I would focus primarily on two questions: What branches of math do you find the most interesting? What type of career do you want?
A degree in mathematics can prepare a person for a career in a rather wide range of different areas.
In terms of your last question. “Complementary minors/dual majors”, I would seriously think about computer science. Data structures, algorithms, and basic computer science competence can all be useful.
One issue is that there are a lot of different types of computer science jobs. To me the ones that also involve a lot of mathematics are interesting. For example in my career I had a number of situations where I needed to solve difficult math problems, then program the solution, then apply it to some actual data and see how well it did.
As one example of this, we have a case where we were using “least squares fit” to fit lines to actual x/y data (the data related to subatomic particles produced by a particle accelerator). We usually got decent fits, but occasionally it just did not look right. Eventually we looked carefully at the math for the software package that we were using and realized that it minimized the sum of “y-squared” across our data, when we should have been minimizing the sum of the squares of the perpendiculars to whatever line would fit the data and it should have been in three dimensions. We did not have software that did this, and this was before there was the Internet to look stuff up, so we solved the mathematical equations to minimize the sum of the perpendicular’s squared. Solving the equations took two of us a week. We programmed this up. The result worked really well, except that occasionally we had slightly off results. One time we had terrible results so I was sent back to look at the math and figure out what we got wrong. Looking through the math, I found that there was one term involving the produce of three numbers all of which were usually zero or very close to zero, where the sign was wrong (oops). We fixed the software (yes, changing one single character), and got great results after that. The whole thing might have taken perhaps three weeks, some of it with two of us working together. However, the main thing might be that for me this was fun and in the end we got the results that we needed.
Which leads to the question: Would you find this fun?
I was a math major in university. I knew quite a few other math majors. One went to law school. One got a master’s in acoustics and became an acoustics engineer (apparently there is a lot of math in figuring out whether your concert hall will have good sound quality across a wide range of frequencies across the full range of seats – computers are also needed to deal with the volume of data). A few became software engineers. Actuaries use math (but I do not personally think that I would find this to be interesting). Encryption uses math. Optimizing package delivery (such as FEDEX and UPS) uses math.
So I think that the type of math that you study may have some impact on what you do with it next. There are lots and lots of different choices in terms of what you do with it next.
One more thing to add: At the point that I graduated with my bachelor’s degree in mathematics, I had no idea what I wanted to do with it or what I would be able to do with it. It worked out anyway. This is something that we each get to figure out over time.
The amount of math that you will learn in four years at Purdue, in addition of course to what you already know, is going to give you a solid start that the vast majority of people just can never fully understand and that can be used in multiple ways. It will only be a start. With a reasonably broad understanding of multiple areas of math I think that you can even have some “major flexibility” after getting your bachelor’s degree, either in picking a job or in going on to a master’s degree in a related field (or first getting a job, working for a couple of years, and then getting a master’s in a related field).
A solid background in mathematics can be used in quite a few ways. Some computer science knowledge can complement your math skills.
And I think that I might also take at least a course in AI and perhaps a course specifically in machine learning somewhere along the way. At a minimum I think that as a potential math major it would be a good idea to really understand what these are in as much detail as you will get in an introductory course. You also might want to at least understand approximately what Operations Research is. Again if there is an introductory course available that might be worth taking at some point. Some of this is going to require a course in probability theory (which you are likely to need to take before some of these other courses).
And Purdue is a great place to learn about a lot of this. Congratulations on having this opportunity!