I'll show you a couple of tips for taking good lecture notes in mathematics

or statistics lectures.

The best way to do that is to give you a short lecture now,

which will go for about a minute, get you to take some notes from that lecture

and then we'll talk about what you wrote down afterwards. Bear in mind when you're

taking lecture notes

that you're trying to create a resource that you can use later on

when it comes to working out how to answer assignment and

test questions. So if you need to get a piece of paper and a pen,

just pause the video and we'll get started.

Ok, here's the problem we going to look at. We have an equation

and we will try and solve it for the variable x

The equation is

1 plus 4 over x equals 21 over x squared.

Now the first thing we need to do with a problem in this format

is get the x's out of the bottom line of the fraction. That will take a

line or two of algebra to tidy up the terms we get

afterwards as well and the problem

now looks like this.

As you can see the x's are out of the bottom line and, better still,

we have a quadratic expression on the left hand side. We have a couple of ways of

dealing with quadratic equations like this. I always look for

the possibility of factorization

first and it turns out this one does resolve into two factors,

x - 7 being one of them, multiplied by

x - 3. Now, of course, not all quadratics are easy to factorize,

some don't factorize at all, and in those cases we have to fall back

on the Quadratic Formula. Now that we've got a factorized

replacement for that quadratic left hand side, we know that when any two numbers

multiplied together produce 0,

it only requires one of those numbers to be 0 themselves.

So, for example, the first factor,

x - 7, could be 0 or

the second one, x - 3, could be 0.

That leads us very quickly to the answers which are

that x is either equal to -7 or

3. Now, that's the end of our

mini lecture. I would say at this stage,

at the very least, you would have on your piece of paper what you see on the screen.

Now, not all maths lectures are like this all the time

but maths is after all a language, a specialized language,

and from time to time lecturers will explain what they're doing in a series

of the algebraic steps on the board. If you're listening to what the lecturer says

while they're doing it,

you can also add to these notes some other very useful features.

For example, between the first and the second line

I explained that I had left out "two or three

steps of algebra".

Usually between two lines in an explanation like this

there's really only one idea that you need to understand.

If you're only expecting to find one idea between two lines

then you may not be able to find out the two or three steps that have been left

out.

So make a little note to remind yourself. Lecturers will do this from time to time,

especially if the steps left out are fairly routine, or

content that you can be expected to know from previous courses.

I also said something very important about

why was doing those steps and the key thing

was that I was trying to get x

out of the bottom line of the fractions.

So I just write "denom" there.

I usually don't have a lot of time to write things down (and probably not a lot

of space)

so a quick note like that will remind us of

why we took those steps. If you know why you're taking

the set of steps, then there's a good chance you'll remember to do it

when you're answering your on assignment questions. A bit further down

I pointed out that the quadratic factorized

but there was an alternative method if that didn't work.

So, we'll make a note of that as well:

"or use the

quad form" for quadratic formula.

That applies to this line here if it doesn't work.

When lecturers set you assignment questions, you can bet your bottom dollar that

they're not going to give you carbon copies

of things they've done in the lecture examples.

They're not interested in your ability to memorize a series of steps for a very

specific situation,

they'd like you to be more creative about your problem solving

and be able to make sensible decisions that are different to the ones in the

lectures.

Finally, we also made the point with the next line

that this step works because

"anything multiply by 0 produces 0",

so we make a little note of that and again that will help us remember

when we've factorized the quadratic, this is the next step.

So, as you can see, we have a set of notes now

which is a combination of what the lecturer wrote on the board, which contains a lot

of information,

as well as some other things we've picked up

from what they were saying and this will help you take excellent maths lecture

notes

and if you're listening to the lecturer, you'll also find that the time goes a

lot faster.