Welcome to math helper,
Personally, I think that the question 'Is math invented or
discovered?' is meaningless. But thinking about _why_ it's meaningless
can lead you to some very interesting ideas about the nature of
meaning!
(For example, if you're lucky it might lead you to read Doug
Hofstadter's wonderful essay 'A Conversation with Einstein's Brain',
in his book _The Mind's I_.) examples on math help; So I hope you'll continue to noodle
around with this issue this even after your essay has been completed.
I hope the above explanation was useful, now let us learn more on online math tutors.
Tuesday, August 17, 2010
Wednesday, August 11, 2010
math intuition
Welcome to free math tutor online,
One way to train my intuition is to compare the problem with something
I've seen plenty of times in real life. I've painted murals, mixing
the colors I want from poster paint. Often I want a light color, and a
little color goes a long way.
I have learned to be very careful not to
add too much color to the white at first. Why? I If I need 1 part blue
to 100 parts white (which is not unreasonable in my experience), and I
put in 2 dabs of blue instead of 1, meet math tutors online for more examples;
I need to add another 100 parts of
white to get the color to be what I wanted!
I can't tell you how many
times I've ended up with far more paint than I needed, by the time I
got the color right. I've learned that it's better to throw away half
the too-dark mixture, rather than try to save the whole batch by
adding white. learn more on math forum.
One way to train my intuition is to compare the problem with something
I've seen plenty of times in real life. I've painted murals, mixing
the colors I want from poster paint. Often I want a light color, and a
little color goes a long way.
I have learned to be very careful not to
add too much color to the white at first. Why? I If I need 1 part blue
to 100 parts white (which is not unreasonable in my experience), and I
put in 2 dabs of blue instead of 1, meet math tutors online for more examples;
I need to add another 100 parts of
white to get the color to be what I wanted!
I can't tell you how many
times I've ended up with far more paint than I needed, by the time I
got the color right. I've learned that it's better to throw away half
the too-dark mixture, rather than try to save the whole batch by
adding white. learn more on math forum.
Sphere of radius
Welcome to free online math tutoring,
We have a sphere of radius R, with a rope of length 2 pi R around its
circumference; then we add L units to that circumference. What is the
new radius of the rope? The new circumference is (2 pi R + L); the new
radius is that divided by 2 pi, or R + L/(2 pi). This means that the
radius is increased by L/(2 pi), which is independent of R.
This seems a little less surprising, perhaps, than if we solved it with specific
numbers, since we don't have a specific unexpectedly large number to
reject outright; we're forced to look at the algebra. more help on online math forum;
But we can still question the algebra once we see what it tells us.
The next step, of course, is to check the answer: plug in actual numbers for R and L,
solve for the change in R, and then add that to R to find what the new
circumference will be. It will be L more than the original, showing
that as long as we accept 2 pi R, our answer is right. read more on math forum.
We have a sphere of radius R, with a rope of length 2 pi R around its
circumference; then we add L units to that circumference. What is the
new radius of the rope? The new circumference is (2 pi R + L); the new
radius is that divided by 2 pi, or R + L/(2 pi). This means that the
radius is increased by L/(2 pi), which is independent of R.
This seems a little less surprising, perhaps, than if we solved it with specific
numbers, since we don't have a specific unexpectedly large number to
reject outright; we're forced to look at the algebra. more help on online math forum;
But we can still question the algebra once we see what it tells us.
The next step, of course, is to check the answer: plug in actual numbers for R and L,
solve for the change in R, and then add that to R to find what the new
circumference will be. It will be L more than the original, showing
that as long as we accept 2 pi R, our answer is right. read more on math forum.
Mathematics intuition
Welcome to free math tutoring online,
The first thing we have to recognize is that our intuition can be
wrong. Mathematicians (and the rest of us) need a healthy dose of
humility, because this happens all the time.
