# Learning To Read Mathematical Notation?

August 12, 2015 1:42 PM Subscribe

I do not have a math background, but I have been learning statistics for work and while I understand the concepts, I am having a really hard time reading mathematical notation (proofs, formulas, etc). It feels like I missed the 101 class in reading the language of mathematics.
Are there particularly good resources out there on reading Mathematical Notation?

I second linking us an example. I have a math degree but I'm not sure what kind of notation you are running into. If it's primarily proofs, the class where I learned that was called Real Analysis so maybe one of those textbooks would help you. I know mine had an introduction on proofs and logic and notation.

posted by FireFountain at 3:29 PM on August 12, 2015

posted by FireFountain at 3:29 PM on August 12, 2015

this page is more focussed on statistics. but it doesn't have angle brackets which is odd (i am having a hard time finding a page that includes angle brackets for expected values, so i am wondering if that's some brit / physics notation that's not generally used).

posted by andrewcooke at 3:31 PM on August 12, 2015

posted by andrewcooke at 3:31 PM on August 12, 2015

You can't approach mathematical notation as though it were a language with a single, well-defined, fixed syntax and set of symbols in which particular notations always have the same meaning.

Notation is more like a natural language: a collection of rules and conventions, some inviolate, others less so, with lots of idioms, some of which are mutually incompatible, and lots of variation between "dialects" (by which I mean conventions within various fields).

The answer is no. There is no reference manual and no way to decipher notation independent of context. You have to just keep reading and writing the language (of statistics, in your case) and absorb it through practice.

posted by BadgerDoctor at 3:37 PM on August 12, 2015 [3 favorites]

Notation is more like a natural language: a collection of rules and conventions, some inviolate, others less so, with lots of idioms, some of which are mutually incompatible, and lots of variation between "dialects" (by which I mean conventions within various fields).

*Are there particularly good resources out there on reading Mathematical Notation?*The answer is no. There is no reference manual and no way to decipher notation independent of context. You have to just keep reading and writing the language (of statistics, in your case) and absorb it through practice.

posted by BadgerDoctor at 3:37 PM on August 12, 2015 [3 favorites]

What helped me was learning some of the greek alphabet so stuff become googleable. Also writing down some equations and asking someone who was familar with it to speak them out loud so I could understand the order of things came out. It really is rote, so using it is what will help you the most.

Also consider using tex or one of it's derivatives. If you can write math in tex, you can speak it and you will quickly learn what everything means and how to talk math to other people.

The page I started with was Summation on wikipedia. Look at the source, which is tex!

posted by bensherman at 4:06 PM on August 12, 2015

Also consider using tex or one of it's derivatives. If you can write math in tex, you can speak it and you will quickly learn what everything means and how to talk math to other people.

The page I started with was Summation on wikipedia. Look at the source, which is tex!

posted by bensherman at 4:06 PM on August 12, 2015

It's also not unreasonable to make flash cards for yourself for common symbols and where you typically encounter them. Every branch of math has its own idiosyncrasies, but if you're mostly sticking to statistics and possibly even mostly sticking to one book, you'll find enough consistency that you could say things to yourself like:

- "Okay, thing that looks kind of like a big capital E... That's a capital sigma. It's usually for summations."

- "So this thing that looks like an x with extra-long descenders is a chi (pronounced "kai") and I'll usually see it when something's talking about how well a fit matches up to some data."

Also, dyscalculia is a thing; if you find that you just really cannot make any headway at all with symbolic notation, that could be the culprit. I've tutored a couple folks with dyscalculia and they had some success with writing out everything in words, which can get very unwieldy very quickly -- that's why we have notation in the first place -- but it beats not getting any of it. (They came to me already diagnosed, so I'm not sure what the process is.)

posted by dorque at 6:28 PM on August 12, 2015

- "Okay, thing that looks kind of like a big capital E... That's a capital sigma. It's usually for summations."

- "So this thing that looks like an x with extra-long descenders is a chi (pronounced "kai") and I'll usually see it when something's talking about how well a fit matches up to some data."

