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-   -   Las Matemáticas — Mathematics (http://forums.tomisimo.org/showthread.php?t=4869)

chileno April 10, 2010 08:27 AM

I remember taking in Algebra, while in High School, something called "equations to the/of 3rd degree" which took imaginary and real numbers to produce two answers...

That was in a past life. :-)

laepelba April 10, 2010 12:21 PM

Quote:

Originally Posted by chileno (Post 79125)
I remember taking in Algebra, while in High School, something called "equations to the/of 3rd degree" which took imaginary and real numbers to produce two answers...

That was in a past life. :-)

Today's curricula are watered down at best. (Don't get me started....) While we teach n-th degree equations in Algebra 1, we don't address those with imaginary roots. So we DO equations with two or more answers. But we leave out the possibility of non-real answers, to be covered in subsequent courses.

chileno April 10, 2010 05:06 PM

Quote:

Originally Posted by laepelba (Post 79137)
Today's curricula are watered down at best. (Don't get me started....) While we teach n-th degree equations in Algebra 1, we don't address those with imaginary roots. So we DO equations with two or more answers. But we leave out the possibility of non-real answers, to be covered in subsequent courses.

In what grade do you cover "group theory"? (teoría de conjunto) I do not really know if that's the term in English. :p

laepelba April 10, 2010 07:31 PM

I think it's a topic in "Discrete Math", which is not a required course of non-math majors. (If it's what I think you're referring to....)

chileno April 10, 2010 08:18 PM

Quote:

Originally Posted by laepelba (Post 79186)
I think it's a topic in "Discrete Math", which is not a required course of non-math majors. (If it's what I think you're referring to....)

Probably. As it has to do with computers and logic. That's where the "truth table" and others come from.

laepelba April 10, 2010 08:22 PM

Yup - that's "Discrete". The truth tables for "logic" are taught in Geometry (I think), but anything more complex is "Discrete".

pjt33 April 11, 2010 10:28 AM

Quote:

Originally Posted by chileno (Post 79177)
In what grade do you cover "group theory"? (teoría de conjunto) I do not really know if that's the term in English. :p

Teoría de conjuntos es "set theory". "Group theory" es teoría de grupos; un grupo consiste en un conjunto C y una function * que satisfacen cuatro axiomas.
  1. Cerrado: si c1 y c2 están en C, (c1 * c2) también está en C.
  2. Existe un elemento de identidad I: es decir que (c1 * I) = c1 para cualquier c1 en C.
  3. * puede invertirse: para cualquier c1 en C existe un c2 tal que (c1 * c2) = I.
  4. * es asociativa: (c1 * c2) * c3 = c1 * (c2 * c3).

chileno April 11, 2010 10:44 AM

Quote:

Originally Posted by pjt33 (Post 79247)
Teoría de conjuntos es "set theory". "Group theory" es teoría de grupos; un grupo consiste en un conjunto C y una function * que satisfacen cuatro axiomas.
  1. Cerrado: si c1 y c2 están en C, (c1 * c2) también está en C.
  2. Existe un elemento de identidad I: es decir que (c1 * I) = c1 para cualquier c1 en C.
  3. * puede invertir: para cualquier c1 en C existe un c2 tal que (c1 * c2) = I.
  4. * es asociativa: (c1 * c2) * c3 = c1 * (c2 * c3).

Sí, "set theory". Recuerdo haber escuchado eso antes, acá en EEUU.

laepelba April 11, 2010 12:16 PM

Quote:

Originally Posted by pjt33 (Post 79247)
Teoría de conjuntos es "set theory". "Group theory" es teoría de grupos; un grupo consiste en un conjunto C y una function * que satisfacen cuatro axiomas.
  1. Cerrado: si c1 y c2 están en C, (c1 * c2) también está en C.
  2. Existe un elemento de identidad I: es decir que (c1 * I) = c1 para cualquier c1 en C.
  3. * puede invertir: para cualquier c1 en C existe un c2 tal que (c1 * c2) = I.
  4. * es asociativa: (c1 * c2) * c3 = c1 * (c2 * c3).

