To try and explain some of the bullet points, because the common sentiment here seems to be that he's speaking an alien language. Terrance is providing a list

To try and explain some of the bullet points, because the common sentiment here seems to be that he's speaking an alien language. Terrance is providing a list of things where if "you already know a fact" about a problem or function, then you can take shortcuts based on that fact. So for example, he mentions: > Reflection symmetry -> suffices to test odd and even functions separately. This means that if you know that there is a "mirror image" in the function around the origin, then you can use this fact. The definition of mirror symmetry is: A function f(x) is even if f(-x) = f(x). The function is odd if f(-x) = -f(x) That's quite a strong statement! You can use this to simplify proofs, eliminate cases, etc... Even if you don't know if the mirror symmetry is odd or even, this doesn't really matter because it's just two scenarios! Just check both and you're done.