[CHALLENGE] Order of Operations

? thank you.!. I will watch it tomorrow. I have little something here now with the fam.
 
eddy2017 said:
that is something to be developed and learned as I go, with time and practice of can anyone find tutorials, videos or books dealing specfically with you are talking about hereabout this so called ''mathematical grammar''?. Thanks
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Two points.

One of the things I dislike about the way algebra is taught is that the linguistic aspect of mathematical notation is implicitly assumed and seldom if ever explicitly taught. When I was 23, I was assigned to supervise a team of college educated apprentice programmers. There was a pretty young woman with an undergraduate degree in mathematics who kept asking me to translate assembly code into mathematics. Not being an extremely attractive man, I listen carefully to what pretty women tell me (a habit that has had its rewards). Anyway, she taught me to think of mathematical notation as a language, and she became a very clever coder. I do not know that there are many formal presentations of mathematical notation as an object of linguistic analysis, but I know of few mathematicians who dispute that mathematical notation is a language.

Second, it is an artificial language, carefully designed to minimize ambiguity. It is not hard to learn once you see that the language itself is not obscure even though the ideas being expressed may be very subtle. If you try to deal with the often exact but subtle meanings expressed in mathematical notation without understanding the lack of ambiguity in the notation itself, much may seem vagueness wrapped in vagueness. Learn what the notations mean, and as a great poem says, light arrives:

Y todo como el diamante,
Antes que luz es carbon.

(I may not have remembered Marti’s poem exactly.)
 
Thank you, Jeff. You have helped me a lot. Thank you for treating me as a friend, not as a member of the forum or just a mere poster. That is refreshing nowadays. Dr Khan, and Dr Peterson and you have always been respectful and helpful. ALways seeing the positive, the good, in my desire to learn. Jomo too!.
Thank you. It means a lot.
 
Oh you mean these. Okay, I am sorry. I never thought it was going to offend you.
 
JeffM said:
Magnificent.
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Yes, magnificent. That is a fitting adjective. I took the first watch but I am planning to break it down little by little taking my time, savoring every bit of info there. Thanks
 
Eddy

I have thought a lot about why learning algebra is so hard when algebra itself is not at all hard. It is because you are asked to learn so many different things at the same time.

You are asked to learn a specialized vocabulary that is used to talk about mathematics. Examples are “term,” “factor,” and “expression.” They are English words, but with special meanings when used about mathematics. If you do not understand what the words mean, explanations using those words are meaningless.

You are also asked to absorb new ideas, such as the distinction between the number three and the numeral 3.

You are also asked to learn to read and write in a new language, mathematical notation. This language was invented to make doing algebra easier, but, for a beginning student, it is like asking the student to do math in Chinese.

None of that is algebra. It is stuff to learn so algebra can be taught, understood, and used.

You are also expected to learn the mechanics of algebra. There are not many, and a machine can do them. But they come surrounded with all the other stuff you are trying to absorb.

Finally, you must learn how to translate problems described in natural languages like English or Spanish into mathematical notation so you can apply the mechanics.

In short, “learning algebra” is learning five different but related things all at the same time. So of course it is hard, and it depends on arithmetic, which many people have trouble with.

I wish I knew a way to present the five different things separately, but I don’t. But it may help you to ask which of the five is creating a difficulty for you on a particular problem. Is it translation? Is it an issue of mechanics? Is it a general concept that you do not grasp? Are you not quite sure what the words used in an explanation mean?
 
BigBeachBananas said:
2-------(m-1)/(x-3) What happened to x?

3-------m(x-1)+n(y-1)/x-y Incorrect. Lack of parenthesis.

4-------x(m-1)/ (x-y)-(2x/y) Correct

5-------x(m-1)/(x-y)- (y/2x) Correct

6-----x(m-1)/(x-y) + k(m-1)/(p-q) Correct

7-----x(m-1)/(x-y)+ k(m-1)+10/(p-q) Incorrect. Lack of parenthesis.
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number 2 you asked what happened to x?
What do you mean? is it not supposed to be in parentheses?
 
