Math Is Fun Forum

Hi bobbym, thanks a lot, but I think I'm missing a bit of theory - perhaps I'm just a bit rusty, lol. I've missed working on my mathematics, but I've recently started a university course in Sanskrit and Linguistics and haven't had the free time .

Anyway, I'm not really sure why:

And also, I don't know why, in the proceeding lines - having expanded the brackets, we are left with the extra y and x.

Thanks for all your help

Hi alexandra

If you don't understand this last point, then just say, but if -3 is smaller than x, then, logically, x must be larger than minus 3, by definition, right?

Hi Ioida

In your preamble write

\usepackage{graphicx}

Graphicx will probably look for the picture in whichever directory the .tex file is in, but it's best to specify the graphicspath - especially if your picture is somewhere else on the system, in which case it won't find it, so write underneath that (yes, two braces, it works better, apparently):

\graphicspath{{filepath}}

Then, wherever you want the picture:

\includegraphics{filename}

It should not be necessary to include the extension. You can also scale the picture using

\includegraphics[scale=x]{filename}

Give x as a decimal, e.g. 0.5 or 1.8.

You can also use the figure environment if you want captions. There is a lot of information about this in the LaTeX manual (http://en.wikibooks.org/wiki/LaTeX). There are also dedicated forums for LaTeX queries, and - indeed - TeX queries in general, and I suggest that for general TeX questions you go there. Not that I'm not completely happy to help, but you're much more likely to find your answer. Also, please remember that this won't work for .gif, I don't think. You should be using .jpg, .png or .pdf.

Hi, yeah, I won't go into the details, but basically LaTeX is a mark-up language, and they way mark-up works - as you will probably have realised - is that if you want your text to appear in a certain way - such as to be in bold face - then you 'mark up' the text. i.e. you use special sequences of characters (called control sequences) to induce an effect (e.g. \textbf{Hi} makes Hi become Hi. textbf is the control sequence and the \ is known as the escape character, which escapes the control sequence. This means that the control sequence is interpreted as a command, rather than just normal text.) Anyway, I probably could have explained that better, but it's not very important, so don't worry if you didn't follow it. The main point is that these control sequences are interpreted by a renderer, which creates the final document. Now, the renderer already 'knows' the basic commands, such as \frac{x}{y}, however, we can also write packages which extend LaTeX beyond these very basic functions. Now, bbold is an example of a package which was written to give LaTeX more functionality. If our renderer doesn't know how to interpret \mathbb{1} in the way we want it to, then we have to load that package, and then the renderer will use the information contained in that package to interpret our control sequence. Otherwise, it will use the standard interpretation. IIn this case, the mathsisfun renderer does know the standard interpretation (bobbym's symbol) but not the interpretation you want. If you ever use your own renderer and write LaTeX for yourself outside of this forum, then you can use the bbold package and extend your own LaTeX capabilities. However, the mathsisfun forum (for very good reasons, mostly simplicity but also to prevent abuse) does not support the loading of extra packages, so we have to make do with the functionality we have.

I think what bob bundy was going for is the 'interpunct' symbol, as it is known in written languages, i.e.

Which is the chain rule. Certainly in vector calculus, to represent the scalar product, this must be used and it is eminently possible to use it for multiplication. It also helps separate the parts of bob bundy's multiplication for didactic purposes elegantly. By the way, bob bundy, the LaTeX for that symbol is \cdot - you may find it helpful in future .

Hi planetdomi,

For your first question, since pq is a product, we can say:

We can split the fraction in this way because we have addition on the top and not on the bottom. If you want to hear more about why, then just ask, from there we can simply cancel the p's and q's:

Since p is common to p and pq and q is common to q and pq.

We can simplify your fraction by expanding the brackets. I was always taught FOIL - first, outside, inside, last, which means that all your like-terms are already collected for you, but you can multiply them however you wish:

This is because x√3 - x√3 obviously gives 0 and √3 times √3 is 3, by the definition of a square root.

Your last question, by the way, is an example of what is sometimes called 'the difference of two squares'. If you have (x - a)(x + a), you will always get:

As you can see by using foil. Since x and a can be any number, we can see that this is always true. This is very useful, if you ever see something of the form:

You can easily factorise it using this rule. So for example:

Is that any clearer?

Interestingly, TMorgan, to print a square root sign in LaTeX you simply have to use \sqrt, which is similar to what you did

Thank you

Well the way it worked this ear was that we were given a load of forms at the start and then you choose a title and a teacher to supervise you and then your supposed to fill the forms out as you progress, talking to your supervisor as you work on your EPQ. Most of the marks are, in fact, awarded for the forms - this is really why it was a waste of time. You spend many hours working on your EPQ but it's all in the form filling, it's just pathetic. Naturally, of course, in out case it didn't work like that, we all went away and then a few days before the respective staggered deadlines we all rushed to our supervisors filled out the forms, made up the dates, pretended we'd taken on-board the advice and got it all sent off. I don't know if the same will be the case with you and your supervisor, but I would be surprised if not. It's unlikely to be excessively well-organised and there are staggered review sheets, but it's unlikely to be too much. Well I was working with two others and we spent most of our summer on the report - which was fine, it was a really good summer, but the forms don't take long in terms of hours a week but are tiresome and time-consuming in the sense that it might take you twenty minutes to get the whole thing all filled out properly. It's supposed to represent about 100 hours' work, though, I think, or something like that.

Yes, you do have to give an a presentation, but the audience probably won't be much. The presentation is just a part of it, I mean, there's the thing, the artifact, the finished project, then loads of forms with the hows and whys and then a presentation full of the hows and whys as well. It's like the world's most excessively tedious piece of standard science coursework. But yes, the presentation will be to your supervisor and then your peers, really, anyone who wants to come - ours was given to our supervisor, a couple of teachers and another young man who was doing an EPQ under the same supervisor. But really, it's generally to whomever you invite/your supervisor invites. I have to say I rather enjoyed giving my presentation - very good fun indeed.

Well, examination centres must be registered with the JCQ I believe, but they are not necessarily schools, there are places - I believe - which are also set-up for this purpose. It is not something which I have ever looked into, though, you should speak to your school's external examinations officer or do some internet research into this. It is, however, possible to sit an examination without your school's facilitation, although it's obviously not necessarily easy or cheap.

I think Bobbym's advice and my advice has been roughly similar so far - along with the contributions of bob bundy - and I don't wish to repeat bobbym's advice in slightly different words at this stage. I shall, however, urge you to consider what he is saying - and, indeed, what he is about to say - carefully, he is a wise and very reasonable mathematician and is giving you sound advice.

That's what we're here for - to enjoy doing some maths together - just post your questions in the forum and we'll do our best