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by max_ 905 days ago
I really like mathematics and I spend some time reading obscure math books for kicks.

I was a very bad math student in highschool I don't think it was because I was "ungifted" like some people would describe it.

Towards the end of high school i.e the last year.

I found out that mathematics can be studied like Biology, History (too late for it to make an impact on my final results).

And that the only way of learning mathematics was not just through practising it mindlessly until you grasp it like the teachers said.

I think the real problem with mathematics is that it has really bad comprehensive literature.

Here are the 3 main problems with maths literature. (What I think would have helped me improve my maths skills by alot)

Reason 1.

Implicitly defined notations. There is really no go to comprehensive resource that describes all math notation clearly so jumping into a new topic is difficult.

Reason 2

No clear definitions of algorithms used in respective math topics.

A great example is http://matrixmultiplication.xyz/ that describes the matrix multiplication algorithm. Step by step. Maths education would be better if all important algorithms in different math fields were described as clearly.

Reason 3

There is no comprehensive dictionary for math theorems. A great example would be something like a table of integrals in calculus, but for all fields.

If all these resources are well documented. I really don't see why someone cannot improve their maths skills even via self study up to graduate level.

3 comments

Oh, thank you for this. I had a similar experience as yours and when I wrote down notes when studying, I ended up with cheatsheets that described things clearly, even though it took me hours tp grok. I never understood if the problem was me or just poor books (I needed to rely solely on the teacher, which is very limiting). I see that there is indeed a problem
Thank you for a great response! I agree with you on communication-styles. Math education could definitely use some more clarity in exposition of procedures and notation. With regards to reason 3, this is true for me at least! Much of my learning during and after bachelors was self study.
> There is really no go to comprehensive resource that describes all math notation clearly so jumping into a new topic is difficult.

Introductory literature for a new topic should always explain new notation. If not, either it’s really badly written or you accidentally chose a non-introductory book.

> There is no comprehensive dictionary for math theorems.

What’s wrong with Wikipedia?