get some english math textbooks used in high schools across europe.
Ask HN: How did you learn math notation?
101–110 of 258 posts
Re: Ask HN: How did you learn math notation?
#102Earlier quoted context omitted.
> 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. One main cause for this belief is that in a programming there is one true noation (or rather, a separate one for each language) that is unambiguous and clearly defined. I dislike maths notation as I find it lacks rigour.
> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.
I graduated in physics so I am no stranger to math notation quirks and I think I also do understand their usefulness at times (conciseness in notation, etc). And it can be dangerous, too. As soon as the notation lures you into doing transformations that are invalid.
Doesn't help that then notation is often poorly defined, and sometimes a weird mix of notations is presented.
Overall the situation is also not pleasant for math people changing topics, or physicists reading papers from physical chemistry professors who 'grew up' in mathematical chemistry.
Re: Ask HN: How did you learn math notation?
#103I learned most of my university math through "Calculus a Complete Course". But it's a bit expensive so I would recommend you buy an older version of the book where you can find a free solution pdf.
But you'll have to be a bit realistic when going through the book, it's going to take a good while.
Re: Ask HN: How did you learn math notation?
#104For about $5 you can find an old (around 1960-1969) edition of the "CRC Handbook of Standard Mathematical Tables. I've owned two of the 17th edition published in 1969, because back then hand calculators didn't exist and many of the functions used in mathematics had to be looked up in books, like what is the square root of 217. Engineers used these handbooks extensively back then. Now, of course, you have the internet…
As someone else who'd like to have a better understanding of formal notation, I think that's a great answer. Thanks for taking the time.
Re: Ask HN: How did you learn math notation?
#105Earlier quoted context omitted.
Scientists and engineers write code with single variables all the time and don’t seem to have any large amount of trouble with it. Long variable names seriously limit the ability to put complexity in one place and make it understandable. Take a look at this and tell me it would be easier to understand if all the symbols were words instead of single characters: https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html
This is pretty understandable because: 1. They explain all abbreviations at the top. 2. There is a lenghty text explaining the formula. 3. It's mathematically pretty easy if you know partial differentation. Also scientists and engineers write pretty horrible code....
It’s not horrible, it’s different, has different goals and different audiences. Context is king, and the bulk of professional programmers criticizing scientist code is just lack of context and a different set of priorities.
From a more science based background i often think programmers write horrible code as i search in vain for where anything actually happens in a sea of abstractions.
Re: Ask HN: How did you learn math notation?
#106I have a notation problem. I want to write "approximately 24 volt" on my printed circuit board, but I have little space. I could write "≈24V", but the wavy symbol makes it look like it is AC instead of DC. How to solve this without adding more characters or changing my circuit?
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Re: Ask HN: How did you learn math notation?
#107Earlier quoted context omitted.
Came here to say the same thing harshly and laced with profanity. I guess I can back off a bit from that now. I was filled with crushing disappointment when I learned mathematical notation is "shorthand" and there isn't a formal grammar. Same goes for learning writers take "shortcuts" with the expectation the reader will "fill in the gaps". Ostensibly this is so the writer can do "less writing" and the reader can do…
You seem to be complaining that math isn't programming, that it's something different, and you've discovered that you don't like how mathematicians do math. Math notation is the way it is because it's what mathematicians have found useful for the purpose of doing and communicating math. If you are upset and disappointed that that's how it is then there's not a lot we can do about it. If there was a better way of doin…
> Math notation is the way it is because it's what mathematicians have found useful for the purpose of doing and communicating math.
That's only really a good description for the most well trod areas, where people habe bothered to iterate. I think a more realistic statement would be:
"Math notation is the way it is because some mathematician found it sufficient to do and communicate math, and others found it tolerable enough to not bother to change."
Personally, though, my problem has always been where publications use letters and symbols to mean things that are just "known" in some subfield that isn't directly referenced. It's not a problem for direct back and forth communication during development, true, but it dramatically increases the burden on someone who wants to jump in.
Re: Ask HN: How did you learn math notation?
#108Earlier quoted context omitted.
The triangle, or “delta”, is used to indicate a tiny change in the following variable. Let’s say you go on a journey, and the distance you’ve travelled so far is “x” and the time so far is “t”. Then your average velocity since the beginning is x / t . But, if you want to know your current velocity, that would be delta x divided by delta t . The delta is usually used in a “limiting” sense - you can get a more accurate…
I would say that delta is typically used to mean difference of any magnitude (i.e. Δt could mean 2 hours).
Yes, small changes usually use lowercase delta, e.g. δt. Not to be confused with the derivative symbol dt, nor with the partial derivative symbol ∂t !
Before I continued my maths learning after highschool (ie before UK A-levels) I learnt the Greek alphabet to make it easier to understand maths notations as I could 'voice' (internally) all the funny glyphs adopted from Greek.
At uni I learnt how to properly write an ampersand (for logic classes) and how to write Aleph and Beth (for pure maths, particularly transcendental numbers).
Some professors have a fondness for the more confusing Greek letters (lowercase xi, lowercase eta) ... is it n or eta, epsilon or xi, ...
Re: Ask HN: How did you learn math notation?
#109Earlier quoted context omitted.
This is pretty understandable because: 1. They explain all abbreviations at the top. 2. There is a lenghty text explaining the formula. 3. It's mathematically pretty easy if you know partial differentation. Also scientists and engineers write pretty horrible code....
It’s not horrible, it’s different, has different goals and different audiences. Context is king, and the bulk of professional programmers criticizing scientist code is just lack of context and a different set of priorities. From a more science based background i often think programmers write horrible code as i search in vain for where anything actually happens in a sea of abstractions.
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Re: Ask HN: How did you learn math notation?
#110Earlier quoted context omitted.
I like the approach they took in Structure and Interpretation of Classical Mechanics, where the whole book is done in Scheme: (define ((Lagrange-equations Lagrangian) q) (- (D (compose ((partial 2) Lagrangian) (Gamma q))) (compose ((partial 1) Lagrangian) (Gamma q))))
I have no idea what the hell that means, and I am quite familiar with Lagrangian mechanics.
https://mitpress.mit.edu/sites/default/files/titles/content/...
It's formula 1.12 at the start of section 1.5 on this page converted into a Scheme representation, in section 1.5.2.