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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?

#11

Post by rullopat »

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.

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

#13

Post by nickcw »

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.

The triangle is a capital Greek Delta and is usually used to indicate a change in something. So ΔT means some change in T.

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

#14

Post by ColinWright »

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.

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've used is where the triangle appears in the formula.

But that can't be it, because just two lines above it we have:

"For a pulse of width Dt, the critical time ..."

So that's stating that "Dt" is the width of the pulse, and should be thought of as a single term.

So maybe that's the wrong formula, or maybe it was just a bad example. So trying to be more helpful, the "triangle" is a Greek capital delta and means different things in different places. However, it is often used to mean "a small change in".

https://en.wikipedia.org/wiki/%CE%94T

FWIW ... at a glance I can't see where that result is derived, it appears simply to be stated without explanation. I might be wrong, I've not read the rest of the paper.

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

#15

Post by ivansavz »

As a starting point you can check out the notation appendices from my books: https://minireference.com/static/excerpts/noBSmathphys_v5_pr... https://minireference.com/static/excerpts/noBSLA_v2_preview.... You can also see this excerpt here on set notation https://minireference.com/static/excerpts/set_notation.pdf

That covers most of the basics, but I think your real question is how to learn all those concepts, not just the notation for them, which will require learning/reviewing relevant math topics. If you're interested in post-high-school topics, I would highly recommend linear algebra, since it is a very versatile subject with lots of applications (more so than calculus).

As ColinWright pointed out, there is no one true notation and sometimes authors of textbooks will use slightly different notation for the same concepts, especially for more advanced topics. For basic stuff though, there is kind of a "most common" notation, that most books use and in fact there is a related ISO standard you can check out: https://people.engr.ncsu.edu/jwilson/files/mathsigns.pdf#pag...

Good luck on your math studies. There's a lot of stuff to pick up, but most of it has "nice APIs" and will be fun to learn.

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

#16

Post by Jensson »

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.

That is a physics based paper, it used physics notation. Can find common ones here (including that triangle):

https://en.wikipedia.org/wiki/List_of_common_physics_notatio...

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

#17

Post by tomerv »

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 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 here is that "For a pulse of width Dt" is the definition of this variable, but this can be easily missed if you're not used to this naming convention.

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

#18

Post by NamTaf »

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.

What you're looking at is calculus, specifically differentiation. This is pretty core to understanding physics, because so much of physics depends on the time-evolving state of things. That's fundamentally what's happening here.

The triangle, for example, is the upper-case greek letter delta, which in calculus represents 'change of'. You might have heard of 'delta-T' with respect to 'change of time'.

In calculus, upper-case delta means 'change over a finite time' vs lower-case delta meaning 'instantaneous change'. The practical upshot, for example, is that the lower-case is the instantaneous rate-of-change at an instant in time, whereas the upper-case is the change over a whole time (e.g. the average rate of change per second for time = 0 seconds to time = 3 seconds).

If you are trying to grok this, I would suggest an introductory calculus or pre-calculus resource. It doesn't have to be a uni textbook - higher-level high school maths usually teaches this. In this particular case, the Khan Academy would be my recommendation because it is about the right level (we're not talking esoteric higher-level university knowledge here) and it is eminently accessable. For example, this link may be a good starter in this instance:

https://www.youtube.com/watch?v=MeU-KzdCBps

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

#19

Post by rullopat »

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"…

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.

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