Excellent! Thanks for all of that great vocabulary!!

laepelba May 23, 2010 12:33 PM

Another question for you all.

I team teach an Algebra class for English-as-a-Second-Language students. I am the "math specialist" and the other teacher is the "ESL specialist". Most of our students are native Spanish speakers. The other teacher knows some Spanish, although I don't remember where/how she learned it. She is not actively studying it.

Recently, I was talking about writing units on measurements that are proportional. For example, in English, if a speed is given in "meters per second", it is written as "m/s". Some of the kids were asking me about "per". I think that at some point in time, I heard something in a similar context that used "por", like if something happened once a day, it would be said "una vez por día". Is that correct or incorrect?

Anyway, I said something to some of the students about "per" in English being like "por" in Spanish. My team teacher jumped in and said, "well, it's like 'cada'. 'Each'." I suppose that makes logical sense to me, but for some reason it seems incorrect.....

So what is the correct way to give a proportional unit?

Thanks!!

chileno May 23, 2010 12:40 PM

Quote:

Originally Posted by laepelba (Post 83538)
Another question for you all.

I team teach an Algebra class for English-as-a-Second-Language students. I am the "math specialist" and the other teacher is the "ESL specialist". Most of our students are native Spanish speakers. The other teacher knows some Spanish, although I don't remember where/how she learned it. She is not actively studying it.

Recently, I was talking about writing units on measurements that are proportional. For example, in English, if a speed is given in "meters per second", it is written as "m/s". Some of the kids were asking me about "per". I think that at some point in time, I heard something in a similar context that used "por", like if something happened once a day, it would be said "una vez por día". Is that correct or incorrect?

Anyway, I said something to some of the students about "per" in English being like "por" in Spanish. My team teacher jumped in and said, "well, it's like 'cada'. 'Each'." I suppose that makes logical sense to me, but for some reason it seems incorrect.....

So what is the correct way to give a proportional unit?

Thanks!!


It depends...

"una (vez) cada día" = "one (time)/once each day"

"una (vez) por día" = "one (time)/once per day"

"una (vez) al día" "one (time) a day"

laepelba May 23, 2010 12:41 PM

Quote:

Originally Posted by chileno (Post 83539)
It depends...

"una (vez) cada día" = "one (time)/once each day"

"una (vez) por día" = "one (time)/once per day"

So what do you say in a mathematics class about units? It "depends" on what?

chileno May 23, 2010 12:45 PM

Quote:

Originally Posted by laepelba (Post 83540)
So what do you say in a mathematics class about units? It "depends" on what?

What do you mean? I gave the possibilities to administer anything in any units you want, we are talking about intervals, don't we? Units can be related to this but you haven't talked yet about what units.

laepelba May 23, 2010 12:48 PM

Well, the units can be all kinds of different things ... m/s, miles/h, km/h, miles/sec, etc.

You said "it depends", but I'm wondering, what does it depend on? In Spanish math classes, do they teach two different scenarios? Sometimes you say "cada" and sometimes you say "por"?

chileno May 23, 2010 12:51 PM

Quote:

Originally Posted by laepelba (Post 83543)
Well, the units can be all kinds of different things ... m/s, miles/h, km/h, miles/sec, etc.

You said "it depends", but I'm wondering, what does it depend on? In Spanish math classes, do they teach two different scenarios? Sometimes you say "cada" and sometimes you say "por"?

Mph is for "each" or "per" and I am talking strictly in English

55mpg

$2.17 a gallon/per gallon

Doesn't it depends in English too? ;)

laepelba May 23, 2010 01:03 PM

I wouldn't ever use "each" in units as a label in English. So I suppose I would never use "cada" in units as a label in Spanish, right?

chileno May 23, 2010 01:14 PM

Quote:

Originally Posted by laepelba (Post 83546)
I wouldn't ever use "each" in units as a label in English. So I suppose I would never use "cada" in units as a label in Spanish, right?

I am not sure.

For each gallon of water, pour 1 cup of bleach.

