Ask HN: How can I learn to read mathematical notation?

#1

Post by cursorial » Thu, Nov 22, 2018, 3:32 PM UTC

There are a lot of fields I'm interested in, such as machine learning, but I struggle to understand how they work as most resources I come across are full of complex mathematical notation that I never learned how to read in school or University.

How do you learn to read this stuff? I'm frequently stumped by an academic paper or book that I just can't understand due to mathematical notation that I simply cannot read.

Re: Ask HN: How can I learn to read mathematical notation?

#2

Post by ColinWright » Thu, Nov 22, 2018, 3:36 PM UTC

I don't know of any easy way to learn to do this from the outside without coming up through the ranks (as it were). The only thing I can suggest is to get a few examples, and ask some friends, colleagues, or on-line forums what they mean. Pick one or two, and ask in different places. The level of assistance you can get from a well asked question in the right place can be extraordinary.

But be aware that mathematical notation is not, without context, unambiguous. So you might need to provide some context for what you're doing, or where you get the examples from. Some people think this is a weakness of mathematical notation to be solved, but I've found it tremendously powerful. There is no doubt, however, that it is an accidental barrier to entry.

So post a picture of a piece of notation, and maybe someone will either explain it, or point you at a book/website that you can read.

Re: Ask HN: How can I learn to read mathematical notation?

#3

Post by cursorial » Thu, Nov 22, 2018, 3:48 PM UTC

ColinWright wrote: post #2

I don't know of any easy way to learn to do this from the outside without coming up through the ranks (as it were). The only thing I can suggest is to get a few examples, and ask some friends, colleagues, or on-line forums what they mean. Pick one or two, and ask in different places. The level of assistance you can get from a well asked question in the right place can be extraordinary. But be aware that mathematical…

Ah, I see, so it's just a matter of reading something, not understanding it, figuring out what it means and learning from that rather than there being a place where I can specifically read up on it.

I guess I just need more practice.

Re: Ask HN: How can I learn to read mathematical notation?

#4

Post by ColinWright » Thu, Nov 22, 2018, 3:52 PM UTC

cursorial wrote: post #3

ColinWright wrote: post #2

I don't know of any easy way to learn to do this from the outside without coming up through the ranks (as it were). The only thing I can suggest is to get a few examples, and ask some friends, colleagues, or on-line forums what they mean. Pick one or two, and ask in different places. The level of assistance you can get from a well asked question in the right place can be extraordinary. But be aware that mathematical…

Ah, I see, so it's just a matter of reading something, not understanding it, figuring out what it means and learning from that rather than there being a place where I can specifically read up on it. I guess I just need more practice.

> ... so it's just a matter of reading something, not understanding it, figuring out what it means and learning from that rather than there being a place where I can specifically read up on it.

Not entirely ... but partially. That's one way you can start to learn. Usually formulas are presented with a broad gloss in English (or other) to let you know roughly what it is saying, with the formula just being a precise way of saying it that can subsequently be used in algebraic manipulations.

Example:

The force due to the Earth's gravity is represented by g at the surface, and falls off as an inverse square. Thus:

F_d = g(R/d)^2

where R is the radius of the Earth.

Re: Ask HN: How can I learn to read mathematical notation?

#5

Post by jjgreen » Thu, Nov 22, 2018, 3:56 PM UTC

From outside, one might think that the notation is universal and unchanging, nothing could be further from the truth: each field has its own take, its own conventions. One even finds groups within a field who "go their own way", and there are national differences too. Sorry.

Realistically, find a paper that interests you, hopefully they will list some expository text in the references (or a paper that they cite does). Get it and read it. There's not really any alternative if you want to understand the notation, it represents complex ideas compactly, so you need at least a basic grounding in those ideas.

Re: Ask HN: How can I learn to read mathematical notation?

#6

Post by peakai » Thu, Nov 22, 2018, 3:58 PM UTC

This used to stump me, but I went through the Cal1/2/3 series at a local university and it made reading ML papers much easier, you could try attending a local school if self-learning is proving too time consuming for you.

Re: Ask HN: How can I learn to read mathematical notation?

#7

Post by mlevental » Thu, Nov 22, 2018, 3:59 PM UTC

here's a dirty seceret: we (people that have mathematical training) don't read the notation very closely either. it's very much like reading code: i don't look very closely unless there's a pattern i don't recognize or one that's broken. so ironically reading notation is about ignoring notation :) the problem for you is that you simply haven't had enough exposure to know what the "patterns" are and hence don't have them chunked/mapped efficiently. unfortunately there's no "royal road" here and you simply have learn to enough math to know what these things are but i encourage you to skip notation that isn't intelligible and continue reading. having done that enough times you will eventually actually understand the notation.