I suppose one of the
benefits of studying math beyond mere arithmetic is that it can teach
us not to trust our assumptions, or even what seems like sound
reasoning, but to look closely at the logic behind what we believe.
examples on online math forum; What seems true, not only in math
but in all of life, may not be! That's just part of growing up.
continue learning on our math forum.
The first thing we have to recognize is that our intuition can be
wrong. Mathematicians (and the rest of us) need a healthy dose of
humility, because this happens all the time.
I suppose one of the
benefits of studying math beyond mere arithmetic is that it can teach
us not to trust our assumptions, or even what seems like sound
reasoning, but to look closely at the logic behind what we believe.
examples on online math forum; What seems true, not only in math
but in all of life, may not be! That's just part of growing up.
continue learning on our math forum.
Math quadratic formula
Welcome to free math,
The quadratic formula,
-b +/- sqrt(b^2 - 4ac)
x = -----------------------
2a
applies whenever you have an equation like
ax^2 + bx + c = 0
So we can start with either the formula, or the equation. visit online math forum; Frankly, the
equation looks as if it will be less work:
ax^2 + bx + c = 0
bx = -ax^2 - c
b = (-ax^2 - c) / x
more exercise on math forum.
The quadratic formula,
-b +/- sqrt(b^2 - 4ac)
x = -----------------------
2a
applies whenever you have an equation like
ax^2 + bx + c = 0
So we can start with either the formula, or the equation. visit online math forum; Frankly, the
equation looks as if it will be less work:
ax^2 + bx + c = 0
bx = -ax^2 - c
b = (-ax^2 - c) / x
more exercise on math forum.
Math Pi
Welcome to free online math tutors,pi shows up in so many other places in mathematics, this guy
might find himself asking: "Why is the ratio of circumference to
diameter close to pi for small circles, but not for large ones?" And
if he investigated that question deeply enough, get more on math forum;he might eventually be discover that there are other ways of measuring distances than always
going along the surface of the earth.
That is, he might learn to think
in terms of three (or more) dimensions, even if he can't directly
experience those dimensions. continue reading on free math help online.
Reading math material
Greetings from math online tutor,
Read the
relevant part _before_ each lecture, rather than hearing it for the
first time in the lecture.
This _sounds_ like a lot of extra work, but it's not. Suppose you
have lectures A, B, and C that cover reading material a, b, and c.
Most students would do this:
Listen to A; read a; listen to B; read b; listen to C; read c.
I'm suggesting that you do this instead:
Read a; listen to A; read b; listen to B; read c; listen to C.
As you can see, it's the same amount of work. Only the order is
different. And the reason the order is so crucial is the one I've
already mentioned: If you don't understand something in the reading
material, you can ask about it in the lecture where the material is
covered, which is no extra trouble for the teacher. online math forum;
But if you try to ask a question about yesterday's material in today's lecture, the
teacher will be impatient to move on, and it's likely that you won't
get the answer you need, if you get one at all. View more on math forum.
Read the
relevant part _before_ each lecture, rather than hearing it for the
first time in the lecture.
This _sounds_ like a lot of extra work, but it's not. Suppose you
have lectures A, B, and C that cover reading material a, b, and c.
Most students would do this:
Listen to A; read a; listen to B; read b; listen to C; read c.
I'm suggesting that you do this instead:
Read a; listen to A; read b; listen to B; read c; listen to C.
As you can see, it's the same amount of work. Only the order is
different. And the reason the order is so crucial is the one I've
already mentioned: If you don't understand something in the reading
material, you can ask about it in the lecture where the material is
covered, which is no extra trouble for the teacher. online math forum;
But if you try to ask a question about yesterday's material in today's lecture, the
teacher will be impatient to move on, and it's likely that you won't
get the answer you need, if you get one at all. View more on math forum.
