In this section, you’ll find information about tools I use in the educational process: LaTeX files, scripts, and programs.
Since 2011, I try to deliver new courses using slides (this doesn’t eliminate the pleasant necessity of running to the blackboard during lectures to draw illustrative pictures, explain material in different words, and so on). As it turns out, slides are very convenient to make in PowerPoint. Before PowerPoint 2010, this was extremely inconvenient, but modern versions excellently support formula input without foreign add-ons like MathType. Previously, I would have said that slides for mathematical courses should be typeset in LaTeX, for example using the Beamer package. But now things are different, especially when graphics and animation need to be inserted occasionally.
Mathematical texts are conveniently typeset in LaTeX: the flexibility and quality of the final result in this system have remained unsurpassed for many years. Since I work on Windows, I personally find the MiKTeX distribution most convenient. It’s relatively simple to install, can automatically download necessary packages from the CTAN repository, and recent versions install the free TeXworks editor by default. Although I use the more advanced WinEdt editor, the free TeXworks is quite suitable for basic tasks. The free TeXnicCenter editor and cloud solutions (see below) can also be recommended.
For typesetting tests in many of my courses, I’ve been using a homemade generator for several years to simplify creating multiple variants, using only LaTeX’s own tools.
You can avoid installing your own LaTeX system by using one of the cloud internet services. Registration takes 5 minutes, and you won’t need to install the bulky LaTeX distribution on your computer. Personally, among online services, I prefer Overleaf. It’s free in the basic version, allows compiling PDF documents right on the internet, viewing compilation errors, and collaborating on documents with multiple users simultaneously (like Google Docs). A similar service Papeeria allows saving on the paid version.
For these tasks, I use Google Spreadsheets. These spreadsheets allow automatic calculation of test scores and similar things. They also make it easy to communicate information to students.
After futile attempts to find a free universal solution, I settled on Camtasia Studio. The program isn’t cheap, with an academic license costing around $170. However, it’s truly a universal solution: it includes a utility for recording computer screen with simultaneous webcam video recording, a simple yet powerful (for non-professionals) video editor, and a PowerPoint add-in that facilitates presentation recording.
Any concept is easier and more reliably remembered when it’s placed in context, connected to already learned concepts. The more such connections, the more reliably the concept will stick in the web of associative links and remain in memory. Moreover, it will be ready to come to mind at the right moment. Conversely, a concept “hanging in the air” will soon be forgotten and bring no benefit.
For some of my courses, I create visual representations of concepts and their relationships (called mind maps) to help students review before exams and reinforce a holistic picture of the course. It’s also useful for students to do this independently based on the connections they see themselves.
There are many different programs for creating interactive concept maps. I use TheBrain service, which:
An example map created using TheBrain can be viewed here.
Interactive engagement with an object allows better understanding and helps overcome fear of it. If a complex concept can be presented visually, an important step toward understanding has already been taken.
I particularly like the Wolfram Demonstrations Project, a collection of demonstrations covering many areas of mathematics. To play the demonstrations, you’ll need to download and install the free Wolfram CDF Player.