I am being serious of using Latex to the point that I’m going to use it to create our next booklet at work and in my next presentations, so I began learning about it a few months ago. In this post, I’m going to share with you the resources that I have been using in learning it which I found extremely helpful. For those who have not heard about Latex yet, it is a typesetting system that can be used for creating professional and technical documents. Most mathematicians use Latex in publishing their research papers. The image below shows a Latex code and its output.
Click image for full view (via Wikipedia)
To create equations like
on websites or blogs, you need to have some basic knowledge about Latex codes for mathematical expressions.
To create Latex documents, you need two things:
- An editor where you will type your code
- A distribution (compiler) which turns the code into a readable document
For the editor, I use Texmaker because it is both available for Windows and MacOS. I use Windows at work, while may personal laptop is a Mac. For the distribution, I recommend using Miktex for Windows or Mactex for Mac. Texmaker, Miktex, and Mactex are all free software!
For learning the basics of Latex, I highly recommend Michelle Krummel’s tutorials on Youtube. Honestly, you only need these tutorials for learning the basics. The tutorials include creating and formatting simple documents, typing mathematical expressions, using packages and macros. There is also a tutorial on creating Beamer presentations. We will talk about Beamer in another post.
Other tutorials can be found on Overleaf’s Documentation page. Overleaf is an online and collaborative Latex editor. I have used it for a few days but I preferred TexMaker.
You only need those two resources to learn the very basics of Latex. I strongly suggest that you finish Michelle Krummel’s tutorials first.
In Geometry, the term construction refers to the ‘drawing’ of geometric objects such as lines and circles with only the use of compass and straightedge. Construction does not allow measurement of both lengths and angles. The earliest study of Geometry, particularly parts of Euclid’s Elements focused on “building” Geometry based on compass and straightedge construction. In the following discussion, we will refer to compass and straightedge construction as simply construction.
Compass and Straightedge
Using dynamic geometry software (DGS), we can extend construction to computers, tablets, and mobile phones. In this post, we will learn how to use GeoGebra to mimic construction. For those who do not know about GeoGebra yet, it is a free multi-platform mathematics software (not just a DGS) that can be used for teaching and learning mathematics. You may download it here and if you want to learn about it extensively, I have created numerous tutorials on how to use it here. Continue reading
Three years ago, I wrote a post about Photomath, a software capable of scanning and solving equations using phone cameras. I haven’t used the software in a while, and recently discovered that it also has added a capability of graphing functions. It can now graph polynomial functions, rational functions, and trigonometric functions, exponential functions, and logarithmic functions. Recent improvements also allows solving for exponential equations, derivative, integrals, and limits.
Shown below are some examples. I scanned handwritten equations of functions and graph them.
To use Photomath, just open it, click the Camera icon and point to then expression or equation.
To view the graph, click the red rectangle containing the equation at the bottom of the screen.
Aside from the graph, the output also shows some important information about the function such as its x and y intercepts, domain, minima/maxima.
I think Photomath is a very good software that can be used for learning mathematics. Students can use this app to verify answers and also to explore graphs. Photomath is a free app and is both available on Android and iOS.
I have shared several decent calculators and graphing tools in this blog, but in this post, I’m going to share the calculators that I actually use nowadays. The calculators I use depend on the task that I’m doing. I use my phone for short and simple calculations, but if I’m studying or working for an hour or more, I use an actual calculator to avoid distractions. Here are the four calculators that I use most of the time.
1.) Calculator (Mac)
When I’m using my laptop, I use the default calculator app of MacOS. This app allows the user to choose among basic, scientific, and programmable modes. It also supports base 8, base 10, and base 16 number systems. Personally, I only use the basic and scientific calculators and I have not tried the programmable calculator yet.
2.) Google’s Calculator App (Android)
Google’s calculator is a simple and beautifully designed app for basic calculations and scientific calculations. It can store previous calculations. I like the simplicity of this app, so I use it most of the time for basic calculations when I’m using my Android phone. This app is compatible with WearOS.
3.) Advanced Calculator FX991 (Android). This is a paid app but I really like it because it mimics the interface of an actual calculator (see image below). I’ve been using it for six months and so far, I really liked it.
4.) Casio FX991 ES Plus. Aside from apps, I also keep a Casio 991ES Plus. It’s not that I wanted to buy this calculator, but it was the only decent calculator in a store the time when I wanted to buy one. So far, so good, I’ve gotten used to it. I think I will be using it for a long time.
That’s all. Maybe you can share the calculators that you’re using in the comment section below.
One of the interesting app I’ve came across recently is Google’s AR Measure App. This app allows you to use your phone camera to pick two points in the real world and get the distance between them. You can use either imperial or metric units in measurement. In addition, you can also save photos for later measurements. For approximating the height of a cabinet or the length of the table, this app can come in handy. And from experience, it’s quite accurate. I tried to measure my Macbook Pro and I was only 1 centimeter off.
Although I have already tried the app in measuring short lengths, I would like to try measuring long ones. I think this can be very useful in teaching trigonometry and trigonometry. For example, we can make students solve for trigonometry problems and then use the app to check if their answer is correct. That is, of course, assuming that the app is accurate at measuring long distances.
Google AR Measure is available for free in Google Play for Android phones that support Google’s ARCore platform. There is an interesting competition though. Apple has the same app which has the same name.