I guess you couldn't cope with that...? ;)

Rest a little a come back with renewed. It is the mind playing tricks at you. :)

laepelba May 23, 2010 01:20 PM

Well, this is something that I've pondered for about a week before posting the question, so I'll continue to pursue it. If you want to stop answering, I'm sure someone else will pick it up...

The example you give (For each gallon of water, pour 1 cup of bleach.), that is typical of a science class. I'm specifically looking for math problems given strictly in the context of a math classroom. And you're describing a process, not giving a quantity with units.

In my class, I would ask something like follows:
- If light travels xxxxx miles in 8 minutes, what is the speed of light given in miles/second?

I would tell English speaking students that "per" means that the denominator is "one", and that they have to convert from 8 minutes to 60 seconds in a minute and make the denominator 1.

I can't think of an instance where I would use "each"........

chileno May 23, 2010 02:46 PM

Quote:

Originally Posted by laepelba (Post 83548)
Well, this is something that I've pondered for about a week before posting the question, so I'll continue to pursue it. If you want to stop answering, I'm sure someone else will pick it up...

Sheesh!

I didn't realize you had been pondering this for some time...

No need to become belligerent. :)

Quote:

Originally Posted by laepelba (Post 83548)
In my class, I would ask something like follows:
- If light travels xxxxx miles in 8 minutes, what is the speed of light given in miles/second?

In this case to express miles/seconds it usual to use "miles per second", right? The same in Spanish

The rest somebody else will have to answer it, as I am not understanding your position. Maybe when I get back to this post I will have an insight or something...

:)

laepelba May 23, 2010 02:51 PM

It wasn't my intention to seem belligerent. Take what I said at face value. I ponder things like this before I ask.... :)

Sounds like "por" is a better choice for what I'm looking for.......

alx May 23, 2010 03:27 PM

Hi there, here's my opinion

@laepelba
We tend to say "metros por segundo" just like you do, even though it should be "metros por cada segundo" (same happens with other x/y units), accordingly with definition of m/s, it is the distance covered by an object for each second elapsed.

I don't know exactly why we say it that way (as children we are taught this), i guess it's a bad custom of ours.

I found this at Wikipedia:
Quote:

Nótese que en la rapidez, o en el valor de la velocidad, la dimensión del tiempo es inversa (m/s en lugar de m•s), por lo que la expresión «metro por segundo» significa «un metro por cada segundo», «un metro en cada segundo», o incluso «un metro dividido por segundo». No se debe confundir con «un metro multiplicado por segundo», lo cual no es una unidad de velocidad.

This is a rough traslation:
Notice that speed-wise, the time dimension is inverse (m/s instead of m*s), thus <<metros por segundo>> means <<un metro por cada segundo>>, «un metro en cada segundo», or even «un metro dividido por segundo».
This must not be mistaken for «un metro multiplicado por segundo» since that's not a speed measuring unit.
Hope it helps.
Let us know if any doubts still remain.

Regards

laepelba May 23, 2010 03:50 PM

Thanks, alx - helps a lot! :)

chileno May 23, 2010 04:45 PM

Quote:

Originally Posted by alx (Post 83555)
Hi there, here's my opinion

@laepelba
We tend to say "metros por segundo" just like you do, even though it should be "metros por cada segundo" (same happens with other x/y units), accordingly with definition of m/s, it is the distance covered by an object for each second elapsed.

Hi alx and laepelba:

That explanation should be the same one in English.

Maybe one tend not to think of things like this until one decides to learn another language, and that's when "idiolects* and idiotsyncracies" start to surface, in both languages.

*(term taught from pjt, I love it!) :)

laepelba June 30, 2010 05:04 PM

Okay, how about this one... In Geometry we talk about "conic sections": circles, parabolas, hyperbolas and ellipses.

Would the vocabulary be as follows?
Las secciónes conicas son los círculos, las parábolas, las hipérbolas, y las elipses.

:?::?::?::?:

chileno June 30, 2010 06:53 PM

Quote:

Originally Posted by laepelba (Post 87582)
Okay, how about this one... In Geometry we talk about "conic sections": circles, parabolas, hyperbolas and ellipses.

