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Ask HN: How did you learn math notation?

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Re: Ask HN: How did you learn math notation?

#21

Post by enriquto »

tomerv wrote: post #17
ColinWright wrote: post #14

Earlier quoted context omitted.

You say "There's a formula with a triangle ..." without telling me where. That's not real helpful, and you're making me do the work to find out what you're talking about. If you want assistance to get started, you need to be more explicit. However, I have done that work, so I've looked, and in the second column of page 210 there's a "formula with a triangle": t_c = 5 \middot 10^{-5} \sqrt( V / Dt ) ... where the "D"…

I think that this is indeed the formula in GP's question. And indeed sometimes math notation is obtuse like that. It looks like 2 terms, but the triangle goes together with the t as a single term. At other times it might be called "dt" and despite looking like a multiplication of 2 variables (d and t, or triangle and t in this case) it's just a single variable with a named made of 2 characters. The important thing he…

> it's just a single variable with a named made of 2 characters.

I have this same problem with programming, when I have to deal with code written by non-mathematicians. They tend to use all these stupid variables with more than one letter and that confuses the heck out of me.

Re: Ask HN: How did you learn math notation?

#22

Post by forgetfulness »

rullopat wrote: post #11
ColinWright wrote: post #2

I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. Yes, conventions have emerged, people tend to use the same sort of notation in a given context, but in the main, the notation should be regarded as an aide memoire , something to guide you. You say that you're struggling because of "the math notations and zero explanation of it i…

I was trying to grasp some of the papers linked in the Valhalla DSP block, for example this one: http://www2.ece.rochester.edu/courses/ECE472/resources/Paper... There is a formula with a triangle and I don't get what's that about, for example.

Looks like you need to grind through an elementary calculus book. With the exercises, you may think you build intuition by reading just the definitions, but half of the understanding is tacit and you get through the exercises.

If you're trying to get into signal processing, it'll involve calculus in complex numbers, and knowledge of that is often gained through plodding through proofs and exercises over and over.

Re: Ask HN: How did you learn math notation?

#23

Post by ColinWright »

rullopat wrote: post #19
ColinWright wrote: post #14

Earlier quoted context omitted.

You say "There's a formula with a triangle ..." without telling me where. That's not real helpful, and you're making me do the work to find out what you're talking about. If you want assistance to get started, you need to be more explicit. However, I have done that work, so I've looked, and in the second column of page 210 there's a "formula with a triangle": t_c = 5 \middot 10^{-5} \sqrt( V / Dt ) ... where the "D"…

Sorry I didn't mean to make you work for me, but it's a PDF and I didn't know how to explain better the position (maybe I should have told you the first formula on page X). For you it was a D, for me it was a triangle and I didn't get the meaning of that Dt. Maybe it's just a too advanced paper for my knowledge.

I'm just saying "D" because I can't immediately type the symbol here and it was easier just to use that. Not least, I didn't know if that was the formula you meant.

But as I say, immediately above the formula it says:

"For a pulse of width ∆t, the critical time ..."

So that really is saying exactly what that cluster of symbols means. There will be things like this everywhere as you read stuff. Things are rarely completely undefined, but you are expected to be reading along.

And you need to work. I just typed this into DDG:

"What does ∆t mean?"

The very first hit is this:

https://en.wikipedia.org/wiki/Delta_%28letter%29

That gives you a lot of context for what the symbol means, and this is the sort of thing you'll need to do. You need to stop, look at the thing you don't understand, read around in the nearby text, then type a question (or two, or three) into a search engine.

Re: Ask HN: How did you learn math notation?

#24

Post by NamTaf »

ColinWright wrote: post #14
rullopat wrote: post #11

Earlier quoted context omitted.

I was trying to grasp some of the papers linked in the Valhalla DSP block, for example this one: http://www2.ece.rochester.edu/courses/ECE472/resources/Paper... There is a formula with a triangle and I don't get what's that about, for example.

You say "There's a formula with a triangle ..." without telling me where. That's not real helpful, and you're making me do the work to find out what you're talking about. If you want assistance to get started, you need to be more explicit. However, I have done that work, so I've looked, and in the second column of page 210 there's a "formula with a triangle": t_c = 5 \middot 10^{-5} \sqrt( V / Dt ) ... where the "D"…

I feel you're coming at this without appreciating your body of prior knowledge. Intended or not, your statment "But that can't be it, because just two lines above it we have..." assumes a whole lot of knowledge.

You and I both know that it reads as one term, but for someone unfamiliar with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items, because the algebraic 'multiply' is so often implied, e.g. 3x = 3 * x as two individual 'things'.

I think there's merit in explaining the concept of delta representing change, because it's not obvious. For example, when I was taught the concept in school, my teacher explicitly started with doing a finite change with numbers, then representing it in terms of 'x' and 'y', then merged them into the delta symbol. That's a substantial intuitive stepping stone and I think it's pretty reasonable that someone may not find this immediately apparent.

Re: Ask HN: How did you learn math notation?