Also, dyscalculia is a thing; if you find that you just really cannot make any headway at all with symbolic notation, that could be the culprit. I've tutored a couple folks with dyscalculia and they had some success with writing out everything in words, which can get very unwieldy very quickly -- that's why we have notation in the first place -- but it beats not getting any of it. (They came to me already diagnosed, so I'm not sure what the process is.)

posted by dorque at 6:28 PM on August 12, 2015

My gut feeling for how to read and use mathematical notation came from my high school algebra, geometry, and calculus classes. Familiarity comes with time.

If you come across a symbol you don't recognize, you can draw it in Detexify. Detexify will often give you the TeX macro name for the symbol, which makes it easier to Google or say.

posted by grouse at 6:42 PM on August 12, 2015 [1 favorite]

If you come across a symbol you don't recognize, you can draw it in Detexify. Detexify will often give you the TeX macro name for the symbol, which makes it easier to Google or say.

posted by grouse at 6:42 PM on August 12, 2015 [1 favorite]

Wikipedia has this page which might be helpful. There's notation and symbols which you can just study, and then there's fluency with algebraic manipulations, which requires practice solving problems.

posted by vogon_poet at 6:58 PM on August 12, 2015

posted by vogon_poet at 6:58 PM on August 12, 2015

As a glossary, this wikipedia table is quite thorough, and tells you not only the meaning of the symbols but also how it's customarily said aloud (in the 2nd subrow of the 3rd column for each definition of the symbol) and an example of its notational usage.

posted by Westringia F. at 10:44 PM on August 12, 2015 [1 favorite]

posted by Westringia F. at 10:44 PM on August 12, 2015 [1 favorite]

This is a subtle issue, but I know what you mean -- I went to college at a very fast-paced, science-only school. We were learning math at breakneck speed, with all of these weird symbols that nobody knew the names of.

Someone would be like, "Oh, the answer is n choose n-1" and I'm like, "WTF does 'choose'" mean?

One thing to try might be to watch some statistics lectures online (on youtube), so that you can read the words on the professor's slides/notes and hear their voice "read" or describe the symbols. (That is how I learned them)

As an example, wait for 1:18 in this video, from Khan Academy: https://www.youtube.com/watch?v=hgtMWR3TFnY

Other's suggestions of using the greek alphabet and looking at LaTeX tables are good, too.

You can also check out Wolfram's math world: http://mathworld.wolfram.com which is an excellent general reference.

posted by amy27 at 11:26 PM on August 12, 2015 [1 favorite]

Someone would be like, "Oh, the answer is n choose n-1" and I'm like, "WTF does 'choose'" mean?

One thing to try might be to watch some statistics lectures online (on youtube), so that you can read the words on the professor's slides/notes and hear their voice "read" or describe the symbols. (That is how I learned them)

As an example, wait for 1:18 in this video, from Khan Academy: https://www.youtube.com/watch?v=hgtMWR3TFnY

Other's suggestions of using the greek alphabet and looking at LaTeX tables are good, too.

You can also check out Wolfram's math world: http://mathworld.wolfram.com which is an excellent general reference.

posted by amy27 at 11:26 PM on August 12, 2015 [1 favorite]

I think the main thing about reading math is that you just have to go really slow and pay a lot of attention. It's not the notation per se that's difficult, it's the density of information that the notation allows. We learn when reading prose how to race through a sentence and pick out the gestalt. But in math, every detail counts, so you have to go slower. And it's usually written in a linear way, so you generally want to wait till you really understand each piece before moving onto the next.

It's also very useful to read math with a pen and paper. So whenever something isn't quite clear, you can write it down for yourself, try rephrasing it in various ways, and play around with it till it makes sense.

Good luck!

Edit: Oops, had a brain fart and didn't realize this post was from 6 months ago! Leaving my comment up in case it's useful to someone later.

posted by gold-in-green at 8:40 PM on January 3, 2016

It's also very useful to read math with a pen and paper. So whenever something isn't quite clear, you can write it down for yourself, try rephrasing it in various ways, and play around with it till it makes sense.

Good luck!

Edit: Oops, had a brain fart and didn't realize this post was from 6 months ago! Leaving my comment up in case it's useful to someone later.

posted by gold-in-green at 8:40 PM on January 3, 2016

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ps in my experience it really helps to sit down and translate it part by part to english. so you read out loud "for all ... there exists .... such that ...".

posted by andrewcooke at 3:16 PM on August 12, 2015