Las Matemáticas — Mathematics

[pjt33]

Originally Posted by laepelba

What's "undécimo" form?

I think that most people would just say that there are cardinal and ordinal numbers. I've read somewhere about "nominal" numbers (numbers that name something like a number on a sports jersey or something like that), but I don't know how conventional that is. In a mathematics class, we talk about real numbers, rational and irrational numbers, integers, whole numbers and natural or counting numbers. Those are probably not practical or "every-day" numbers that anyone but a math teacher would use.....

Algebraic, transcendental, imaginary, complex, surreal, ... But this is a different distinction from cardinal vs ordinal (in either sense - 3 vs 3rd or set-theoretic).

And I don't think many people talk about "quaternion numbers" (just "quaternions"), but computer games programmers use them a lot.

[laepelba]

Originally Posted by pjt33

Algebraic, transcendental, imaginary, complex, surreal, ... But this is a different distinction from cardinal vs ordinal (in either sense - 3 vs 3rd or set-theoretic).

And I don't think many people talk about "quaternion numbers" (just "quaternions"), but computer games programmers use them a lot.

Yes - I think that so many of those "groups" or "designations" of numbers are only used in mathematics...

But ... I have never heard of "quaternions". What exactly are they??

[chileno]

Ok I got it.

Go to http://spanish.about.com/od/spanishv.../a/ordinal.htm

for a complete list of ordinals.

and this one: http://www.learn-spanish-online.de/g..._fractions.htm

for a list of fractional numbers. :-)

[laepelba]

Originally Posted by laepelba

Yes - I think that so many of those "groups" or "designations" of numbers are only used in mathematics...

But ... I have never heard of "quaternions". What exactly are they??

Originally Posted by chileno

Ok I got it.

Go to http://spanish.about.com/od/spanishv.../a/ordinal.htm

for a complete list of ordinals.

and this one: http://www.learn-spanish-online.de/g..._fractions.htm

for a list of fractional numbers. :-)

Thanks for the links! They are fantastic!

By the way - you didn't answer my question about the "quaternions". What are they?

[pjt33]

Originally Posted by laepelba

But ... I have never heard of "quaternions". What exactly are they??

Chileno didn't mention them: I did. They're one of the division ring* extensions of the reals (along with complex numbers and octonions). Short version: they're what complex numbers would be if they had three orthogonal imaginary parts. They turn out to give a useful representation for rotations in 3D.

* This is a correction from earlier.

[chileno]

Originally Posted by pjt33

Chileno didn't mention them: I did. They're one of the field extensions of the reals (along with complex numbers and octonions). Short version: they're what complex numbers would be if they had three orthogonal imaginary parts. They turn out to give a useful representation for rotations in 3D.

Trigonometry and Calculus, right?

[pjt33]

Originally Posted by chileno

Trigonometry and Calculus, right?

Algebra.

[laepelba]

Originally Posted by pjt33

Algebra.

Not basic Algebra, though. Complex numbers aren't even introduced until a post-Geometry Algebra II course....

[pjt33]

Originally Posted by laepelba

Not basic Algebra, though. Complex numbers aren't even introduced until a post-Geometry Algebra II course....

I know more about the future subjunctive in Spanish than I do about US mathematics syllabi. Buscares por donde buscares dudo que encontrares nada sobre ello en ningún libro moderno de gramática porque ya no existe, pero de todas formas me es más útil.

[laepelba]

Basic Algebra really only gets into very simple equation solving and line graphing. There are some other brief introductory topics like statistical graphing and a VERY brief intro to parabolas and quadratic equations, etc. Everything is VERY basic! Complex numbers would be out of the question!

[chileno]

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]

Originally Posted by chileno

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]

Originally Posted by laepelba

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.

[laepelba]

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]

Originally Posted by laepelba

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]

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

[pjt33]

Originally Posted by chileno

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

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]

Originally Posted by pjt33

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]

Originally Posted by pjt33

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]

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!!