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algebra / calculus
whats the difference between algebra and calculus?
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Both are topics in mathematics.
Algebra is all the a^2 + b^3 = 12 stuff.
Calculus splits into two: differentiation and integration. You know you use that y=mx+c stuff to find the gradient of a straight line? Well differentiation is used to do this for a curved line -- it lets you find the gradient at any point on the line.
Integration can be seen as the inverse of differentiation. If you take some equation for a curved line and differentiate it to find the gradient at a certain point along the curve, you can use integration to get back to the original equation for the line (plus a constant, if no other information is given).
Or, integration can be seen as the area under a curve. You can define upper and lower bounds, like cutting a curve that is infinitely long into a small little strip, and then calculate the area underneath it.
Algebra is all the a^2 + b^3 = 12 stuff.
Calculus splits into two: differentiation and integration. You know you use that y=mx+c stuff to find the gradient of a straight line? Well differentiation is used to do this for a curved line -- it lets you find the gradient at any point on the line.
Integration can be seen as the inverse of differentiation. If you take some equation for a curved line and differentiate it to find the gradient at a certain point along the curve, you can use integration to get back to the original equation for the line (plus a constant, if no other information is given).
Or, integration can be seen as the area under a curve. You can define upper and lower bounds, like cutting a curve that is infinitely long into a small little strip, and then calculate the area underneath it.
Loosehead that is unfair.....you can teach a person the difference between football and rugby in 1 hr. But integration and diffrentiation....i still have nightmares about it and i can honestly say i did not understand a word of it in college. I gave up trying to make sense out of it and just read the whole thing by heart. Thank god i dont have to use that bloody thing......in fact 99.99999999999% of people who are made to study this rubbish never use that knowledge ever again in their lives.
The point matt is that you don't have to know the intricasies, only that Algebra and calculus are 2 seperate branches of maths. Both are huge areas in their own right but I reckon 20 minutes with a Maths teacher would teach anyone the difference.
immi66 I wasn't intending to be condescending sorry if it came across that way.
immi66 I wasn't intending to be condescending sorry if it came across that way.
Knowing the difference between calculus and algebra and actually understanding both of them are very different.
I finally got an understanding of calculus about 2 years after I thought I did - I'd thought I understood it at A-Level but realised I didn't when I actually grasped the intricaces of the concepts at Uni.
Maybe most people don't use it once they've been taught it - but that's the same with languages, cooking, design & technology etc. The important thing is that some people decide they do want to study it further and put it to use.
Everyone is different and everyone has different goals and aims - thankfully - but unless people study the basics, they'll never know if they want to take it further.
I finally got an understanding of calculus about 2 years after I thought I did - I'd thought I understood it at A-Level but realised I didn't when I actually grasped the intricaces of the concepts at Uni.
Maybe most people don't use it once they've been taught it - but that's the same with languages, cooking, design & technology etc. The important thing is that some people decide they do want to study it further and put it to use.
Everyone is different and everyone has different goals and aims - thankfully - but unless people study the basics, they'll never know if they want to take it further.
Simply put, immi, algebra is all to do with finding out the answer to values you don't know, sums etc by using equations with a, b c etc. For example:
a + 2 = 6
Therefore, a = 6-2 = 4
Where a was the value you didn't know before.
Calculus concerns graphs, and the gradients of lines and curves.
(Since differentiation and integration typically come at the end of any maths course, people generally think that they are concepts more difficult to grasp. I actually find calculus to be a beautifully logical branch of maths, although I have reached the limits of my understanding in this area.) Hope this helps simplify it a bit!
a + 2 = 6
Therefore, a = 6-2 = 4
Where a was the value you didn't know before.
Calculus concerns graphs, and the gradients of lines and curves.
(Since differentiation and integration typically come at the end of any maths course, people generally think that they are concepts more difficult to grasp. I actually find calculus to be a beautifully logical branch of maths, although I have reached the limits of my understanding in this area.) Hope this helps simplify it a bit!
Calculus is all to do with variation. The steepness of the curve or straight line is really just how it varies at different points.
This is why calculus is used to much in physics. Much of physics is all about variation, and so calculus is just a neat way of describing it (maths is just a language, and it's the most exact language for describing what we want to describe).
One example is distance. I'm sure you're familiar with the concept of distance. But what if you want to see how the distance varies as time goes by? Often we want to do this, and we call it speed. Again, something I'm sure you're familiar with. So if you're in a car and move at the exact speed all the time, you could draw the distance you make as time goes by on a graph, and you'd have a straight line. The steepness of the line is what we call speed, and since speed is constant in this example, the steepness is constant, and so it's a straight line.
But what if the speed is not constant? I mean, usually it isn't. Usually if you're sat waiting for the traffic lights to change, your speed will be zero, and then you're slowly increase your speed. So this graph that was a straight line is now going to be a curved line, as the steepness (the speed, remember) isn't the same at every point you've driven. So to find the steepness of the curve at a certain point (the speed you were going at that point), you need calculus (specifically differentiation). It's just a tool you use to find the steepness, which is representing the speed.
This is why calculus is used to much in physics. Much of physics is all about variation, and so calculus is just a neat way of describing it (maths is just a language, and it's the most exact language for describing what we want to describe).