How to remember formulas
Welcome to math online tutor,
One trick you can use when trying to remember patterns or principles
is to encode them as examples. For example, for the life of me I can
never remember whether (a^b)^c is a^(b+c) or a^(bc). So whenever I
need to know, I drag out this example:
(a * a) * (a * a) * (a * a) = a^6, so (a^2)^3 = a^6
which means that it must be (bc), and not (b+c). Does this get
tiresome? You bet. Is it preferable to guessing wrong? You bet!
Two other tricks I can recommend are:
Try teaching what you've learned to someone else. This is probably
the single most effective way of learning anything, especially if the
other person is having difficulty learning it. learn more on math forum; It forces you to think
of new ways to understand the material, in order to avoid presenting
it in the same old way. more examples on online math tutoring.
One trick you can use when trying to remember patterns or principles
is to encode them as examples. For example, for the life of me I can
never remember whether (a^b)^c is a^(b+c) or a^(bc). So whenever I
need to know, I drag out this example:
(a * a) * (a * a) * (a * a) = a^6, so (a^2)^3 = a^6
which means that it must be (bc), and not (b+c). Does this get
tiresome? You bet. Is it preferable to guessing wrong? You bet!
Two other tricks I can recommend are:
Try teaching what you've learned to someone else. This is probably
the single most effective way of learning anything, especially if the
other person is having difficulty learning it. learn more on math forum; It forces you to think
of new ways to understand the material, in order to avoid presenting
it in the same old way. more examples on online math tutoring.
Remembering formulas
Welcome to free math help online,
I can sympathize with you, because I have a similar problem. I've
_never_ been able to remember formulas, and the way that I've had to
compensate is that whenever I learn a new formula, I have to learn how
to derive it from first principles - by which I mean, the things that
are so basic that I _can't_ forget them.
(One of the luckiest breaks I ever caught in my life was when I took
second-semester calculus in college. examples on math forum; That's the semester when you
have to memorize about a zillion formulas that all look pretty much
the same - one plus or minus the sine or cosine of plus or minus
something, under or over the square root of something similar - so I
fully expected to fail. But on the first day, the professor said: "I
don't expect you to remember anything that I can't remember, and the
only thing that I can remember is that cos^2 + sin^2 equals 1." So
you're not alone!)
I hope the above explanation was useful, now let us study more on online math forum.
I can sympathize with you, because I have a similar problem. I've
_never_ been able to remember formulas, and the way that I've had to
compensate is that whenever I learn a new formula, I have to learn how
to derive it from first principles - by which I mean, the things that
are so basic that I _can't_ forget them.
(One of the luckiest breaks I ever caught in my life was when I took
second-semester calculus in college. examples on math forum; That's the semester when you
have to memorize about a zillion formulas that all look pretty much
the same - one plus or minus the sine or cosine of plus or minus
something, under or over the square root of something similar - so I
fully expected to fail. But on the first day, the professor said: "I
don't expect you to remember anything that I can't remember, and the
only thing that I can remember is that cos^2 + sin^2 equals 1." So
you're not alone!)
I hope the above explanation was useful, now let us study more on online math forum.
Friday, August 6, 2010
Math Derivations
Welcome to online math tutoring,
Mathematicians can come up with some pretty weird stuff,
but the individual steps in each derivation are built entirely on
processes like the one outlined above.
Additionally, mathematical
publications are very closely scrutinized by several mathematicians
other than the author before being published, and are often criticized
by even more after publication.
All of this amounts to a good
assurance that theorems do in fact follow from assumptions. more explanations on free online math tutor and math forum.
Mathematicians can come up with some pretty weird stuff,
but the individual steps in each derivation are built entirely on
processes like the one outlined above.
Additionally, mathematical
publications are very closely scrutinized by several mathematicians
other than the author before being published, and are often criticized
by even more after publication.
All of this amounts to a good
assurance that theorems do in fact follow from assumptions. more explanations on free online math tutor and math forum.
