You can subscribe free to my basic C++ course via the "courses" tab on this site; my plans for the next lot of videos in this course are to show you how to build a "particle fire" simulation program; sceenshots shown below.
While not a game, you'll learn some of the elements of game programming if you put this together.
I chose to create this particular program partly because, well, it looks nice; partly because pixel manipulation gives you a really good workout with C++, and partly because besides looking nice, particle swarms also have applications in AI.
I chose to develop a graphics program rather than an AI program for this course -- it's easier and more visual -- but you can adapt the code to solving equations without a huge amount of extra programming (only for the hardcore programmers out there though!).