JeffM said:
Eddy

I have thought a lot about why learning algebra is so hard when algebra itself is not at all hard. It is because you are asked to learn so many different things at the same time.

You are asked to learn a specialized vocabulary that is used to talk about mathematics. Examples are “term,” “factor,” and “expression.” They are English words, but with special meanings when used about mathematics. If you do not understand what the words mean, explanations using those words are meaningless.

You are also asked to absorb new ideas, such as the distinction between the number three and the numeral 3.

You are also asked to learn to read and write in a new language, mathematical notation. This language was invented to make doing algebra easier, but, for a beginning student, it is like asking the student to do math in Chinese.

None of that is algebra. It is stuff to learn so algebra can be taught, understood, and used.

You are also expected to learn the mechanics of algebra. There are not many, and a machine can do them. But they come surrounded with all the other stuff you are trying to absorb.

Finally, you must learn how to translate problems described in natural languages like English or Spanish into mathematical notation so you can apply the mechanics.

In short, “learning algebra” is learning five different but related things all at the same time. So of course it is hard, and it depends on arithmetic, which many people have trouble with.

I wish I knew a way to present the five different things separately, but I don’t. But it may help you to ask which of the five is creating a difficulty for you on a particular problem. Is it translation? Is it an issue of mechanics? Is it a general concept that you do not grasp? Are you not quite sure what the words used in an explanation mean?
Click to expand...
jeff said: 'have thought a lot about why learning algebra is so hard when algebra itself is not at all hard. It is because you are asked to learn so many different things at the same time'.
Ain't that true?. Yes, a mouthful!.
 
JeffM said:
Two points.

One of the things I dislike about the way algebra is taught is that the linguistic aspect of mathematical notation is implicitly assumed and seldom if ever explicitly taught. When I was 23, I was assigned to supervise a team of college educated apprentice programmers. There was a pretty young woman with an undergraduate degree in mathematics who kept asking me to translate assembly code into mathematics. Not being an extremely attractive man, I listen carefully to what pretty women tell me (a habit that has had its rewards). Anyway, she taught me to think of mathematical notation as a language, and she became a very clever coder. I do not know that there are many formal presentations of mathematical notation as an object of linguistic analysis, but I know of few mathematicians who dispute that mathematical notation is a language.

Second, it is an artificial language, carefully designed to minimize ambiguity. It is not hard to learn once you see that the language itself is not obscure even though the ideas being expressed may be very subtle. If you try to deal with the often exact but subtle meanings expressed in mathematical notation without understanding the lack of ambiguity in the notation itself, much may seem vagueness wrapped in vagueness. Learn what the notations mean, and as a great poem says, light arrives:

Y todo como el diamante,
Antes que luz es carbon.

(I may not have remembered Marti’s poem exactly.)
Click to expand...
Nothing is truer than this. I have seen it .
Quoting JeffM: "mathematical notation is implicitly assumed and seldom if ever explicitly taught".
Uhm food for thought.
 
BigBeachBananas said:
2-------(m-1)/(x-3) What happened to x?

3-------m(x-1)+n(y-1)/x-y Incorrect. Lack of parenthesis.

4-------x(m-1)/ (x-y)-(2x/y) Correct

5-------x(m-1)/(x-y)- (y/2x) Correct

6-----x(m-1)/(x-y) + k(m-1)/(p-q) Correct

7-----x(m-1)/(x-y)+ k(m-1)+10/(p-q) Incorrect. Lack of parenthesis.
Click to expand...
My bad.
------x(m-1)/(x-3)
 
3-------m(x-1)+n(y-1)/x-y Incorrect. Lack of parenthesis.
m(x+1)+ n(y-1)/(x-y)
 
eddy2017 said:
3-------m(x-1)+n(y-1)/x-y Incorrect. Lack of parenthesis.
m(x+1)+ n(y-1)/(x-y)
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We are getting closer, not entirely correct yet. Missing another set of parenthesis. Ask yourself, do you just want n(y-1) or do you want the entire numerator divided by (x-y)?
 
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