Mathematical realm
Welcome to math online tutor,
mathematical realm, when I say that 2+3 = 5, I am not
saying that any particular 2 and 3 items are the same as any
particular 5 items. I am saying, in an abbreviated form, that whenever
I put together 2 of something and 3 more of them, I will have 5 in
all. Also, I am not somehow "combining" a "2" and a "3" to make
something new that is identical to "5";
I am performing an operation
on two numbers that is the abstract representation of putting together
two sets of things, in order to determine the number of things in the
combined set. math help If you prefer, you can say I am simply stating a
relation among the numbers 2, 3, and 5.
I hope the above explanation was useful, let me take you through free math tutoring.
mathematical realm, when I say that 2+3 = 5, I am not
saying that any particular 2 and 3 items are the same as any
particular 5 items. I am saying, in an abbreviated form, that whenever
I put together 2 of something and 3 more of them, I will have 5 in
all. Also, I am not somehow "combining" a "2" and a "3" to make
something new that is identical to "5";
I am performing an operation
on two numbers that is the abstract representation of putting together
two sets of things, in order to determine the number of things in the
combined set. math help If you prefer, you can say I am simply stating a
relation among the numbers 2, 3, and 5.
I hope the above explanation was useful, let me take you through free math tutoring.
Arithmetic and Math
Welcome to math help online,
Arithmetic is just one branch of mathematics, namely that involving
basic techniques of calculation with numbers. When you add, subtract,
multiply, divide, take square roots, and so on, you are doing
arithmetic.
When you solve an equation you are doing algebra. When you
determine relations between shapes or find their area, you are doing
free math geometry (though the latter calculation will be done by applying
arithmetic to the geometric formulas).
Most of what young children learn in math is arithmetic.
Hope the above explanation was useful, now let us study online math tutoring.
Arithmetic is just one branch of mathematics, namely that involving
basic techniques of calculation with numbers. When you add, subtract,
multiply, divide, take square roots, and so on, you are doing
arithmetic.
When you solve an equation you are doing algebra. When you
determine relations between shapes or find their area, you are doing
free math geometry (though the latter calculation will be done by applying
arithmetic to the geometric formulas).
Most of what young children learn in math is arithmetic.
Hope the above explanation was useful, now let us study online math tutoring.
Math and Art
Welcome to online math tutoring,
There may be much in common between mathematics and art, and since
art is also difficult to define, it is difficult to discuss this
relation. Certainly, there are definitions of art that would allow the
inclusion of mathematics as an art. The creation of mathematics
requires creativity, and I think most mathematicians would agree that
some constructs are more beautiful than others, so that there is an
aesthetic aspect to mathematics.
In any case, mathematics certainly is a human endeavor involving the
exchange of ideas between human beings. math help com It has been around for
millennia, and shows no signs of abatement.
These ideas are debatable and reflect my own personal opinion. Also,
this response is really too short to explore all the aspects your
question addresses math forum.
There may be much in common between mathematics and art, and since
art is also difficult to define, it is difficult to discuss this
relation. Certainly, there are definitions of art that would allow the
inclusion of mathematics as an art. The creation of mathematics
requires creativity, and I think most mathematicians would agree that
some constructs are more beautiful than others, so that there is an
aesthetic aspect to mathematics.
In any case, mathematics certainly is a human endeavor involving the
exchange of ideas between human beings. math help com It has been around for
millennia, and shows no signs of abatement.
These ideas are debatable and reflect my own personal opinion. Also,
this response is really too short to explore all the aspects your
question addresses math forum.
Thursday, August 5, 2010
What is Algebra ?
Let me help you on math help & study what is algebra,Algebra is a branch of mathematics. Algebra plays an important role in our day to day life.
The algebra executes the four basic operations such as addition, subtraction, multiplication and division. The most important terms involved in algebra expressions, equations and polynomial.
In Algebra, besides numerals we use symbols and alphabets in place of unknown numbers to make a statement. Hence, algebra may be regarded as an extension of Arithmetic.
you get more help in math and online math help in our blog posts.
I hope the above explanation was useful.
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