We will start by revisiting the topic of graphs and study trees, which are graphs which contain no cycles. This provides a good starting point to understanding more complicated concepts in graphs, which are widely used throughout the STEM fields.
Next, we will introduce the idea of mathematical induction and sequences, dealing with recursive definitions and how to use information about the current state to deduce something about the next state. In maths and computer science, variables and states are often defined recursively, so it is important to be able to handle these, even if it is not possible to write down explicitly a formula or completely describe the current state.
Finally, we will push students' logical reasoning abilities harder, with more challenging iterations of previously seen topics from the junior courses, as well as an introduction to true tables. In the final lesson, some interesting logical paradoxes will be given to pick their brains and test that they have really understood the material.
This course should be of interest to anyone who might have an interest in pursuing a natural science, as the ideas are widely applicable and are especially common in computer science.