that could determine “the areas in [one's] math knowledge which are in need of improvement” suggests Khan Academy (website, Wikipedia). From what I recall of how it works, Khan Academy, which offers a range of subjects,^[1]

• will present a range of practice exercises and use one's answers thereto to decide what one already knows and what one should study and
• offers many short videos and readings with which to do that studying, although one is largely free to substitute, or to supplement with, other learning materials, if one prefers (for example, once you do reach linear algebra and calculus, you might like to try 3Blue1Brown (website, Wikipedia), whose host, Grant Sanderson, happens to have started out producing videos for Khan Academy).

I think Khan Academy is a generally well-made platform presenting (and slightly gamifying) a good range of mathematical exercises in such a way that it's easy to flow from one to the next.

Incidentally, since you mention linear algebra, I note that Khan Academy's linear algebra content, as of 2020, is not as developed as its calculus and lower-level content. If you decide you like Khan Academy's model of short problem sets mixed with short videos, then, for linear algebra, you could consider Lemma, which I discuss in answer #3893378. Lemma has a much more developed course in linear algebra and, unlike Khan Academy, is (as far as I'm aware) intended to be a complete resource by which to learn the subject (whereas Khan Academy is intended as a supplement to classroom instruction). If, alternatively, you prefer reading over watching, you could try the award-winning free linear algebra textbook of Jim Hefferon, which I recommend in answer #3907967.

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[1]: These currently include “Algebra 1”, “Geometry”, “Algebra 2”, “Trigonometry”, “Precalculus”, “Statistics & probability”, …, “Multivariable calculus”, “Differential equations”, and “Linear algebra”, as well as subjects outside mathematics.