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.

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.

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.

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.