I’m currently getting my Master’s in Math at Portland State University so that I can teach community college mathematics. I’m specifically hoping to teach calculus, statistics, and linear algebra, so I’m trying to pick classes that will give me deeper knowledge of these subjects. In particular, I’m hoping the degree will give me deep enough knowledge to be able to teach multivariable and vector calculus. Since we are required to take at least two 600 level sequences, next year I’m thinking of taking the Mth 614-616 sequence called “Modern Analysis”. I’m currently taking Mth 512, which is part of the 500 level Real Analysis sequence, and is the prerequisite for Modern Analysis. I’m getting 100% in the class this term so I expect to be ready for Modern Analysis next year. As far as I’m aware, Modern Analysis is the only 600 level analysis sequence that will be offered next year. Here is the course description (copied from here) for all three courses in the sequence:
Topics from nonlinear analysis, harmonic analysis, analytic functions, ordered vector spaces, analysis on Lie groups, and operator theory.
It seems like the class will obviously cover very high-level material, but I’m concerned it might not relate enough to multivariable/vector calculus. However, I’m not that familiar with these topics, so maybe there’s more of a connection than I currently realize. Would a sequence like this give me deep enough knowledge to teach a multivariable/vector calculus course at a community college? Thank you for your help!