Would the vocabulary be as follows?
Las secciónes conicas son los círculos, las parábolas, las hipérbolas, y las elipses.

:?::?::?::?:

¿Por qué no "Secciones cónicas: (los) círculos, (las) parábolas, (las) hipérbolas, y (las) elipses"? ;)

You got it.

laepelba October 30, 2010 04:12 AM

How about the word "countability" (In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.) In Spanish, "countable" would be "contable" or "numerable", right? How about the noun form, then?

AngelicaDeAlquezar October 30, 2010 06:07 AM

My teachers never used any equivalent (we only talked about "conjuntos contables"), and although I've never seen the word used in this sense, the DRAE gives contabilidad".
I suppose it will be correct to say "la contabilidad de un conjunto", to talk about it's quality of being countable.

laepelba October 30, 2010 06:55 AM

Quote:

Originally Posted by AngelicaDeAlquezar (Post 98322)
My teachers never used any equivalent (we only talked about "conjuntos contables"), and although I've never seen the word used in this sense, the DRAE gives contabilidad".
I suppose it will be correct to say "la contabilidad de un conjunto", to talk about it's quality of being countable.

Thanks - that's what I thought. But the word "contabilidad" came in a "word of the day" email as "accounting" or "bookkeeping", and I wasn't sure if it also applied to more "pure" mathematics as "countability".

In the RAE, are you looking at: "Aptitud de las cosas para poder reducirlas a cuenta o cálculo." ?? I suppose the reason I wasn't sure about that particular definition was because it seemed to be *not* about pure mathematics.

Anyway, thanks for the answer. It's actually a word we use quite frequently, but ONLY in reference to sets of numbers.

aleCcowaN October 30, 2010 03:25 PM

rotor / rotacional = curl / rotor
divergencia = divergence
gradiente = gradient
nabla (del) = del (nabla)

irmamar October 31, 2010 05:32 AM

Un conjunto es contable o numerable si es finito. ;)

laepelba October 31, 2010 10:08 AM

Quote:

Originally Posted by irmamar (Post 98420)
Un conjunto es contable o numerable si es finito. ;)

Did you say here that a set is "countable" if it is "finite"? I do not agree. The set of natural numbers is countable, AND it is infinite. Likewise the set of rational numbers. Likewise the set of positive, even numbers. And so on....

irmamar October 31, 2010 12:32 PM

Many years have passed since I studied 'teoría de conjuntos', but not all the infinite sets are countable, are they? The points of a straight line are not countable (son no contables). Rational or natural numbers set are countable, but not real numbers set (or I think so). :thinking: Well, you'll know better than I. ;) :)

laepelba October 31, 2010 12:34 PM

No, for example, the irrational numbers are both infinite AND uncountable. In fact, between any two natural numbers there are an uncountable and infinite number of irrational numbers. :D

irmamar October 31, 2010 12:41 PM

Thanks :). I should revise my rusty maths. :thinking: :)

laepelba October 31, 2010 03:20 PM

Nah - since when do you need to know the countability or non-countability of finite sets? :)

irmamar November 01, 2010 06:42 AM

I had to study hard maths and I liked them. But when I changed my degree (I was studying Computer Engineering) I forgot all that I studied so hard. So I think it must be somewhere in my brain and, when I'll finish my current degree, I want to go back with which I left (if I feel like then, of course). ;)

Perikles November 01, 2010 07:03 AM

I might get into trouble for this: :kiss:

Quote:

Originally Posted by irmamar (Post 98583)
I had to study hard for maths and I liked them it (singular). But when I changed my degree (I was studying Computer Engineering) I forgot all that I studied so hard. So I think it must be somewhere in my brain and, when I'll I (present) finish my current degree, I want to go back with which to the one I left (if I feel like it then, of course). ;)


Cloudgazer November 01, 2010 09:11 PM

Quote:

Originally Posted by irmamar (Post 98420)
Un conjunto es contable o numerable si es finito. ;)

Esto es verdad (por definición). :)

Quote:

Originally Posted by laepelba (Post 98442)
Did you say here that a set is "countable" if it is "finite"? I do not agree. The set of natural numbers is countable, AND it is infinite. Likewise the set of rational numbers. Likewise the set of positive, even numbers. And so on....

