Basically all these subjects can be taught in a more or less mathematical way- in a way with more proofs or with a more practical intuitive way. You should look at the Curriculum of your university and/or ask professors/TAs.
- Mathematics for Statistics
As you are pretty new to quantitative subjects you should go for this one. It is a good idea. It probably includes some real analyses and some matrix algebra. Most data analysis is based on concepts of linear algebra (e.g. inverse, pseudo-inverse, transpose of a matrix)
This one might be interesting for you as you have a finance background and modelling is often used in quantitative finance. There you have many stochastic processes, e.g. Marcov Processes.
Regression analysis is the basis for supervised machine learning and forecasting. Especially in business/economics it is still the most widespread quantitative area. You should really take this course. If you have deeply understood the idea behind regression it might be easier for you to understand other Supervised ML algorithms particularly classification.
Sounds more theoretical. It might give you a more theoretical view on "Applied modelling". So if you are really interested in random processes, e.g. MCMC, it might be a good one to choose.
- Categorical Data Analysis
Might be a specific case of regression analysis for count data. You should better take the basic "regression Analysis" course. Here they might teach you some models like Poisson and Negative Binomial regressions which are rather less used in the industry except of insurances.
Might be a specific case of regression analysis for count data. You should better take the basic "regression Analysis" course. Here they might teach you some models like Kaplan Meier and Hazard functions which are rather less used in the industry except of insurances.
It might be better to talk to former students, TAs or Professors at your university like @NickCox stated. It might also be good to show the course descriptions to someone who is proficient in the area. However based on the names of the course I would take Mathematics for Statistics and Regression Analysis and one topic you are interested in. Applied Modelling might be a good choice.