#25

Post by User23 »

ColinWright wrote: post #2

I think a real problem in this area is the belief that there is "one true notation" and that everything is unambiguous and clearly defined. Yes, conventions have emerged, people tend to use the same sort of notation in a given context, but in the main, the notation should be regarded as an aide memoire , something to guide you. You say that you're struggling because of "the math notations and zero explanation of it i…

Edsger Dijkstra, who was a mathematician by training, wrote a wonderful little monograph on this subject called The notational conventions I adopted, and why[1]. I am particularly fond of his commented equational proof format.

[1] https://www.cs.utexas.edu/users/EWD/transcriptions/EWD13xx/E...

Re: Ask HN: How did you learn math notation?

#26

Post by smitty1e »

hatmatrix wrote: post #7

I think the problem is that there is no authoritative text, that I know of, and as ColinWright says, the same ideas can be notated differently by different fields or sometimes by different authors in the same field (though often they converge if they are in the same community). Wikipedia has been helpful sometimes but otherwise I have found reading a lot of papers on the same topic has been useful. However, this is k…

The Greek alphabet would like to thank all the scholars for the centuries of overloading and offer a "tee hee hee" to all of the students tormented by attendant ambiguities.

Tough love, kids.

Re: Ask HN: How did you learn math notation?

#27

Post by ColinWright »

NamTaf wrote: post #24
ColinWright wrote: post #14

Earlier quoted context omitted.

You say "There's a formula with a triangle ..." without telling me where. That's not real helpful, and you're making me do the work to find out what you're talking about. If you want assistance to get started, you need to be more explicit. However, I have done that work, so I've looked, and in the second column of page 210 there's a "formula with a triangle": t_c = 5 \middot 10^{-5} \sqrt( V / Dt ) ... where the "D"…

I feel you're coming at this without appreciating your body of prior knowledge. Intended or not, your statment "But that can't be it, because just two lines above it we have..." assumes a whole lot of knowledge. You and I both know that it reads as one term, but for someone unfamiliar with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items, because the algebraic 'multi…

I agree completely that I'm coming at this with a lot of background knowledge, but if I'm reading in an unfamiliar field and I see a symbol I don't recognise, I look in the surrounding text to see if the symbol appears nearby. As I say, "Δt" appears immediately above ... that's a clue. As you say, it's drilled in at school that everything is represented by a single glyph, and if these are juxtaposed then it means multiplication, and that is another thing to unlearn.

But I think the problem isn't the specifics of the "Δ", it's the meta-problem of believing that symbols have a "one true meaning" instead of being defined by the scope.

I agree that explaining the delta notation would be helpful, but that's like giving someone a fish, or making them a fire. They are fed for one day, or warm for one night, it's the underlying misconceptions that need addressing so they can learn to fish and be fed, or set on fire and be warm, for the remainder of their life.

Re: Ask HN: How did you learn math notation?

#28

Post by dwheeler »

There is no single authoritative source for mathematical notation. That said, there are a lot of common conventions. You could do worse than this NIST document if it's just a notation question:

https://dlmf.nist.gov/front/introduction

Of course, if the real problem is that you need to learn some mathematical constructs, that is a different problem. The good news is that there's a lot of material online, the bad news is that not all of it is good... I often like Khan Academy when it covers the topic.

I wish you luck!

Re: Ask HN: How did you learn math notation?

#29

Post by analog31 »

Maybe a problem is trying to learn it by reading it.

I was a college math major, and I admit that I might have flunked out had I been told to learn my math subjects by reading them from the textbooks without the support of the classroom environment. It may be that the books are "easy to read if a teacher is teaching them to you."

Talking and writing math also helped me. Maybe it's easier to learn a "language" if it's a two way street and involves more of the senses.

Perhaps a substitute to reading the stuff straight from a book might be to find some good video lectures. Also, work the chapter problems, which will get your brain and hands involved in a more active way.

As others might have mentioned, there's no strict formal math notation. It's the opposite of a compiled programming language. In fact, math people who learn programming are first told: "The computer is stupid, it only understands exactly what you write." In math, you're expected to read past and gloss over the slight irregularities of the language and fill in gaps or react to sudden introduction of a new symbol or notational form by just rolling with it.

Re: Ask HN: How did you learn math notation?

#30

Post by CornCobs »

Mathematics is a lingo and notations are mostly convention. Luckily people generally follow the same conventions, so my best advice if you want to learn about a specific topic is to work through the introductory texts! If you want to learn calculus find an introductory college text. Statistics? There are traditional textbooks like Introduction to Statistical Learning. The introductory texts generally do explain notation which may become assumed knowledge for more advanced texts, or as you seem to be wanting to read, academic papers. If those texts are still too difficult, then maybe move down to highschool text first.

Think about it this way. A scientist, wanting to communicate his ideas with fellow academics, is not going to spend more than half the paper on pedantics and explaining notations which everyone in their field would understand. Else what is the purpose of creating the notations? They might as well write their formulas and algorithms COBOL style!

Ultimately mathematics, like most human-invented languages, is highly tribal and has no fixed rules. And I believe we are much richer for it! Mathematicians constantly invent new syntax to express new ideas. If there was some formal reference they had to keep on hand every time they need to write an equation that would hamper their speed of thought and creativity. How would one even invent something new if you need to get the syntax approved first!

TL;DR: Treat math notation as any other human language. Find some introductory texts on the subject matter you are interested in to be "inducted" into the tribe

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