Fíjate en que Irma no dijiste "si y sólo si", es decir, "sii" o "iff", sólo dijiste "si". Un conjunto tiene que ser numerable si es finito. Su afirmación no dice nada acerca de las propiedades de los conjuntos infinitos, que pueden ser numerables o no, como nos has apuntado. :D

pjt33 November 02, 2010 01:13 AM

Quote:

Originally Posted by Perikles (Post 98590)
I might get into trouble for this: :kiss:

I think the initial correction is wrong. I understood it rather as "I had to study advanced maths".

irmamar November 02, 2010 01:29 AM

My dear Cloud. Welcome back :kiss:

Yes, that '<=>' . How do you say "si y sólo si" in English? If and only if? :thinking:

Perikles, later I'll talk to you... seriously. :D :kiss:

Perikles November 02, 2010 02:49 AM

Quote:

Originally Posted by pjt33 (Post 98644)
I think the initial correction is wrong. I understood it rather as "I had to study advanced maths".

Ah yes - makes more sense.

Quote:

Originally Posted by irmamar (Post 98646)
. How do you say "si y sólo si" in English? If and only if? :thinking:".

Yes - if and only if, shortened to iff amongst mathematicians (especially when using txt msgs.:rolleyes:)

Quote:

Originally Posted by pjt33 (Post 98644)
Perikles, later I'll talk to you... seriously. :D :kiss:

:crazy::crazy: :rose:

laepelba November 02, 2010 02:52 AM

Yes, it's "if and only if", and he's most definitely correct about that. Your statement with the "if" is correct as stands. Wow - I've been teaching Algebra 1 for tooooooo long! :)

pjt33 November 02, 2010 02:33 PM

Quote:

Originally Posted by Perikles (Post 98653)
:crazy::crazy: :rose:

Get your attributions right, sir!

:p

Perikles November 02, 2010 04:18 PM

Quote:

Originally Posted by pjt33 (Post 98728)
Get your attributions right, sir!

:p

Ooops. How the hell did that happen? :o

laepelba March 03, 2011 04:48 AM

Would it be possible to add the following to the list of "fields":
  • Geometry
  • Analysis
  • Topology
  • Probability
  • Statistics
  • Discrete Mathematics
  • Number Theory
  • Arithmetic
  • Combinatorics
  • Differential Equations
  • Logic

Thanks!! :)

AngelicaDeAlquezar March 03, 2011 09:20 AM

That's too long to be done just like that. You can make the lists of the vocabulary you want to learn and then we'll be able to help you find the equivalents, so they'll be added to the tables. :)

Cloudgazer March 03, 2011 10:54 AM

Had a spare moment, so:

Geometría (la) = Geometry
Análisis (el) = Analysis
Topología (la) = Topology
Probabilidad (la) = Probability
Estadística (la) = Statistics
Matemática discreta (la) = Discrete Mathematics
Teoría de números (la) = Number Theory
Aritmética (la) = Arithmetic
Combinatoria (la) = Combinatorics
Ecuaciones diferenciales (las) = Differential Equations
Lógica (la) = Logic

AngelicaDeAlquezar March 03, 2011 12:33 PM

:D Thank you, Cloud... I thought she wanted to have vocabulary of each field added. ;)

I'll insert them later, when I have some spare time to format the tables. :)

laepelba March 03, 2011 06:23 PM

Thanks, both of you! Sorry I mis-stated my request, Malila. I definitely wouldn't have asked for vocabulary without specifying. The other day I found myself wanting to talk about the field of study of "Statistics" in general, and realized that I don't know the names of most of the fields of study within the umbrella of Mathematics when speaking Spanish. Thanks so much, Cloudy. :)

This comprehensive page of mathematical terms comes in very handy. I fully intend to add vocabulary to it from some lists that I have (especially Algebra vocabulary) when I have some free time......

Cloudgazer March 04, 2011 04:26 PM

No hay de qué. :)


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