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  • In this shortcast

  • 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.

In this shortcast

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