# Is there a resource for learning to read mathematical notation/equations/formulae?

Ideally, I am looking for an online resource. But a book or any other would help already.

Background: I am a senior teaching assistant in the field of business and statistics. Most of my students have not had formal training in mathematics, and neither have I. I notice many of our students have difficulty following the professor's lectures for the trivial reason that they do not know mathematical notation (the professor does have a math background). In my experience as a schoolkid and student, no-one has ever explained how to read an equation. The only reason I know, is that I have cobbled it together from what my professors have said while pointing to their equations, which they always acted we knew how to read already.

I have made some effort to look for such a resource with my search engine, but have not found anything approaching what I mean.

Caveat: I appreciate that there are many subfields of mathematics, and that they use vastly different notations. A general resource would interest me most (and be most useful to future readers of this question), but in my case I am specifically in need of the notations needed in statistical calculations, so: sum, estimate, average, indexing, etc.

• Do you mean something like en.wikipedia.org/wiki/Glossary_of_mathematical_symbols Sep 28 at 14:34
• Perhaps youtube.com/watch?v=ooqQZ-_f_bg (U. Adelaide, "Understanding Maths Notation"), goes from elementary math through calculus notations. I don't know a source that discusses the different meanings of "=" (identity, condition, equation to be solved, assignment/definition). Students with a weak background in math often do not distinguish these meanings. -- Overall, it's learning a new language and takes a lot of practice to be able to readily understand a lecture. Sep 28 at 14:35
• @Raciquel, this is great. Can you make it into an answer? Sep 28 at 15:37
• Is it only the math notation they are not understanding or the math in general? @Racquel below makes an excellent point. "Being told that, say, a capital sigma means summing numbers up does not prepare the student to follow the lecturer at the same speed that the lecturer will be reasoning about sums in their presentation. [...] fluency allows one, [occasionally], to predict what the next step in the lecture will be. That ability certainly makes the lecture more readily understood. Generally, math teachers seem to think that fluency is best attained by solving relevant math problems." Sep 28 at 22:07
• I think we need a bit more information as I don't see how a TA in statistics does not have knowledge of maths notation - How do they define the mean without that knowledge. Sep 30 at 13:08

The video, https://www.youtube.com/watch?v=ooqQZ-_f_bg (U. Adelaide, "Understanding Maths Notation"), goes from elementary math through calculus notations.

I don't know a source that discusses the different meanings of "=" (identity, condition, equation to be solved, assignment/definition). Students with a weak background in math often do not distinguish these meanings.

Overall, learning new math notation is like learning a new language. It takes a lot of practice to be able to readily understand a lecture. Being told that, say, a capital sigma means summing numbers up does not prepare the student to follow the lecturer at the same speed that the lecturer will be reasoning about sums in their presentation. I will say that fluency allows one, at least half the time, to predict what the next step in the lecture will be. That ability certainly makes the lecture more readily understood. Generally, math teachers seem to think that fluency is best attained by solving relevant math problems. If the student does not want to put in the work to be fluent, at least being able to decipher their notes will make their notes much more useful. I hope the video addresses that. I assume the students probably do not need to be fluent; otherwise, there should be mathematics prerequisite for the course. But if some want to be good at something, they ought to be aware of what choices they have to strive for that goal.

Here's a general workflow for identifying the meaning of an unknown mathematical symbol/expression:

1. use an online tool (like webdemo.myscript.com/views/math) to convert a drawing of the symbol/expression into Latex commands
2. ask ChatGPT (chat.openai.com, free version 3.5 is fine) what the math symbol/expression given by those Latex commands means
3. [added in response to Sue's comment] based on ChatGPT's explanation, perform Google searches for more specific information/examples/fact-checking as needed

Here's an demonstration on the expression $$\displaystyle \sum_{i=1}^n \textrm E[X_i],$$ which seems highly relevant to your specific use-case.

Step 1: Drawing $$\to$$ Latex Commands Step 2: Latex Commands $$\to$$ Summary

Step 3: Summary $$\to$$ More Specific Information / Examples / Fact-Checking  • Except that chatgpt often gives clearly false answers. It might be an ok first step, but you'd certainly want to check afterwards, to see if it just made things up. Sep 28 at 16:10
• Of course. That would be a good step 3. Will update answer. Sep 28 at 17:16

If you are a teaching assistant, you should ask your professor to give a short instruction of the notation he uses, this would be much better for you and the students. He could do it in a lecture or just give out a short paper with the commonly used notation an examples of use. like $$\sum_{k=1}^5 k^2= 1^2+2^2+3^2+4^2+5^2$$ This would be much better than any source in the net or book.

Questions about [reading-aloud] [mathematics] expressions are on-topic on the English Language Learners stack exchange. For example, this question asks how to read an equation including a summation, and another equation including integrals and limits. One of the answers has links to 3 guides.

Another question on this MathEducators stack exchange discusses why math uses shorthand so much.

Quarter of a loaf answer, but one of the things I like about some texts is that they will have a list of symbols, to include even Greek alphabet. And will have a glossary. It seems most appropriate for lower level books and within that foe review texts. And still only a sad small subsection of books do this. But in my mind a book is a tool snd these sorts of features, also add in a good index make the learning tool more helpful. So practically, what I suggest is just looking at several textbooks and seeing if a few have front or back sections like this that you like and can then plagiarize. The texts I know that do this well are the 1940s era US War Dept Ed Manuals. But if you just physically look through some college algebra a calc and such texts at a brick and mortar library you should find some good ones, maybe a bit more in older books. Also, take a look at, DC minus one, Ayres schaums review for college algebra...think it is called first year math.

Just reread head post and saw you were looking for stats stuff. Again, would just look at some entry level review texts. Also...an incredible resource of this sort of thing is Michael Linberg EIT Reference Manual. Chock full of formula and symbol lists, for all STEM topics.

I'm guessing that the sigma (summation) notation is the problem.

Example: Maybe integral notation (another kind of summation) from calculus?

Example: • If I have to read $\sum 2n-1$ I'd interpret it as $\left( \sum 2n \right) - 1$, but I would never write this myself. Instead I'd write the more explicit $\left( \sum 2n \right) - 1$ so as to avoid confusion with $\sum \left( 2n - 1 \right)$
– Stef
Sep 28 at 16:21
• @stef I simply copied the image from the link to the Khan Academy page. I presented no interpretation of it. Technically, you may be right, but, since you raise the point, I'm guessing that the author (not me) omitted brackets for readability, with implicit bracketing around (2n -1). This is supported by comments at the link. Sep 30 at 15:36
• That's actually pretty disappointing from Khan Academy. Almost every math source I know uses the convention that $\sum 2n - 1$ should be parsed as $\left( \sum 2n \right) - 1$, not $\sum \left( 2n - 1 \right)$, and using a different convention is just bound to generate confusion in the students. What if I write $\sum 2n + \sum 2m$, is it supposed to be $\sum \left( 2n + \sum 2m \right)$? :-(
– Stef
Oct 1 at 13:19