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Mathematical terminology

de nornen, 2017-aprilo-16

Mesaĝoj: 8

Lingvo: English

nornen (Montri la profilon) 2017-aprilo-16 23:08:22

Maybe some English native speaker can help me out with how to spell out some mathematical terms in English.

I have gathered from some mathematical youtube videos that the term x/y is read by native speakers as either "x divided (by) y" or "x over y", but how do you read out a differential quotient, like say "dx/dy". Would you still say "dx over dy" or is there another word you use? I am asking because e.g. in German you say "x/y" as "x durch y" (=x through y), but generally in calculus you pronounce "dx/dy" as "dx nach dy" (=x toward y). So, is it simply "dx over dy" or do you have another way of spelling out differential quotients?

How do you pronounce partial integrals, for example "∂f(a,t)/∂t" and "∂f(a,t)/∂a"? How do you express with derivations "over" what (which variable) you derived?

I have the same question about integrals. For instance, "∫ e^(-at) dt". Would that be "the integral of e to the power of minus a t dt" or something like "the integral of e to the power of minus a t ??? dt" or "the integral of e to the power of minus a t ??? (the) time"? What is the preposition for "???"?

I thank you very much in advance.

Mustelvulpo (Montri la profilon) 2017-aprilo-17 20:54:26

"Over" works in all the circumstances you described- for example "dx over dy." I'd say that when naming a quantity less than zero (say -5), while both "minus five " and "negative five" are acceptable. "Negative" is used more often to avoid confusion with subtraction. For example "negative 3 minus negative 5 is 2." Saying minus twice in a row could be confusing.

nornen (Montri la profilon) 2017-aprilo-18 04:32:54

Thank you so much, mustelvulpo.

Just to make sure that I understood you correctly:
"x/t" can be read as "eks over tee".
"dx/dt" can be read as "dee eks over dee tee".
"∫ e^(-at) dt" can be read as "the integral of e to the power of negative a tee over dee tee" or "...over the time".
(This actually sounds a bit strange to me, but hey! I am not a native speaker. I would have interpreted "the integral of e to the power of negative a tee over dee tee" as "∫ e^(-at) / dt", although this makes no sense at all)

Is it correct to assume that in English you prefer "minus" for the binary -, while you prefer "negative" for the unary -?

Just one last doubt: I gather that f' is read "eff prime" (denoting the first derivative of f over something). But how do you read f'' or f'''? "f prime prime"? "f twice prime"? "f second"? "f secunda"? "f bis"? "f's second cousing thrice removed"?

Yet another doubt (lol): What do you call these buggers: "∮f(x)dx"?

david_uk (Montri la profilon) 2017-majo-05 14:07:59

Nothing Mustelvulpo says is actually wrong. But they are mostly americanisms. The conventions in England are a little different.

We would rarely say negative 5 instead of minus 5, even if it leads to a "minus minus" phrase.

dx/dy is usually spoken as "dee x by dee y", but "dee x over dee y" would make just as much sense and be easily understood.

I have never heard anyone refer to an integral .. over dt. My lecturers at University would always say "with respect to t". You could also add "over the interval a to b", if your integral had limits.

f'' would be "f double prime", then "triple", "quadrupal",....

The last one is a line integral with respect to x. I am not sure if there is a specific term that is generally used for a closed loop. I guess it would be "a closed-loop line integral w.r.t. x".

There could also be other conventions in other English speaking countries like Australia. It's possible engineers use different conventions as well.

nornen (Montri la profilon) 2017-majo-11 19:10:48

Thank you very much, David.

Especially the "dee x by dee y" part is very important to me.

So "∫ e^(-at) dt" would be "the integral with respect to t of e to the power of minus a tee", right?

Lately I heard some Australian mathematician speaking, and he read "x² - 1" as "eks squared take one". Does this sound normal to you? Would you prefer "eks squared minus one"?

In the mathematics, how to you pronounce the number 0 and the digit 0? I thought it was "nought", but actually I hear any combination of "nought", "zero" and "oh". How would you read "0", "3.02" and "0.0001"?

Thanks in advance. You are really helping me a lot.

david_uk (Montri la profilon) 2017-majo-12 16:28:11

"the integral with respect to t of e to the power of minus a tee" would be OK, but normally we would say it the other way around: "the integral of e to the power of minus a tee with respect to t" . Probably because that is closer to the mathematical notation.

"eks squared take one" is OK, but I have not heard it often. It is proably an Australian thing. I think "eks squared minus one" would be more common, but you might also hear "take away one" or "less one". Any of them would be OK. Sorry I cannot be more precise.

This probably does not help much, but 0 can be "nought", "zero" or "oh". I don't think there is any real convention.

For "0" I might say "nought" or "zero", but not "oh".

For "3.02" I would say "three point oh two" or "three point zero two". I don't really have a preference, but I think Americans are more likely to say "zero". And you would probably hear some people say "three point nought two".

For "0.0001" I might say "nought point oh oh oh one" or "nought point zero zero zero one" or "zero point zero zero zero one" or....

The safest thing to do is to use "zero" everywhere. Everyone will understand that, and it will never sound wrong.

david_uk (Montri la profilon) 2017-majo-12 17:09:37

The safest thing to do is to use "zero" everywhere. Everyone will understand that, and it will never sound wrong.
Actually outside of mathematics there could be some exceptions.

Jame Bond will always be "double-oh-seven".
"Room 101" and "History 101" will always be "one-oh-one".

kdl5000 (Montri la profilon) 2017-majo-13 23:42:47

Interesting topic!
It is probably an Australian thing.
The Australians seem to be particularly productive ... Do you know the mnemonic "all stations to central", ASTC, in connection with trigonometric functions? I heard it in a video lecture by an Aussie by the name of Adrian Banner ("The Calculus Lifesaver"), http://press.princeton.edu/video/banner/, very first video (fast forward the 2-hour recording to 1hr:33 mins).

Any math teachers out there? I'm trying to find a few practitioners in various languages (de, en, es, eo, fr, it, nl, pl) who might provide me with some feedback: I'm compiling a multilingual glossary of high-school math terms and phraseology. I've explained the project a little in Esperanto in the thread https://lernu.net/forumo/temo/23600). My active use of those languages (apart from English, Esperanto and German) is a bit shaky, so I hope to communicate in de/en/eo with anyone able to help me. I do, however, read all the other languages and do in fact compile the glossary from native-language source material, i.e, textbooks, video lectures etc., not from existing bi- or multilingual dictionaries (though I do check those as well, in particular Marc Bavant's excellent "Matematika vortaro kaj oklingva leksikono" http://katalogo.uea.org/katalogo.php?inf=7069).

Hope to hear from you here or drop me a line. Thanks & cheers!

klausleith@yahoo.com

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