One example is distance. I'm sure you're familiar with the concept of distance. But what if you want to see how the distance varies as time goes by? Often we want to do this, and we call it speed. Again, something I'm sure you're familiar with. So if you're in a car and move at the exact speed all the time, you could draw the distance you make as time goes by on a graph, and you'd have a straight line. The steepness of the line is what we call speed, and since speed is constant in this example, the steepness is constant, and so it's a straight line.
But what if the speed is not constant? I mean, usually it isn't. Usually if you're sat waiting for the traffic lights to change, your speed will be zero, and then you're slowly increase your speed. So this graph that was a straight line is now going to be a curved line, as the steepness (the speed, remember) isn't the same at every point you've driven. So to find the steepness of the curve at a certain point (the speed you were going at that point), you need calculus (specifically differentiation). It's just a tool you use to find the steepness, which is representing the speed.
Blimey, the mathematicians arent being very nice to you Immi
Algebra as the name suggests came from the East, you have a problem and you say the answer is X , and you do a bit of arithmetic along with the x , and at the very end you get x equals 4.56 which is the answer.
Calculus came from Leibnitz and Newton independently but almost simultaneously, Jan - Jun 1676 I think. They were looking at different problems, L at areas under curves and also gradients of curves. N was looking at planetary orbits. The pathlines look like ellipses but in real life (ha!) of course the planets dont trail bits of string behind them.
And amazingly the maths - calculus - defined as the mathematics of variations I think - turn out to be the same.
L and N then spent the next thrity years saying and writing I found it ! No Ifound it! No you didnt find it, I found it !
N did a bit of rewriting history and said he could not have described the moons orbit/mass without calculus which he did around 1666 -but unfortunately his notebooks do not bear this out - that is he did it without calculus
Both men were reckoned to be outstanding in their own lifetimes and so every scrap they wrote was preserved, and that is how we can date their discoveries.
There is a book on history of math and calculus - Ideas of space and time by Jeremy Gray
which I cant really recommend, I mean who giv es a t+ss about the history of math ideas ?
PP
Algebra as the name suggests came from the East, you have a problem and you say the answer is X , and you do a bit of arithmetic along with the x , and at the very end you get x equals 4.56 which is the answer.
Calculus came from Leibnitz and Newton independently but almost simultaneously, Jan - Jun 1676 I think. They were looking at different problems, L at areas under curves and also gradients of curves. N was looking at planetary orbits. The pathlines look like ellipses but in real life (ha!) of course the planets dont trail bits of string behind them.
And amazingly the maths - calculus - defined as the mathematics of variations I think - turn out to be the same.
L and N then spent the next thrity years saying and writing I found it ! No Ifound it! No you didnt find it, I found it !
N did a bit of rewriting history and said he could not have described the moons orbit/mass without calculus which he did around 1666 -but unfortunately his notebooks do not bear this out - that is he did it without calculus
Both men were reckoned to be outstanding in their own lifetimes and so every scrap they wrote was preserved, and that is how we can date their discoveries.
There is a book on history of math and calculus - Ideas of space and time by Jeremy Gray
which I cant really recommend, I mean who giv es a t+ss about the history of math ideas ?
PP
to be honest, i'd just seen an american kids show where the characters went to a calculus class and i was wondering if calculus was just the american word for algebra. now i know different!
thanks for the explanation tho. although some of them went waaaaaaaaaaaaaaaaaaayyyy over my head. Peter Pedants was the most helpful - that is to say it was the one that made the most sense.
thanks guys for being as specific as ever :D
thanks for the explanation tho. although some of them went waaaaaaaaaaaaaaaaaaayyyy over my head. Peter Pedants was the most helpful - that is to say it was the one that made the most sense.
thanks guys for being as specific as ever :D
Immi, yes, they're totally different. Well, algebra is a base that lots of other topics in maths use. Calculus uses algebra. Algebra is far more fundamental in its concepts than calculus.
I believe they teach it in america in the last or later years of high school, age 17 or 18 or so, when we're at college and study basic calculus in a-level maths.
I believe they teach it in america in the last or later years of high school, age 17 or 18 or so, when we're at college and study basic calculus in a-level maths.
Encountered this thread by accident, and added a lay contribution, super-simplified description: I'm an not a mathematician.
Someone once told me that the difference between algebra and calculus was that algebra described characteristics of static objects, while calculus described dynamic events, e.g. a description of an object's shape and size vs. an object's trajectory. I believe a mechanical/electrical engineer told me this, as he said it was analogous to the difference between civil engineering and mechanical engineering. To wit, he asked, "What's the difference between a mechanical engineer and a civil engineer?" Ans.: The mechanical engineer builds machines such as weapons, the civil engineer builds targets.
The answer is probably inaccurate, but it satisfied me. I have the impression, too, that algebra is a subset of calculus, since it seems that you have to be able to describe an object in order to describe its activity.
Someone once told me that the difference between algebra and calculus was that algebra described characteristics of static objects, while calculus described dynamic events, e.g. a description of an object's shape and size vs. an object's trajectory. I believe a mechanical/electrical engineer told me this, as he said it was analogous to the difference between civil engineering and mechanical engineering. To wit, he asked, "What's the difference between a mechanical engineer and a civil engineer?" Ans.: The mechanical engineer builds machines such as weapons, the civil engineer builds targets.
The answer is probably inaccurate, but it satisfied me. I have the impression, too, that algebra is a subset of calculus, since it seems that you have to be able to describe an object in order to describe its activity.
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