books about mathematics

[Pro Gamer]

I have seen that in asia and non english speaking european countries people generally use manipulations in order to solve math unlike english speakers. for example how would you solve x+1/x=5 so find the value of x^2+1/x^2? americans would usually try to solve for x then put the value in the expression but we simply square the both sides of the first equation then subtract 2 from both sides and it will give us the value of x^2+1/x^2. i wonder if there are english books which mention such manipulations and tricks

 

[Jedster]

I have seen that in asia and non english speaking european countries people generally use manipulations in order to solve math unlike english speakers. for example how would you solve x+1/x=5 so find the value of x^2+1/x^2? americans would usually try to solve for x then put the value in the expression but we simply square the both sides of the first equation then subtract 2 from both sides and it will give us the value of x^2+1/x^2. i wonder if there are english books which mention such manipulations and tricks

I received my maths education in England and would have done as the emboldened.
There is no reason to solve for x as the question didn't ask that.

 

[Jedster]

i know but those manipulations are not common on internet(mainly because internet is ruled by america) so all we get on internet are american nonsense methods of math. are you on A level or university?

I have a maths degree. I was taught quadratics for O-level (mid 1960s).
I had great teachers.
Thanks for the memories your post invoked.

 

[Pro Gamer]

I have a maths degree. I was taught quadratics for O-level (mid 1960s).
I had great teachers.
Thanks for the memories your post invoked.

60s? so how old are you right now?

 

[Jedster]

60s? so how old are you right now?

75
What's your age?

 

[ratiocinator]

I have seen that in asia and non english speaking european countries people generally use manipulations in order to solve math unlike english speakers. for example how would you solve x+1/x=5 so find the value of x^2+1/x^2? americans would usually try to solve for x then put the value in the expression but we simply square the both sides of the first equation then subtract 2 from both sides and it will give us the value of x^2+1/x^2. i wonder if there are english books which mention such manipulations and tricks

This is absolutely standard algebra. I have no idea why you think it's confined to the non-English spearing world. I don't see how anybody in the world could take on further education (let alone university level) in anything like mathematics, science, or engineering without this level of basic understanding.

ETA: Sorry but I can't give you any books. It's a long time since I learned this level, and, even if I could remember the textbooks, they may well not be available now.

 

[Yerda]

I have seen that in asia and non english speaking european countries people generally use manipulations in order to solve math unlike english speakers. for example how would you solve x+1/x=5 so find the value of x^2+1/x^2? americans would usually try to solve for x then put the value in the expression but we simply square the both sides of the first equation then subtract 2 from both sides and it will give us the value of x^2+1/x^2.

I guess I'm a dummy, but will it?

EDIT:
Misread that as (x+1)/x = 5. Makes more sense now I can read it properly. As you were

 

[Pro Gamer]

75
What's your age?

18

 

[Pro Gamer]

This is absolutely standard algebra. I have no idea why you think it's confined to the non-English spearing world. I don't see how anybody in the world could take on further education (let alone university level) in anything like mathematics, science, or engineering without this level of basic understanding.

ETA: Sorry but I can't give you any books. It's a long time since I learned this level, and, even if I could remember the textbooks, they may well not be available now.

i can show you a lot more advanced manipulations but it's just about seeing patterns. if 4x+1/3x=8 then find the value of 3x+1/4x and here all you need to do is multiply both sides by 3/4 and you will get the answer. this is even basic not even intermediate or advanced. intermediate level algebraic manipulations would be something like this

 

[Shaul]

As a teacher I saw that sort of thing taught here in America. I have also seen elementary students doing calculus here too. It just depends on the quality of the school.

 

[Pro Gamer]

As a teacher I saw that sort of thing taught here in America. I have also seen elementary students doing calculus here too. It just depends on the quality of the school.

CALCULUS IN ELEMENTARY?

 

[Pro Gamer]

probably private schools for the rich

 

[Shaul]

CALCULUS IN ELEMENTARY?

Yes, calculus in elementary. While not common it was not rare either. The school was self paced and used advanced in-house developed pedagogy. It was a charter school which was open to everyone free of charge. Most of the students were from lower socio-economic homes. Granted, it was an excellent school.

 

[Pro Gamer]

Yes, calculus in elementary. While not common it was not rare either. The school was self paced and used advanced in-house developed pedagogy. It was a charter school which was open to everyone free of charge. Most of the students were from lower socio-economic homes. Granted, it was an excellent school.

education in 1980s was tougher than present day