Paul's Online Notes
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You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

In order to display the mathematics on this site I use MathJax. The mathematics "source" is LaTeX and the MathJax "processor" converts that source into "viewable" mathematics. Below is a little more information about the decision to do this if you are curious as to why the change in how math is displayed on the site.

For example, the following LaTeX code,

\[ a x^{2} + b x + c = 0  \hspace{0.5in} \Rightarrow \hspace{0.5in}  x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} \]

will produce the following (probably) very familiar mathematical formula.

\[a x^{2} + b x + c = 0 \hspace{0.5in} \Rightarrow \hspace{0.5in} x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} \]

Quick note about the LaTeX in the pages... If you are thinking of using the "source" of the mathematics to learn LaTeX. Don't do it! The tool I used to convert the source documents into LaTeX generally did a good job but the result is often UGLY LaTeX "code" and not how I would have done it if I was writing it in LaTeX from the start. It put a lot of extra "junk" into the LaTeX that just isn't needed most of the time and if I had taken the time to remove that and generally clean it up it would have, quite likely, taken me closer to 3 YEARS (!! Yikes !!) to convert all the pages.

Okay, on to some of the configuration options that MathJax provides. Please note as well that the options here are provided by the MathJax folks and not me and as such I can't provide tech support for something in these options that doesn't work. Sorry.

If you right click on any equation (such as the one above) a menu will open that will allow you to "configure" a handful of MathJax options. Here is a listing of the menu items and descriptions of each of them (well, descriptions of those that I'm confident that I know what they are anyway...). MathJax will set a cookie on your computer to remember any changes you make to the default settings.

More Info about the change

If you've been using the site for a while you probably know that previously I used images to display the mathematics. When I first started doing this site that was the only really reliable method of displaying mathematics on the web as most browsers just had not reached the point where more sophisticated methods could be used. Things have now progressed to the point where images are not only not needed anymore but in fact produce unacceptable results on some platforms (most notably mobile platforms).

However, because of the decision to use images none of the source material that is used to actually generate the pages on the site are in a form that can easily be used to take advantage of the new tools for displaying mathematics on the web. Because of this I have put off converting to one of the newer tools. Until now. While rewriting the back end of the site to make it more agile and easier to maintain I decided to figure out a way to use the new tools. The results are web pages that should look pretty much the same regardless of platform and because images are no longer being used to display the mathematics pages should load faster and look much better on mobile devices (or at least as well as long math equations are ever going to look on mobile devices anyway....).

An added benefit is that pages should now be readable by anyone needing to use a screen reader. MathJax should be compatible with ChromeVox, Texthelp and JAWS and they are working to add other screen readers.

The only drawback is that, as noted, the original source documents were not in a format that the new technologies can use. So, to generate the pages on the site I first need to use a tool to convert all the mathematics over to LaTeX and while the tool I used generally works fairly well I had to go in and hand edit many of the equations to be "readable" by MathJax. That means that I will, on occasion, miss something and/or errors will slip into the material. If you see an equation that is just gibberish and/or just doesn't look quite right feel free to contact me and I'll take a look at it and see if I can fix it up.