Teaching Computer Programming Using Mathematics: Examples from Middle-School and Graduate School

Our goal is to provide integrated lessons where computer programming concepts are introduced based on mathematics. We consider the development of lessons that would be interesting to our students. At the middle school level, digital video generation is used to introduce coding. At the graduate level, we look at the convergence of machine learning models during training. We introduce middle-school students to computer programming through the use of variables, linear equations, and basic algebraic expressions. We motivate students to create digital images using NumPy arrays by experimenting with number representations and coordinate systems. The students create digital videos by building their video characters and moving them around from frame to frame. At the graduate level, we describe how Real Analysis can be applied in Optimization Theory. The students saw and appreciated the connections between Mathematics and Computer Programming. In the graduate course, the students appreciated the rigorous results on the convergence of neural network models. The approach also produced conditions for guaranteeing that the neural network models are uniformly continuous. We have found that the students strongly appreciated the integration of mathematical concepts into basic and advanced coding courses.